Template-Type: ReDIF-Article 1.0 Author-Name: Paul Emms Author-X-Name-First: Paul Author-X-Name-Last: Emms Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: Optimal Management of an Insurer’s Exposure in a Competitive General Insurance Market Abstract: The qualitative behavior of the optimal premium strategy is determined for an insurer in a finite and an infinite market using a deterministic general insurance model. The optimization problem leads to a system of forward-backward differential equations obtained from Pontryagin’s Maximum Principle. The focus of the modelling is on how this optimization problem can be simplified by the choice of demand function and the insurer’s objective. Phase diagrams are used to characterize the optimal control. When the demand is linear in the relative premium, the structure of the phase diagram can be determined analytically. Two types of premium strategy are identified for an insurer in an infinite market, and which is optimal depends on the existence of equilibrium points in the phase diagram. In a finite market there are four more types of premium strategy, and optimality depends on the initial exposure of the insurer and the position of a saddle point in the phase diagram. The effect of a nonlinear demand function is examined by perturbing the linear price function. An analytical optimal premium strategy is also found using inverse methods when the price function is nonlinear. Journal: North American Actuarial Journal Pages: 77-105 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597541 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597541 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:77-105 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Ludkovski Author-X-Name-First: Michael Author-X-Name-Last: Ludkovski Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Title: Relative Hedging of Systematic Mortality Risk Abstract: We study indifference valuation mechanisms for mortality contingent claims under stochastic mortality age structures. Our focus is on capturing the internal cross-hedge between components of an insurer’s portfolio, especially between life annuities and life insurance. We carry out an exhaustive analysis of the dynamic exponential premium principle, which is the representative nonlinear valuation rule in our framework. Using this valuation rule we derive formulas for optimal quantity of contracts to sell. Our results are further enhanced by asymptotic expansions that show the relative effects of model parameters. We also compare the exponential premium principle to other valuation rules. Furthermore, we provide numerical examples to illustrate our approach. Journal: North American Actuarial Journal Pages: 106-140 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597542 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597542 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:106-140 Template-Type: ReDIF-Article 1.0 Author-Name: Hua Chen Author-X-Name-First: Hua Author-X-Name-Last: Chen Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Title: An Option-Based Operational Risk Management Model for Pandemics Abstract: In this paper we employ the theory of real option pricing to address problems in the area of operational risk management. We develop a two-stage model to help firms determine the optimal suspension-reactivation triggers in the events of pandemics. In the first stage, we propose a regime-dependent epidemic model to simulate the spread of the virus, depending on whether the firm is active or inactive. In the second stage, we view the reactivation decision as a call option and the suspension decision as a put option, and use dynamic programming methods to obtain the optimal switching thresholds. Our method can be regarded as a quantitative implementation of the CDC’s instructions for pandemic preparation. We find that when they take the uncertainty of disease transmission into consideration, firms are more conservative about the decisions of suspension and reactivation. We also find that when firms incur switching costs, the suspension threshold increases with costs, whereas the reactivation threshold decreases with costs. By adopting disease control policies, firms can increase their values in both regimes. Journal: North American Actuarial Journal Pages: 54-76 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597540 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597540 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:54-76 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Author-Name: Guy Coughlan Author-X-Name-First: Guy Author-X-Name-Last: Coughlan Author-Name: David Epstein Author-X-Name-First: David Author-X-Name-Last: Epstein Author-Name: Alen Ong Author-X-Name-First: Alen Author-X-Name-Last: Ong Author-Name: Igor Balevich Author-X-Name-First: Igor Author-X-Name-Last: Balevich Title: A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States Abstract: We compare quantitatively eight stochastic models explaining improvements in mortality rates in England and Wales and in the United States. On the basis of the Bayes Information Criterion (BIC), we find that, for higher ages, an extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort effect fits the England and Wales males data best, while for U.S. males data, the Renshaw and Haberman (RH) extension to the Lee and Carter model that also allows for a cohort effect provides the best fit. However, we identify problems with the robustness of parameter estimates under the RH model, calling into question its suitability for forecasting. A different extension to the CBD model that allows not only for a cohort effect, but also for a quadratic age effect, while ranking below the other models in terms of the BIC, exhibits parameter stability across different time periods for both datasets. This model also shows, for both datasets, that there have been approximately linear improvements over time in mortality rates at all ages, but that the improvements have been greater at lower ages than at higher ages, and that there are significant cohort effects. Journal: North American Actuarial Journal Pages: 1-35 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597538 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597538 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:1-35 Template-Type: ReDIF-Article 1.0 Author-Name: Mathieu Boudreault Author-X-Name-First: Mathieu Author-X-Name-Last: Boudreault Author-Name: Christian-Marc Panneton Author-X-Name-First: Christian-Marc Author-X-Name-Last: Panneton Title: Multivariate Models of Equity Returns for Investment Guarantees Valuation Abstract: In this paper we investigate the valuation of investment guarantees in a multivariate (discrete-time) framework. We present how to build multivariate models in general, and we survey the most important multivariate GARCH models. A direct multivariate application of regime-switching models is also discussed, as is the estimation of these models using maximum likelihood and their comparison in a multivariate setting. The computation of the CTE provision is further presented. We have estimated the models with a multivariate dataset (Canada, United States, United Kingdom, and Japan), and we compared the quality of their fit using multiple criteria and tests. We observe that multivariate GARCH models provide a better overall fit than regime-switching models. However, regime-switching models appropriately represent the fat tails of the returns distribution, which is where most GARCH models fail. This leads to significant differences in the value of the CTE provisions, and, in general, provisions computed with regime-switching models are higher. Thus, the results from this multivariate analysis are in line with what was obtained in the literature of univariate models. Journal: North American Actuarial Journal Pages: 36-53 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597539 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597539 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:36-53 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Minimizing the Probability of Lifetime Ruin with Deferred Life Annuities Abstract: We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a deferred life annuity. Although we let the admissible set of strategies of annuity purchasing process be the set of increasing adapted processes, we find that the individual will not buy a deferred life annuity unless she can cover all her consumption via the annuity and have enough wealth left over to sustain her until the end of the deferral period. Journal: North American Actuarial Journal Pages: 141-154 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597543 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597543 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:141-154 Template-Type: ReDIF-Article 1.0 Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: “The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model,” Shuanming Li, October 2008 Journal: North American Actuarial Journal Pages: 155-156 Issue: 1 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597544 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597544 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:1:p:155-156 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Hua Author-X-Name-First: Lei Author-X-Name-Last: Hua Author-Name: Michelle Xia Author-X-Name-First: Michelle Author-X-Name-Last: Xia Title: Assessing High-Risk Scenarios by Full-Range Tail Dependence Copulas Abstract: Copulas with a full-range tail dependence property can cover the widest range of positive dependence in the tail, so that a regression model can be built accounting for dynamic tail dependence patterns between variables. We propose a model that incorporates both regression on each marginal of bivariate response variables and regression on the dependence parameter for the response variables. An ACIG copula that possesses the full-range tail dependence property is implemented in the regression analysis. Comparisons between regression analysis based on ACIG and Gumbel copulas are conducted, showing that the ACIG copula is generally better than the Gumbel copula when there is intermediate upper tail dependence. A simulation study is conducted to illustrate that dynamic tail dependence structures between loss and ALAE can be captured by using the one-parameter ACIG copula. Finally, we apply the ACIG and Gumbel regression models for a dataset from the U.S. Medical Expenditure Panel Survey. The empirical analysis suggests that the regression model with the ACIG copula improves the assessment of high-risk scenarios, especially for aggregated dependent risks. Journal: North American Actuarial Journal Pages: 363-378 Issue: 3 Volume: 18 Year: 2014 Month: 7 X-DOI: 10.1080/10920277.2014.888009 File-URL: http://hdl.handle.net/10.1080/10920277.2014.888009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:3:p:363-378 Template-Type: ReDIF-Article 1.0 Author-Name: Robert J. Erhardt Author-X-Name-First: Robert J. Author-X-Name-Last: Erhardt Author-Name: Richard L. Smith Author-X-Name-First: Richard L. Author-X-Name-Last: Smith Title: Weather Derivative Risk Measures for Extreme Events Abstract: We consider pricing weather derivatives for use as protection against weather extremes by using max-stable processes to estimate risk measures. These derivatives are not currently traded on any open markets, but their use could help some institutions manage weather risks from extreme events. The central challenge is to model the dependence of payments, which increases the risk of holding multiple weather derivatives. The method described utilizes results from spatial statistics and extreme value theory to first model extremes in the weather as a max-stable process, and then simulate payments for a general collection of weather derivatives. As the joint likelihood function for max-stable processes is unavailable, we use two approaches: The first is based on the composite likelihood, and the second is based on approximate Bayesian computing (ABC). Both capture the spatial dependence of payments. To incorporate parameter uncertainty into the pricing model, we use bootstrapping with the composite likelihood approach, while the ABC method naturally incorporates parameter uncertainty. We show that the additional risk from the spatial dependence of payments can be quite substantial, and that the methods discussed can compute standard actuarial risk measures in both a frequentist and Bayesian setting. Journal: North American Actuarial Journal Pages: 379-393 Issue: 3 Volume: 18 Year: 2014 Month: 7 X-DOI: 10.1080/10920277.2014.910472 File-URL: http://hdl.handle.net/10.1080/10920277.2014.910472 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:3:p:379-393 Template-Type: ReDIF-Article 1.0 Author-Name: Sujith Asanga Author-X-Name-First: Sujith Author-X-Name-Last: Asanga Author-Name: Alexandru Asimit Author-X-Name-First: Alexandru Author-X-Name-Last: Asimit Author-Name: Alexandru Badescu Author-X-Name-First: Alexandru Author-X-Name-Last: Badescu Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: Portfolio Optimization under Solvency Constraints: A Dynamical Approach Abstract: We develop portfolio optimization problems for a nonlife insurance company seeking to find the minimum capital required that simultaneously satisfies solvency and portfolio performance constraints. Motivated by standard insurance regulations, we consider solvency capital requirements based on three criteria: ruin probability, conditional Value-at-Risk, and expected policyholder deficit ratio. We propose a novel semiparametric formulation for each problem and explore the advantages of implementing this methodology over other potential approaches. When liabilities follow a Lognormal distribution, we provide sufficient conditions for convexity for each problem. Using different expected return on capital target levels, we construct efficient frontiers when portfolio assets are modeled with a special class of multivariate GARCH models. We find that the correlation between asset returns plays an important role in the behavior of the optimal capital required and the portfolio structure. The stability and out-of-sample performance of our optimal solutions are empirically tested with respect to both the solvency requirement and portfolio performance, through a double rolling window estimation exercise. Journal: North American Actuarial Journal Pages: 394-416 Issue: 3 Volume: 18 Year: 2014 Month: 7 X-DOI: 10.1080/10920277.2014.910127 File-URL: http://hdl.handle.net/10.1080/10920277.2014.910127 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:3:p:394-416 Template-Type: ReDIF-Article 1.0 Author-Name: Tzuling Lin Author-X-Name-First: Tzuling Author-X-Name-Last: Lin Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Title: Applications of Mortality Durations and Convexities in Natural Hedges Abstract: Defining and deriving the mortality durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel shift, respectively, in μs (the forces of mortality), qs (the one-year death probabilities), ps (the one-year survival probabilities), ln (μ)s, (q/p)s, and ln (q/p)s, this article applies 24 proposed duration/convexity matching strategies classified into seven groups to determine the weights of two products in an insurance portfolio. The hedging performances of some qualified matching strategies selected as representatives are evaluated by comparing their Value at Risk (VaR) values and variance reduction ratios for a base scenario. We also test some specific scenarios for the population basis risk, model risk, volatility and jump risks, and interest rate risk to see the impacts on the matching strategies. Numerical examples show that some convexity matching strategies overall outperform the others in the VaR value and in the effectiveness of hedging both longevity and mortality risks for two kinds of insurance portfolios. Journal: North American Actuarial Journal Pages: 417-442 Issue: 3 Volume: 18 Year: 2014 Month: 7 X-DOI: 10.1080/10920277.2014.911108 File-URL: http://hdl.handle.net/10.1080/10920277.2014.911108 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:3:p:417-442 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Cohen Author-X-Name-First: Michael Author-X-Name-Last: Cohen Title: “Two Paradigms for The Market Value of Liabilities”, Robert R. Reitano, October 1997 Journal: North American Actuarial Journal Pages: 125-125 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595659 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595659 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:125-125 Template-Type: ReDIF-Article 1.0 Author-Name: Krzysztof Ostaszewski Author-X-Name-First: Krzysztof Author-X-Name-Last: Ostaszewski Title: “In Defense of Pay-as-You-Go (Paygo) Financing of Social Security”, Robert L. Brown, October 1997 Journal: North American Actuarial Journal Pages: 17-20 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595638 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595638 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:17-20 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: “In Defense of Pay-as-You-Go (Paygo) Financing of Social Security”, Robert L. Brown, October 1997 Journal: North American Actuarial Journal Pages: 16-17 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595637 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595637 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:16-17 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: Author’s Reply: In Defense of Pay-as-You-Go (Paygo) Financing of Social Security - Discussion by Bernard Dussault; Fred Kilbourne; Robert J. Myers; Krzysztof M. Ostaszewski, October 1997 Journal: North American Actuarial Journal Pages: 20-20 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595639 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595639 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:20-20 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: In Defense of Pay-as-You-Go (Paygo) Financing of Social Security Abstract: Today’s proposals to create larger social security funds and then invest them in the private sector are intended to create more rapid economic growth, which would make it easier to pay social security benefits in the long run. These proposals are also aimed at enhancing intergenerational equity by making today’s workers pay for a greater proportion of their future benefits.The important public policy issues inherent in such proposals are numerous: questions of whether prefunded social security plans are demographically immune; whether prefunding social security can increase gross national savings and worker productivity; whether there are better ways to create a healthy economy; whether social security is best offered as a defined-benefit plan or a defined-contribution plan. This paper explores each of these important public policy issues in the context of the social security systems of Canada and the U.S. Journal: North American Actuarial Journal Pages: 1-13 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595634 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595634 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:1-13 Template-Type: ReDIF-Article 1.0 Author-Name: Bernard Dussault Author-X-Name-First: Bernard Author-X-Name-Last: Dussault Title: “In Defense of Pay-as-You-Go (Paygo) Financing of Social Security”, Robert L. Brown, October 1997 Journal: North American Actuarial Journal Pages: 14-16 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595635 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595635 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:14-16 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Kilbourne Author-X-Name-First: Fred Author-X-Name-Last: Kilbourne Title: “In Defense of Pay-as-You-Go (Paygo) Financing of Social Security”, Robert L. Brown, October 1997 Journal: North American Actuarial Journal Pages: 16-16 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595636 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595636 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:16-16 Template-Type: ReDIF-Article 1.0 Author-Name: Gregory Savord Author-X-Name-First: Gregory Author-X-Name-Last: Savord Title: “Forecasting Social Security Actuarial Assumptions”, Edward W. Frees; Yueh-Chuan Kung; Marjorie A. Rosenberg; Virginia R. Young; Siu-Wai Lai, October 1997 Journal: North American Actuarial Journal Pages: 78-78 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595650 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595650 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:78-78 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Yueh-Chuan Kung Author-X-Name-First: Yueh-Chuan Author-X-Name-Last: Kung Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Author-Name: Siu-Wai Lai Author-X-Name-First: Siu-Wai Author-X-Name-Last: Lai Title: Authors’ Reply: Forecasting Social Security Actuarial Assumptions - Discussion by John A. Beekman; Cecil J. Nesbitt; Krzysztof M. Ostaszewski; Gregory Savord; Richard S. Foster, October 1997 Journal: North American Actuarial Journal Pages: 81-82 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595652 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595652 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:81-82 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Foster Author-X-Name-First: Richard Author-X-Name-Last: Foster Title: “Forecasting Social Security Actuarial Assumptions”, Edward W. Frees; Yueh-Chuan Kung; Marjorie A. Rosenberg; Virginia R. Young; Siu-Wai Lai, October 1997 Journal: North American Actuarial Journal Pages: 79-81 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595651 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595651 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:79-81 Template-Type: ReDIF-Article 1.0 Author-Name: Anthony Asher Author-X-Name-First: Anthony Author-X-Name-Last: Asher Title: “Deterministic Modeling of Defined-Contribution Pension Funds”, Zaki Khorasanee, October 1997 Journal: North American Actuarial Journal Pages: 99-100 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595654 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595654 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:99-100 Template-Type: ReDIF-Article 1.0 Author-Name: Zaki Khorasanee Author-X-Name-First: Zaki Author-X-Name-Last: Khorasanee Title: Deterministic Modeling of Defined-Contribution Pension Funds Abstract: Formulas are derived to model the response of a money purchase, defined-contribution pension fund to the following types of investment shock: (1) an instantaneous fall in the value of the fund assets and (2) a permanent, uniform reduction in the rate of earned interest. An alternative defined-contribution fund, incorporating a variable defined-benefit scale, is then proposed, and its responses to the same investment shocks are compared with those of the money purchase fund. The comparison shows that the variable defined-benefit approach offers a useful alternative to the money purchase principle for defined-contribution pension funds. Journal: North American Actuarial Journal Pages: 83-99 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595653 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595653 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:83-99 Template-Type: ReDIF-Article 1.0 Author-Name: Zaki Khorasanee Author-X-Name-First: Zaki Author-X-Name-Last: Khorasanee Title: Author’s Reply: Deterministic Modeling of Defined-Contribution Pension Funds - Discussion by Anthony Asher; Daniel Dufresne, October 1997 Journal: North American Actuarial Journal Pages: 101-103 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595656 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595656 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:101-103 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Dufresne Author-X-Name-First: Daniel Author-X-Name-Last: Dufresne Title: “Deterministic Modeling of Defined-Contribution Pension Funds”, Zaki Khorasanee, October 1997 Journal: North American Actuarial Journal Pages: 100-101 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595655 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595655 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:100-101 Template-Type: ReDIF-Article 1.0 Author-Name: David Babbel Author-X-Name-First: David Author-X-Name-Last: Babbel Title: “Two Paradigms for The Market Value of Liabilities”, Robert R. Reitano, October 1997 Journal: North American Actuarial Journal Pages: 122-125 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595658 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595658 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:122-125 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Reitano Author-X-Name-First: Robert Author-X-Name-Last: Reitano Title: Two Paradigms for The Market Value of Liabilities Abstract: Asset/liability management (ALM) theory and practices of insurers have matured and developed from early applications to guaranteed investment contracts (GICs) to all annuity and insurance products today. An important and logical next step of inquiry is the definition of, and calculation procedures for, the market value of an insurance liability. Because all ALM strategies have as their goal the management of some value of assets in relation to some value of liabilities, this inquiry will provide at last a canonical basis for ALM: the management of relative market values.To set the stage for this exploration, the theory and application of pricing in a complete market are reviewed, as are the practical limitations of this theory in the real, and far from complete, financial markets. The notion of an ad hoc pricing model is developed, and examples are reviewed and critiqued. These models, though imperfect compared with pricing in a complete market, bridge the gap between pricing theory and practice.The current state of the liabilities market is also discussed, and this market is seen to naturally split into a “long” and a “short” submarket. Of particular interest is the theoretical possibility of these markets becoming broad-based, deep and active, and the conclusions are relevant to the issue of long/short price equalization.Two paradigms are then explored for defining and subsequently calculating an insurance liability market value. A “paradigm” is a generalized model or framework for accomplishing the task at hand. Each paradigm reflects observable market trading activity, however infrequent, and each is based on methods of valuation consistent with finance-theoretic approaches that are routinely used for the market valuation of assets.In addition, each paradigm allows for a sequence of ad hoc valuation methodologies, which differ in the extent to which various risks are explicitly modeled versus judgmentally reflected in a risk spread. These paradigms are discussed and contrasted, and arguments made for the potential evolution of the respective values if a “liability” market began trading actively. Practical constraints on the realization of this evolution are also noted.The last section of this paper discusses a host of considerations related to the application of option-pricing theory to insurance company liabilities. Journal: North American Actuarial Journal Pages: 104-122 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595657 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595657 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:104-122 Template-Type: ReDIF-Article 1.0 Author-Name: Krzysztof Ostaszewki Author-X-Name-First: Krzysztof Author-X-Name-Last: Ostaszewki Title: “Forecasting Social Security Actuarial Assumptions”, Edward W. Frees; Yueh-Chuan Kung; Marjorie A. Rosenberg; Virginia R. Young; Siu-Wai Lai, October 1997 Journal: North American Actuarial Journal Pages: 77-78 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595649 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595649 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:77-78 Template-Type: ReDIF-Article 1.0 Author-Name: Cecil Nesbitt Author-X-Name-First: Cecil Author-X-Name-Last: Nesbitt Title: “Forecasting Social Security Actuarial Assumptions”, Edward W. Frees; Yueh-Chuan Kung; Marjorie A. Rosenberg; Virginia R. Young; Siu-Wai Lai, October 1997 Journal: North American Actuarial Journal Pages: 76-77 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595648 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595648 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:76-77 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Yueh-Chuan Kung Author-X-Name-First: Yueh-Chuan Author-X-Name-Last: Kung Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Author-Name: Siu-Wai Lai Author-X-Name-First: Siu-Wai Author-X-Name-Last: Lai Title: Forecasting Social Security Actuarial Assumptions Abstract: This paper presents a forecasting model of economic assumptions that are inputs to projections of the Social Security system. Social Security projections are made to help policy-makers understand the financial stability of the system. Because system income and expenditures are subject to changes in law, they are controllable and not readily amenable to forecasting techniques. Hence, we focus directly on the four major economic assumptions to the system: inflation rate, investment returns, wage rate, and unemployment rate. Population models, the other major input to Social Security projections, require special demographic techniques and are not addressed here.Our approach to developing a forecasting model emphasizes exploring characteristics of the data. That is, we use graphical techniques and diagnostic statistics to display patterns that are evident in the data. These patterns include (1) serial correlation, (2) conditional heteroscedasticity, (3) contemporaneous correlations, and (4) cross-correlations among the four economic series. To represent patterns in the four series, we use multivariate autoregressive, moving average (ARMA) models with generalized autoregressive, conditionally heteroscedastic (GARCH) errors.The outputs of the fitted models are the forecasts. Because the forecasts can be used for nonlinear functions such as discounting present values of future obligations, we present a computer-intensive method for computing forecast distributions. The computer-intensive approach also allows us to compare alternative models via out-of-sample validation and to compute exact multivariate forecast intervals, in lieu of approximate simultaneous univariate forecast intervals. We show how to use the forecasts of economic assumptions to forecast a simplified version of a fund used to protect the Social Security system from adverse deviations. We recommend the use of the multivariate model because it establishes important lead and lag relationships among the series, accounts for information in the contemporaneous correlations, and provides useful forecasts of a fund that is analogous to the one used by the Social Security system. Journal: North American Actuarial Journal Pages: 49-70 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595646 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595646 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:49-70 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Title: “Forecasting Social Security Actuarial Assumptions”, Edward W. Frees; Yueh-Chuan Kung; Marjorie A. Rosenberg; Virginia R. Young; Siu-Wai Lai, October 1997 Journal: North American Actuarial Journal Pages: 75-76 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595647 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595647 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:75-76 Template-Type: ReDIF-Article 1.0 Author-Name: J. David Cummins Author-X-Name-First: J. Author-X-Name-Last: David Cummins Author-Name: Richard Derrig Author-X-Name-First: Richard Author-X-Name-Last: Derrig Title: Authors’ Reply: Fuzzy Financial Pricing of Property-Liability Insurance - Discussion by David Appel; Lawrence A. Berger; Krzysztof M. Ostaszewski; Oakley E. Van Slyke, October 1997 Journal: North American Actuarial Journal Pages: 44-44 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595644 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595644 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:44-44 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Fafian Author-X-Name-First: Joseph Author-X-Name-Last: Fafian Title: Mortality Experience of National Basketball Association Players Journal: North American Actuarial Journal Pages: 45-48 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595645 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595645 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:45-48 Template-Type: ReDIF-Article 1.0 Author-Name: Luke Girard Author-X-Name-First: Luke Author-X-Name-Last: Girard Title: “Two Paradigms for The Market Value of Liabilities”, Robert R. Reitano, October 1997 Journal: North American Actuarial Journal Pages: 127-129 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595661 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595661 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:127-129 Template-Type: ReDIF-Article 1.0 Author-Name: Krzysztof Ostaszewski Author-X-Name-First: Krzysztof Author-X-Name-Last: Ostaszewski Title: “Fuzzy Financial Pricing of Property-Liability Insurance”, J. David Cummins; Richard A. Derrig, October 1997 Journal: North American Actuarial Journal Pages: 41-42 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595642 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595642 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:41-42 Template-Type: ReDIF-Article 1.0 Author-Name: J. Peter Duran Author-X-Name-First: J. Author-X-Name-Last: Peter Duran Title: “Two Paradigms for The Market Value of Liabilities”, Robert R. Reitano, October 1997 Journal: North American Actuarial Journal Pages: 125-127 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595660 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595660 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:125-127 Template-Type: ReDIF-Article 1.0 Author-Name: Oakley Van Slyke Author-X-Name-First: Oakley Author-X-Name-Last: Van Slyke Title: “Fuzzy Financial Pricing of Property-Liability Insurance”, J. David Cummins; Richard A. Derrig, October 1997 Journal: North American Actuarial Journal Pages: 42-44 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595643 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595643 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:42-44 Template-Type: ReDIF-Article 1.0 Author-Name: J. David Cummins Author-X-Name-First: J. Author-X-Name-Last: David Cummins Author-Name: Richard Derrig Author-X-Name-First: Richard Author-X-Name-Last: Derrig Title: Fuzzy Financial Pricing of Property-Liability Insurance Abstract: This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach. Journal: North American Actuarial Journal Pages: 21-40 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595640 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595640 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:21-40 Template-Type: ReDIF-Article 1.0 Author-Name: David Appel Author-X-Name-First: David Author-X-Name-Last: Appel Author-Name: Lawrence Berger Author-X-Name-First: Lawrence Author-X-Name-Last: Berger Title: “Fuzzy Financial Pricing of Property-Liability Insurance”, J. David Cummins; Richard A. Derrig, October 1997 Journal: North American Actuarial Journal Pages: 41-41 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595641 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595641 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:41-41 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Title: “Actuarial Issues in the Novels of Jane Austen,” Daniel D. Skwire, January 1997 Journal: North American Actuarial Journal Pages: 144-146 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595665 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595665 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:144-146 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Two Paradigms for the Market Value of Liabilities - Discussion by David F. Babbel; Michael Cohen; J. Peter Duran; Luke N. Girard; Thomas S.Y. Ho; Craig Merrill Journal: North American Actuarial Journal Pages: 135-137 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595664 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595664 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:135-137 Template-Type: ReDIF-Article 1.0 Author-Name: Craig Merrill Author-X-Name-First: Craig Author-X-Name-Last: Merrill Title: “Two Paradigms for The Market Value of Liabilities”, Robert R. Reitano, October 1997 Journal: North American Actuarial Journal Pages: 131-135 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595663 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595663 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:131-135 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Ho Author-X-Name-First: Thomas Author-X-Name-Last: Ho Title: “Two Paradigms for The Market Value of Liabilities”, Robert R. Reitano, October 1997 Journal: North American Actuarial Journal Pages: 129-131 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595662 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595662 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:129-131 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Skwire Author-X-Name-First: Daniel Author-X-Name-Last: Skwire Title: Author’s Reply: Actuarial Issues in the Novels of Jane Austen - Discussion by Beda Chan Journal: North American Actuarial Journal Pages: 146-147 Issue: 4 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595666 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595666 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:146-147 Template-Type: ReDIF-Article 1.0 Author-Name: Derek Smith Author-X-Name-First: Derek Author-X-Name-Last: Smith Title: “Federal Regulation of Use of Genetic Information by Insurers: What Constitutes Unfair Discrimination?”, Ellwood F. Oakley III, January, 1999 Journal: North American Actuarial Journal Pages: 131-132 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595783 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595783 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:131-132 Template-Type: ReDIF-Article 1.0 Author-Name: Karen Rothenberg Author-X-Name-First: Karen Author-X-Name-Last: Rothenberg Title: Social Implications of Genetic Testing Abstract: This paper examines the social implications of predictive genetic testing and its impact on the insurance industry. Although the Human Genome Project has the potential to improve the health of our nation, it also may serve as a means of highlighting genetic differences among individuals and ethnic groups. Thus, if we are to reach the full promise of the Project, society must address the public’s fears of genetic discrimination in insurance and employment contexts. Following an analysis of state and federal legislation on genetic privacy and discrimination, the paper concludes with a challenge to the insurance industry to work with the medical community and health care advocates to formulate a public policy approach that promotes informed consent and the fair use of genetic information. Journal: North American Actuarial Journal Pages: 133-136 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595784 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595784 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:133-136 Template-Type: ReDIF-Article 1.0 Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Title: “Understanding Relationships Using Copulas,” Edward Frees and Emiliano Valdez, January 1998 Journal: North American Actuarial Journal Pages: 137-142 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595785 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595785 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:137-142 Template-Type: ReDIF-Article 1.0 Author-Name: Benjamin Wurzburger Author-X-Name-First: Benjamin Author-X-Name-Last: Wurzburger Title: “Risk-Adjusted Economic Value Analysis,” Alastair G. Longley-Cook, January 1998 Journal: North American Actuarial Journal Pages: 142-146 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595786 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595786 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:142-146 Template-Type: ReDIF-Article 1.0 Author-Name: Alastair Longley-Cook Author-X-Name-First: Alastair Author-X-Name-Last: Longley-Cook Title: “Author’s Reply: Risk-Adjusted Economic Value Analysis,” Benjamin W. Wurzburger, January 1998 - Discussion by Benjamin W. Wurzburger Journal: North American Actuarial Journal Pages: 146-148 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595787 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595787 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:146-148 Template-Type: ReDIF-Article 1.0 Author-Name: Barnet Berin Author-X-Name-First: Barnet Author-X-Name-Last: Berin Title: Ambachtsheer, Keith P., and Ezra, Don D., 1998, Journal: North American Actuarial Journal Pages: 149-150 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595788 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:149-150 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Cowman Author-X-Name-First: Edward Author-X-Name-Last: Cowman Title: Bruce, William D., 1996, A Fifty-Year Labor of Love: Journal: North American Actuarial Journal Pages: 150-150 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595789 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595789 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:150-150 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Holmes Author-X-Name-First: Bruce Author-X-Name-Last: Holmes Title: “The Future of Risk Classification in the Age of Predictive DNA-Based Testing”, Donald C. Chambers, January 1999 Journal: North American Actuarial Journal Pages: 29-31 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595766 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595766 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:29-31 Template-Type: ReDIF-Article 1.0 Author-Name: Donald Chambers Author-X-Name-First: Donald Author-X-Name-Last: Chambers Title: The Future of Risk Classification in the Age of Predictive DNA-Based Testing Abstract: This paper describes the epic genetic testing issue within the context of the insurer’s decadeslong struggle against increasing numbers of people who question the fairness and social legitimacy of risk classification.The fact that this uniquely personal and emotional genetics issue is now erupting at the very time that our industry seems preoccupied with other challenges begs the question of our industry’s ability to manage this issue in a way that will preserve the basic fabric of our being. A major goal of this paper is to articulate a visionary tenpart industry management strategy.Four specific and critically important industry management recommendations are made. Although some will be easier than others to accomplish, each is exceedingly important. Journal: North American Actuarial Journal Pages: 21-28 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595765 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595765 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:21-28 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Hall Author-X-Name-First: Mark Author-X-Name-Last: Hall Title: Restricting Insurers’ Use of Genetic Information Journal: North American Actuarial Journal Pages: 34-46 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595768 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595768 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:34-46 Template-Type: ReDIF-Article 1.0 Author-Name: Arnold Dicke Author-X-Name-First: Arnold Author-X-Name-Last: Dicke Title: “The Future of Risk Classification in the Age of Predictive DNA-Based Testing”, Donald C. Chambers, January 1999 Journal: North American Actuarial Journal Pages: 31-33 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595767 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595767 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:31-33 Template-Type: ReDIF-Article 1.0 Author-Name: John Krinik Author-X-Name-First: John Author-X-Name-Last: Krinik Title: “What Does Genetic Technology Have to Do with Ethics?”, Ray Moseley and Bill Allen, January, 1999 Journal: North American Actuarial Journal Pages: 112-115 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595780 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595780 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:112-115 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Author-Name: Richard MacMinn Author-X-Name-First: Richard Author-X-Name-Last: MacMinn Author-Name: Maureen Carter Author-X-Name-First: Maureen Author-X-Name-Last: Carter Title: Genetic Testing, Insurance Economics, and Societal Responsibility Abstract: Three major perspectives emerge when the discussion of the implications of genetic testing on the insurance industry commences. One viewpoint, strongly advocated by certain consumer groups and ethicists on the basis of societal responsibility, categorically denies any necessity for connecting the results of genetic testing and issuance of insurance. By contrast, the insurance industry, upon examining the economics and dynamics of participation in voluntary insurance markets, lives in fear of a world filled with asymmetrical information (counter to the axioms for competitive markets), adverse selection (action by the insured as a result of asymmetric information to the perceived economic disadvantage of the insurer), and ultimately even the possibility of potential market failure or insurance company insolvency. An actuarial perspective considering the benefits (to the insurer) of this new genetic information concentrates primarily on the possibility of developing improved quantitative assessments of risk and better calculations of the actuarial present value of future loss costs based on the new statistically significant information gained from genetic testing. The strengths and weaknesses and facts and fallacies of each of these perspectives are examined in this paper, and potential solutions to the ultimate role of genetic testing in insurance underwriting and rate making are considered from the perspectives of the major players in this debate. Journal: North American Actuarial Journal Pages: 1-20 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595764 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595764 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Ellwood Oakley Author-X-Name-First: Ellwood Author-X-Name-Last: Oakley Title: Federal Regulation of Use of Genetic Information by Insurers Abstract: This paper analyzes policy developments at the national level during 1997, including proposed federal legislation and the response of the insurance industry. With broad bipartisan support, it appears that some form of federal regulation is likely within the next two sessions of Congress. The debate appears to be centering on two issues: the definition of genetic information and whether regulation will extend to a blanket prohibition on testing. The insurance industry is suggesting that restrictions based on an “unfair discrimination” standard would permit coverage and cost distinctions based on actuarially sound data, while the health care industry is opposed to any discrimination based on genetic information. A utilitarian ethical perspective would likely support restrictions on testing for life insurance but not health insurance. Journal: North American Actuarial Journal Pages: 116-127 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595781 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:116-127 Template-Type: ReDIF-Article 1.0 Author-Name: Erle Peacock Author-X-Name-First: Erle Author-X-Name-Last: Peacock Title: “Federal Regulation of Use of Genetic Information by Insurers: What Constitutes Unfair Discrimination?”, Ellwood F. Oakley III, January, 1999 Journal: North American Actuarial Journal Pages: 127-131 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595782 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595782 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:127-131 Template-Type: ReDIF-Article 1.0 Author-Name: Erle Peacock Author-X-Name-First: Erle Author-X-Name-Last: Peacock Title: “Restricting Insurers’ Use of Genetic Information: A Guide to Public Policy”, Mark A. Hall, January 1999 Journal: North American Actuarial Journal Pages: 46-50 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595769 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595769 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:46-50 Template-Type: ReDIF-Article 1.0 Author-Name: Arnold Dicke Author-X-Name-First: Arnold Author-X-Name-Last: Dicke Title: “The Current State of Genetic Testing: An Insurance Industry Perspective on the Rush to Legislate”, Charles S. Jones, Jr., January, 1999 Journal: North American Actuarial Journal Pages: 65-66 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595774 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595774 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:65-66 Template-Type: ReDIF-Article 1.0 Author-Name: J. Alexander Lowden Author-X-Name-First: J. Author-X-Name-Last: Alexander Lowden Title: Ethical Issues Resulting from Genetic Technology Abstract: Genetic tests are laboratory procedures that identify changes in our genes. Most human disease results, in whole or in part, from alterations in genes. Because the tests are expected to have incredible predictive power and because they may tell us personal information before we are ready to receive it, testing requested by a third party could be considered an infringement on privacy. Furthermore, the technology is new and thus subject to errors in interpretation that could result in unfair discrimination against the person who has been tested. Genes are inherited and are found not only in a single individual but also in some blood relatives. A genetic test therefore involves many people and invades the privacy of all. This paper questions the right of insurers to demand genetic tests but notes that by concealing the results of tests, applicants may practice adverse selection. If ethics are rules of conduct that society requires, then insurers will need to reexamine their ethical responsibilities in the light of this new technology. Journal: North American Actuarial Journal Pages: 67-78 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595775 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595775 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:67-78 Template-Type: ReDIF-Article 1.0 Author-Name: Charles Jones Author-X-Name-First: Charles Author-X-Name-Last: Jones Title: The Current State of Genetic Testing Abstract: Recent advances in genetic technology and progress in the multinational Human Genome Project are providing scientists with the ability to look into and manipulate the very makeup of life: the DNA molecule. We can already examine many dozens of plant and animal genes for disease producing abnormalities. In the near future, we will have the ability to alter specific genes in living tissue. This genetic technology holds great promise in our quest for preventing, diagnosing, treating, and predicting disease, not just in humans, but in all forms of life.But there are some problems. Philosophically many are not ready for the implications of this technology. There are social and ethical issues that have not been well addressed, and which have, in part, resulted in an unprecedented amount of legislative activity over the past four years aimed at restricting access to and use of genetic information. The ability of the U.S. insurance industry to risk-select may be severely hampered if these restrictions are widely applied. Journal: North American Actuarial Journal Pages: 56-63 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595772 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595772 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:56-63 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Holmes Author-X-Name-First: Bruce Author-X-Name-Last: Holmes Title: “The Current State of Genetic Testing: An Insurance Industry Perspective on the Rush to Legislate”, Charles S. Jones, Jr., January, 1999 Journal: North American Actuarial Journal Pages: 63-64 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595773 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595773 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:63-64 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Title: “Modeling the Impact of Genetics on Insurance”, Angus S. Macdonald, January, 1999 Journal: North American Actuarial Journal Pages: 101-105 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595778 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595778 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:101-105 Template-Type: ReDIF-Article 1.0 Author-Name: Ray Moseley Author-X-Name-First: Ray Author-X-Name-Last: Moseley Author-Name: Bill Allen Author-X-Name-First: Bill Author-X-Name-Last: Allen Title: What Does Genetic Technology Have to Do with Ethics? Abstract: A number of problematic issues have arisen in anticipation of the potential role of molecular tests for genetic predispositions to illness in risk assessment by insurance underwriters. We argue in this paper that the regrettable history and current risks of genetic discrimination warrant a presumption that genetic predisposition status should not be used in any nonmedical contexts, unless compelling evidence can demonstrate that serious harm will result to third-party interests without such use. We argue that insurers should not be able to initiate testing for genetic predisposition. We also argue that there are many reasons to doubt whether patients’ test results will result in such serious adverse selection as to cause substantial harm to insurance markets, except possibly at higher policy amounts in life or disability income insurance. We conclude that the burden of proof must be on insurers to demonstrate necessity of use in specific cases in which test availability shows high probability of imminent, serious harm to insurance markets. Journal: North American Actuarial Journal Pages: 106-112 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595779 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595779 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:106-112 Template-Type: ReDIF-Article 1.0 Author-Name: John Krinik Author-X-Name-First: John Author-X-Name-Last: Krinik Title: “Ethical Issues Resulting from Genetic Technology”, J. Alexander Lowden, January, 1999 Journal: North American Actuarial Journal Pages: 78-82 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595776 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595776 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:78-82 Template-Type: ReDIF-Article 1.0 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: Modeling the Impact of Genetics on Insurance Abstract: The role of probabilistic models in the debate over genetics and insurance is discussed. A Markov model is used to show that, under quite extreme assumptions, adverse selection in life insurance ought to be controllable. The statistical problems of estimating small differences in mortality are discussed; these might limit the use of many genetic disorders as rating factors. The influence of the insurance industry on policy-making, especially through its support of research, is discussed. It is suggested that participating contracts are suitable and simple vehicles to carry the genetic risks in life insurance. Journal: North American Actuarial Journal Pages: 83-101 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595777 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595777 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:83-101 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Title: Preface to the Issue on Genetic Testing Journal: North American Actuarial Journal Pages: iii-iv Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595792 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595792 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: Serena Tiong Author-X-Name-First: Serena Author-X-Name-Last: Tiong Title: Houthakker, H.S., and Williamson, P.J., 1996, Journal: North American Actuarial Journal Pages: 150-151 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595790 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595790 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:150-151 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Miller Author-X-Name-First: Robert Author-X-Name-Last: Miller Title: Wainer, H., 1997, Visual Revelations: Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot, Copernicus, New York, 180 pages, $35.00, ISBN 0-387-94902-X. Journal: North American Actuarial Journal Pages: 151-152 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595791 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:151-152 Template-Type: ReDIF-Article 1.0 Author-Name: Derek Smith Author-X-Name-First: Derek Author-X-Name-Last: Smith Title: “Restricting Insurers’ Use of Genetic Information: A Guide to Public Policy”, Mark A. Hall, January 1999 Journal: North American Actuarial Journal Pages: 50-51 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595770 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595770 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:50-51 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Johansen Author-X-Name-First: Robert Author-X-Name-Last: Johansen Title: Effective Underwriting in the Genetic Testing Era Abstract: This paper notes that prior to the availability of genetic test results, conventional life insurance underwriting had produced satisfactory mortality results even though a number of applicants insured at standard or better must have had serious genetic markers. The paper discusses the problems that may affect underwriting when an applicant is aware of a genetic risk factor.The paper suggests use of pre-genetic testing era underwriting methodology, including medical history and family history, with strict financial underwriting to control antiselection. A set of underwriting rules is provided. The need for a sales organization that can produce a substantial amount of business is cited as necessary for success.To spread equitably any excess cost on account of insuring persons with genetic markers, a risk pool is suggested. The pool manager would also inform a company of additional applications to other companies by genetically impaired applicants.The purpose of the proposal is to deflect ill-advised political solutions and, at the same time, to control expenses by ensuring a high ratio of paid-for policies to applications. Journal: North American Actuarial Journal Pages: 52-55 Issue: 1 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595771 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595771 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:1:p:52-55 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Search for Predictors of Exceptional Human Longevity: Using Computerized Genealogies and Internet Resources for Human Longevity Studies - Discussion by Bert Kestenbaum Journal: North American Actuarial Journal Pages: 135-138 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597489 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597489 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:135-138 Template-Type: ReDIF-Article 1.0 Author-Name: Bert Kestenbaum Author-X-Name-First: Bert Author-X-Name-Last: Kestenbaum Title: “Search for Predictors of Exceptional Human Longevity: Using Computerized Genealogies and Internet Resources for Human Longevity Studies,” Natalia S. Gavrilova and Leonid A. Gavrilov, January 2007 Journal: North American Actuarial Journal Pages: 132-135 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597488 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597488 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:132-135 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Philippe Boucher Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Boucher Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Montserrat Guillén Author-X-Name-First: Montserrat Author-X-Name-Last: Guillén Title: Risk Classification for Claim Counts Abstract: This paper presents and compares different risk classification models for the annual number of claims reported to the insurer. Generalized heterogeneous, zero-inflated, hurdle, and compound frequency models are applied to a sample of an automobile portfolio of a major company operating in Spain. A statistical comparison between models is performed with the help of various specification tests (Score and Hausman tests for nested models, Vuong test or information criteria for nonnested ones). Interesting results about claiming behavior are obtained. Journal: North American Actuarial Journal Pages: 110-131 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597487 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597487 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:110-131 Template-Type: ReDIF-Article 1.0 Author-Name: Saralees Nadarajah Author-X-Name-First: Saralees Author-X-Name-Last: Nadarajah Title: “On the Class of Erlang Mixtures with Risk Theoretic Applications,” Gordon E. Willmot and Jae-Kyung Woo, April 2007 Journal: North American Actuarial Journal Pages: 142-144 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597492 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597492 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:142-144 Template-Type: ReDIF-Article 1.0 Author-Name: X. Lin Author-X-Name-First: X. Author-X-Name-Last: Lin Author-Name: Xiaoming Liu Author-X-Name-First: Xiaoming Author-X-Name-Last: Liu Title: Markov Aging Process and Phase-Type Law of Mortality Abstract: In this article, we propose a finite-state Markov process with one absorbing state to model human mortality. A health index called physiological age is introduced and modeled by the Markov process. Under this model the time of death follows a phase-type distribution. The model possesses many desirable analytical properties useful for mortality analysis. Closed-form expressions are available for many quantities of interest including the conditional survival probabilities of the time of death and the actuarial present values of the whole life insurance and annuity. The heterogeneity or frailty effect of a cohort can be expressed explicitly. The model is also able to explain some stylized facts of observed mortality data. We fit the model to some Swedish population cohort data and life tables compiled by the U.S. Social Security Administration. The fitting results are very satisfactory. Journal: North American Actuarial Journal Pages: 92-109 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597486 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597486 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:92-109 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: A Risk Model with Multilayer Dividend Strategy - Discussion by Cheung; Ramin Okhrati Journal: North American Actuarial Journal Pages: 141-142 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597491 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597491 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:141-142 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Title: “Moments of the Dividend Payments and Related Problems in a Markov-Modulated Risk Model,” Shaunming Li and Yi Lu, April 2007 Journal: North American Actuarial Journal Pages: 145-148 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597494 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597494 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:145-148 Template-Type: ReDIF-Article 1.0 Author-Name: Lee Dunham Author-X-Name-First: Lee Author-X-Name-Last: Dunham Author-Name: Geoffrey Friesen Author-X-Name-First: Geoffrey Author-X-Name-Last: Friesen Title: An Empirical Examination of Jump Risk in U.S. Equity And Bond Markets Abstract: Actuaries manage risk, and asset price volatility is the most fundamental parameter in models of risk management. This study utilizes recent advances in econometric theory to decompose total asset price volatility into a smooth, continuous component and a discrete (jump) component. We analyze a data set that consists of high-frequency tick-by-tick data for all stocks in the S&P 100 Index, as well as similar futures contract data on three U.S. equity indexes and three U.S. Treasury securities during the period 1999-2005. We find that discrete jumps contribute between 15% and 25% of total asset risk for all equity index futures, and between 45% and 75% of total risk for Treasury bond futures. Jumps occur roughly once every five trading days for equity index futures, and slightly more frequently for Treasury bond futures. For the S&P 100 component stocks, on days when a jump occurs, the absolute jump is between 80% and 90% of the total absolute return for that day. We also demonstrate that, in the cross section of individual stocks, the average jump beta is significantly lower than the average continuous beta. Cross-correlations within the bond and stock markets are significantly higher on days when jumps occur, but stockbond correlations are relatively constant regardless of whether or not a jump occurs. We conclude with a discussion of the implications of our findings for risk management. Journal: North American Actuarial Journal Pages: 76-91 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597485 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597485 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:76-91 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: On the Class of Erlang Mixtures with Risk Theoretic Applications - Discussion by Saralees Nadarajah Journal: North American Actuarial Journal Pages: 144-144 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597493 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597493 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:144-144 Template-Type: ReDIF-Article 1.0 Author-Name: Martin le Roux Author-X-Name-First: Martin Author-X-Name-Last: le Roux Title: A Long-Term Model of the Dynamics of the S&P500 Implied Volatility Surface Abstract: In this paper we present an econometric model of implied volatilities of S&P500 index options. First, we model the dynamics the CBOE VIX index as a proxy for the general level of implied volatilities. We then describe a parametric model of the implied volatility surface for options with a term of up to two years. We show that almost all of the variation in the implied volatility surface can be explained by the VIX index and one or two other uncorrelated factors. Finally, we present a model of the dynamics of these factors. Journal: North American Actuarial Journal Pages: 61-75 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597484 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597484 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:61-75 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author Reply: An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets by Zinoviy Landsman and Michael Sherris - Discussion by Edward Furman; Ricardas Zitikis Journal: North American Actuarial Journal Pages: 150-150 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597496 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597496 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:150-150 Template-Type: ReDIF-Article 1.0 Author-Name: Andreas Milidonis Author-X-Name-First: Andreas Author-X-Name-Last: Milidonis Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Title: Estimation of Distress Costs Associated with Downgrades Using Regimeswitching Models Abstract: We use a unique dataset of bond downgrades from a niche rating company that has been found to be reacting faster to publicly available information than its competitors. Using regime-switching models we propose risk measures to quantify stock return disturbances (distress costs) associated with the timing of downgrades. These risk measures are based on the Capital Asset Pricing Model (CAPM) and use the estimated parameters of the regime-switching models. We observe a noticeable switch from a low-volatility to a high-volatility regime one day before the day of downgrades. On average the volatility in stock returns triples around the time of downgrades, and the stock return process remains in the high-volatility regime for about three days. Using our proposed risk measure we find that stock returns are associated with distress costs of about 22*d% (where “d” is the daily market price of risk) over a window of 10 days before and after downgrades. These costs can be further separated between bond-rating companies that are designated by the SEC as nationally recognized to rate debt and those that are not. Journal: North American Actuarial Journal Pages: 42-60 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597483 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597483 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:42-60 Template-Type: ReDIF-Article 1.0 Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Arthur Renshaw Author-X-Name-First: Arthur Author-X-Name-Last: Renshaw Title: “Pension Plan Valuation and Mortality Projection: A Case Study with Mortality Data,” Hélène Cossette, Antoine Delwarde, Michel Denuit, Frédérick Guillot, and Étienne Marceau, April 2007 Journal: North American Actuarial Journal Pages: 148-150 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597495 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597495 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:148-150 Template-Type: ReDIF-Article 1.0 Author-Name: Philip Booth Author-X-Name-First: Philip Author-X-Name-Last: Booth Author-Name: Alan Morrison Author-X-Name-First: Alan Author-X-Name-Last: Morrison Title: Regulatory Competition and Life Insurance Solvency Regulation in the European Union and United States Abstract: The economic reasons for life insurance regulation have not been well developed in the finance literature. In this paper we discuss some justifications that have been advanced for regulation and argue that they are not persuasive. The most rigorous arguments in favor of the regulation of life insurance companies are as follows. First, regulation can prevent the adverse affects of information asymmetries in markets for illiquid contracts. Second, regulation can be used to ensure that insurers commit to contracts. In the case of life insurers these contracts may be incomplete, and it may be difficult to determine the terms of the contracts objectively; this is particularly so with U.K. with-profit contracts, for example. These justifications for regulation, combined with a public choice analysis of regulation, lead us to conclude that regulation should be voluntary and provided by competing private and government agencies. Finally we propose a method of moving toward such a regulatory framework starting from the current regulatory institutions in the United States and the European Union (EU). An approach based on the “mutual recognition” concept used, at least in theory, in the EU would provide an approximation to the regulatory approach we believe can be justified by economic principles. Journal: North American Actuarial Journal Pages: 23-41 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597482 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597482 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:23-41 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Sun Siang Liew Author-X-Name-First: Sun Siang Author-X-Name-Last: Liew Title: Asset Allocation with Hedge Funds on the Menu Abstract: Hedge funds have become an increasingly important asset class in recent years. This paper discusses the asset allocation decision of an investor who is considering investing in hedge funds. We develop a simple procedure that may help in making this decision when the assets consist of a core equity portfolio, the risk-free asset, and a hedge fund. A regime-switching framework is used to model the joint returns of the hedge fund and the equity market. We use monthly intervals so that the regimes can change only at most once a month. Within each regime the returns on the two risky assets are bivariate lognormal with constant parameters. These parameters are estimated from the empirical data. We show how to determine the optimal allocation of an investor, such as a pension plan, to hedge fund assets. Our procedure is based on the maximization of expected utility, and we use different horizons. We restrict the admissible strategies to buy-andhold strategies, so we do not allow for portfolio balancing. We illustrate the procedure with examples. We find that bias in the hedge fund expected return has an important impact on the results. We note that some hedge fund strategies have substantial left-tail risk to which investors may be very averse. This type of risk aversion is not adequately captured by the standard expected utility model, but it could be added as a constraint. Journal: North American Actuarial Journal Pages: 1-21 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597481 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597481 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:1-21 Template-Type: ReDIF-Article 1.0 Author-Name: Ramin Okhrati Author-X-Name-First: Ramin Author-X-Name-Last: Okhrati Title: “A Risk Model with Multilayer Dividend Strategy,” Hansjörg Albrecher and Jürgen Hartinger, April 2007 Journal: North American Actuarial Journal Pages: 138-141 Issue: 4 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597490 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597490 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:4:p:138-141 Template-Type: ReDIF-Article 1.0 Author-Name: Charles Vinsonhaler Author-X-Name-First: Charles Author-X-Name-Last: Vinsonhaler Author-Name: Nalini Ravishanker Author-X-Name-First: Nalini Author-X-Name-Last: Ravishanker Author-Name: Jeyaraj Vadiveloo Author-X-Name-First: Jeyaraj Author-X-Name-Last: Vadiveloo Author-Name: Guy Rasoanaivo Author-X-Name-First: Guy Author-X-Name-Last: Rasoanaivo Title: Multivariate Analysis of Pension Plan Mortality Data Abstract: This paper uses the logistic regression model to examine private pension plan data for 1989–95 collected by the Retirement Plans Experience Committee of the Society of Actuaries. When only one explanatory variable, such as annuity class size, is used in modeling mortality rates, the model provides a reasonable fit to the data. Multiple explanatory variables give less satisfactory results. Journal: North American Actuarial Journal Pages: 126-135 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595989 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595989 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:126-135 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Robin Damm Author-X-Name-First: Robin Author-X-Name-Last: Damm Author-Name: Ishmael Sharara Author-X-Name-First: Ishmael Author-X-Name-Last: Sharara Title: A Macro-Economic Indicator of Age at Retirement Abstract: This paper explores the relationship between the Wealth Transfer Index (WTI), a statistic defined by Brown and Bilodeau (1997), and retirement age, which is the age at which the workers in an economy cease to be economically productive. Appropriately expressed as a ratio of consumption demand to labor productivity, WTI is a barometer for the demand for wealth placed on the workers of an economy. This paper explains why a relationship between this statistic and retirement age must exist. Using Canadian historical median retirement age data compiled by Statistics Canada and calculated values of the WTI for the same period, three linear regression models are fitted. The conclusion from these models indicates that there is a strong positive correlation between the WTI and average retirement age.This paper also briefly looks at the well-documented demographic shift expected to occur in Canada because of the baby boom–baby bust tidal wave. The aged dependency ratio is expected to increase dramatically, reaching 45% in 2036. A practical application of the WTI model suggests that the baby boom cohort may experience a rise in the normal retirement age in the period 2017–34. They will, in effect, be forced to retire at ages that will allow for an “acceptable” transfer of wealth from the workers to dependent Canadians. Using one of the fitted linear regression models, and projected values of the WTI, the paper concludes by projecting the median retirement age to 2041 for Canadian workers. Journal: North American Actuarial Journal Pages: 1-7 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595979 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595979 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:1-7 Template-Type: ReDIF-Article 1.0 Author-Name: Bernard Dussault Author-X-Name-First: Bernard Author-X-Name-Last: Dussault Title: “Including Homemakers in Social Security,” Robert L. Brown, Robin Damm, and Ishmael Sharara, October 2000 Journal: North American Actuarial Journal Pages: 139-140 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595991 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595991 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:139-140 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Pai Author-X-Name-First: Jeffrey Author-X-Name-Last: Pai Title: “Multivariate Analysis of Pension Plan Mortality Data”, Charles Vinsonhaler; Nalini Ravishanker; Jeyaraj Vadiveloo; Guy Rasoanaivo, April 2001 Journal: North American Actuarial Journal Pages: 135-138 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595990 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595990 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:135-138 Template-Type: ReDIF-Article 1.0 Author-Name: Bernard Dussault Author-X-Name-First: Bernard Author-X-Name-Last: Dussault Title: “A Macro-Economic Indicator of Age at Retirement”, Robert L. Brown; Robin Damm; Ishmael Sharara, April 2001 Journal: North American Actuarial Journal Pages: 7-10 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595980 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595980 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:7-10 Template-Type: ReDIF-Article 1.0 Author-Name: J. F. Carrière Author-X-Name-First: J. F. Author-X-Name-Last: Carrière Author-Name: C. F. Hill Author-X-Name-First: C. F. Author-X-Name-Last: Hill Title: Analysis of Incremental Returns of Canadian Mutual Funds Abstract: This paper presents some stochastic models of mutual fund returns to explain the risks associated with the net incremental return over a benchmark due to active investment management practices. This model can describe the stochastic behavior of the returns on established funds, but, more importantly, it also models the uncertainty or risk associated with new funds or funds with no track record. Using Canadian data, the paper also shows how to estimate the parameters of the model and check the model assumptions. Journal: North American Actuarial Journal Pages: 27-39 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595982 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595982 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:27-39 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Browne Author-X-Name-First: Mark Author-X-Name-Last: Browne Author-Name: James Carson Author-X-Name-First: James Author-X-Name-Last: Carson Author-Name: Robert Hoyt Author-X-Name-First: Robert Author-X-Name-Last: Hoyt Title: Dynamic Financial Models of Life Insurers Abstract: The Society of Actuaries seeks to provide actuaries of life insurance companies with a systematic approach for estimating the adverse effects of economic developments that could impede insurer performance. Toward that end, this study combines market and economic factors with insurerspecific data to form dynamic financial models of life insurers. Empirical analysis is based on annual data from 1985 through 1995 for 1,593 life insurers. By identifying important exogenous and insurer-specific factors related to life insurer performance, this study provides a basis for actuaries to build dynamic financial models for individual insurers. The study also identifies and describes several Web sites that provide access to relevant economic and financial data. Journal: North American Actuarial Journal Pages: 11-26 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595981 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595981 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:11-26 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: A Regime-Switching Model of Long-Term Stock Returns Abstract: In this paper I first define the regime-switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the regime-switching model is derived. Prices of European options using the regime-switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the regime-switching lognormal model results with those using the more traditional lognormal stock return model. Journal: North American Actuarial Journal Pages: 41-53 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595984 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595984 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:41-53 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheldon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheldon Lin Title: “Analysis of Incremental Returns of Canadian Mutual Funds”, J. F. Carrière; C. F. Hill, April 2001 Journal: North American Actuarial Journal Pages: 39-40 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595983 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595983 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:39-40 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Møller Author-X-Name-First: Thomas Author-X-Name-Last: Møller Title: Hedging Equity-Linked Life Insurance Contracts Abstract: This paper examines a portfolio of equity-linked life insurance contracts and determines risk-minimizing hedging strategies within a discrete-time setup. As a principal example, I consider the Cox-Ross-Rubinstein model and an equity-linked pure endowment contract under which the policyholder receives max(ST, K) at time T if he or she is then alive, where ST is the value of a stock index at the term T of the contract and K is a guarantee stipulated by the contract. In contrast to most of the existing literature, I view the contracts as contingent claims in an incomplete model and discuss the problem of choosing an optimality criterion for hedging strategies. The subsequent analysis leads to a comparison of the risk (measured by the variance of the insurer’s loss) inherent in equity-linked contracts in the two situations where the insurer applies the risk-minimizing strategy and the insurer does not hedge. The paper includes numerical results that can be used to quantify the effect of hedging and describe how this effect varies with the size of the insurance portfolio and assumptions concerning the mortality. Journal: North American Actuarial Journal Pages: 79-95 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595986 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595986 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:79-95 Template-Type: ReDIF-Article 1.0 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Author-Name: Delme Pritchard Author-X-Name-First: Delme Author-X-Name-Last: Pritchard Title: Genetics, Alzheimer’s Disease, and Long-Term Care Insurance Abstract: This paper applies a model of Alzheimer’s disease (AD) developed by Macdonald and Pritchard (2000) to the question of the potential for adverse selection in long-term care (LTC) insurance introduced by the existence of DNA tests for variants of the ApoE gene, the ε4 allele of which is known to predispose one to earlier onset of AD. It computes the expected present values (EPVs) of model LTC benefits with respect to AD for each of five ApoE genotypes, weighted average EPVs with and without adverse selection, and sample underwriting ratings. The paper concludes that adverse selection could increase costs significantly in a small LTC insurance market only if current population genetic risk is not much smaller than that observed in case-based studies, and if carriers of the ε4 allele are very much more likely to buy LTC insurance. Finally, the paper considers the cost of a combined retirement package, providing both pension and LTC insurance, and shows that it can reduce adverse selection. Journal: North American Actuarial Journal Pages: 54-78 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595985 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595985 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:54-78 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Kahan Author-X-Name-First: Daniel Author-X-Name-Last: Kahan Title: “Who Says Financial Services Integration Is in Consumers’ Best Interests?” Joseph M. Belth, July 2000 Journal: North American Actuarial Journal Pages: 141-142 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595993 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595993 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:141-142 Template-Type: ReDIF-Article 1.0 Author-Name: David Spiegelhalter Author-X-Name-First: David Author-X-Name-Last: Spiegelhalter Title: “Actuarial Modeling with MCMC and BUGs”, David P. M. Scollnik, April 2001 Journal: North American Actuarial Journal Pages: 124-125 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595988 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595988 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:124-125 Template-Type: ReDIF-Article 1.0 Author-Name: Caterina Lindman Author-X-Name-First: Caterina Author-X-Name-Last: Lindman Title: “Including Homemakers in Social Security,” Robert L. Brown, Robin Damm, and Ishmael Sharara, October 2000 Journal: North American Actuarial Journal Pages: 140-141 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595992 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:140-141 Template-Type: ReDIF-Article 1.0 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: Actuarial Modeling with MCMC and BUGs Abstract: In this paper, the author reviews some aspects of Bayesian data analysis and discusses how a variety of actuarial models can be implemented and analyzed in accordance with the Bayesian paradigm using Markov chain Monte Carlo techniques via the BUGS (Bayesian inference Using Gibbs Sampling) suite of software packages. The emphasis is placed on actuarial loss models, but other applications are referenced, and directions are given for obtaining documentation for additional worked examples on the World Wide Web. Journal: North American Actuarial Journal Pages: 96-124 Issue: 2 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595987 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595987 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:96-124 Template-Type: ReDIF-Article 1.0 Author-Name: Barry Freedman Author-X-Name-First: Barry Author-X-Name-Last: Freedman Title: Efficient Post-Retirement Asset Allocation Abstract: To examine post-retirement asset allocation, an extension to the classic Markowitz risk-return framework is suggested. Assuming that retirees make constant (real dollar) annual withdrawals from their portfolios, reward and risk measures are defined to be the mean and standard deviation of wealth remaining at end of life. Asset returns and time of death are both treated as random variables. Assuming constant lifetime asset allocation, the risk and reward measures can be evaluated analytically, and an efficient frontier can be determined. Life annuities can be used to extend the left-hand (low-risk) side of the efficient frontier. The desired level of wealth at end of life can be used to choose a desirable portfolio on the efficient frontier. The desirable portfolio strongly depends on the withdrawal rate. It is suggested (although not proven) that asset allocations strategies that vary with age do not add efficiency in this model, and asset allocation strategies that vary with wealth can add efficiency. Journal: North American Actuarial Journal Pages: 228-241 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597519 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597519 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:228-241 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander Muermann Author-X-Name-First: Alexander Author-X-Name-Last: Muermann Title: Market Price of Insurance Risk Implied by Catastrophe Derivatives Abstract: Insurance derivatives facilitate the trading of insurance risks on capital markets, such as catastrophe derivatives that were traded on the Chicago Board of Trade. Simultaneously, insurance risks are traded through reinsurance portfolios. In this paper we make inferences about the market price of risk implied by the information embedded in the prices of these two assets. Journal: North American Actuarial Journal Pages: 221-227 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597518 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597518 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:221-227 Template-Type: ReDIF-Article 1.0 Author-Name: Greg Taylor Author-X-Name-First: Greg Author-X-Name-Last: Taylor Title: A Simple Model of Insurance Market Dynamics Abstract: This paper constructs and studies a simple but realistic model of an insurance market. The model has a minimalist construction in the sense that the number of parameters defining it is strictly limited and the elimination of any one of them would destroy its realism. There are 11 essential parameters. Each of the parameters has a physical interpretation. Some determine competitive effects within the market, some barriers to entry, and so on. The effect of each on various aspects of the market is examined in the presence of simulated loss experience. The aspects of the market considered include stability of premium rates, profitability, and market concentration. Some of the parameters are capable of use as regulatory controls. Two parameters, in addition to the original 11, are explicit price controls. Despite its simplicity, the model displays considerably complex behavior. Some results are intuitive, but some are not. For this reason, regulatory controls need to be applied with great caution lest they induce perverse effects, possibly even the reverse of those intended. The effect of the parameters on market behavior is first studied in the absence of catastrophic events from the loss experience. Subsequently, the effect of a single such event is studied. Journal: North American Actuarial Journal Pages: 242-262 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597520 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597520 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:242-262 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Title: Moments of Discounted Dividends for a Threshold Strategy in the Compound Poisson Risk Model Abstract: We consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lower-order moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability. Journal: North American Actuarial Journal Pages: 299-318 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597523 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597523 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:299-318 Template-Type: ReDIF-Article 1.0 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Title: Ordering Ruin Probabilities Resulting from Layer-Based Claim Amounts for Surplus Process Perturbed by Diffusion Abstract: In this paper we study orders of pairs of ruin probabilities resulting from two claim severity random variables X and Y for a continuous time surplus process perturbed by diffusion, each of which is the underlying risk Z with or without a deductible and/or a policy limit imposed, called a layer of Z. The deductibles and policy limits for X and Y could be the same or different. Under some condition regarding the relative security loadings, we find that the layer with a policy limit and the layer with a deductible yield the lowest and highest ruin probabilities, respectively, provided that Z has a decreasing failure rate, and the layer with and the layer without both a deductible and a policy limit produce the smallest and largest ruin probabilities, respectively, provided that Z has an increasing failure rate. Numerical examples are also given to illustrate the results of the proposed theorems for ordering ruin probabilities resulting from layers of two random variables distributed as a single exponential and a mixture of two exponentials. Journal: North American Actuarial Journal Pages: 319-335 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597524 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:319-335 Template-Type: ReDIF-Article 1.0 Author-Name: Joonghee Huh Author-X-Name-First: Joonghee Author-X-Name-Last: Huh Author-Name: Adam Kolkiewicz Author-X-Name-First: Adam Author-X-Name-Last: Kolkiewicz Title: Computation of Multivariate Barrier Crossing Probability and its Applications in Credit Risk Models Abstract: In this paper we consider computational methods of finding exit probabilities for a class of multivariate diffusion processes. Although there is an abundance of results for one-dimensional diffusion processes, for multivariate processes one has to rely on approximations or simulation methods. We adopt a Large Deviations approach to approximate barrier crossing probabilities of a multivariate Brownian Bridge. We use this approach in conjunction with simulation methods to develop an efficient method of obtaining barrier crossing probabilities of a multivariate Brownian motion. Using numerical examples, we demonstrate that our method works better than other existing methods. We mainly focus on a three-dimensional process, but our framework can be extended to higher dimensions. We present two applications of the proposed method in credit risk modeling. First, we show that we can efficiently estimate the default probabilities of several correlated credit risky entities. Second, we use this method to efficiently price a credit default swap (CDS) with several correlated reference entities. In a conventional approach one normally adopts an arbitrary copula to capture dependency among counterparties. The method we propose allows us to incorporate the instantaneous variance-covariance structure of the underlying process into the CDS prices. Journal: North American Actuarial Journal Pages: 263-291 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597521 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597521 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:263-291 Template-Type: ReDIF-Article 1.0 Author-Name: David Bernstein Author-X-Name-First: David Author-X-Name-Last: Bernstein Title: Intergenerational Transfers and Insurance Policy Design Abstract: Group health insurance policies offering an identical benefit package to every member of the group result in lower expected health benefits for younger cohorts than older cohorts. The dispersion in insurance benefits across age groups differs among insurance policies. Simulation results presented in this paper demonstrate that a shift from comprehensive health insurance to high-deductible health insurance decreases the share of expected benefits going to younger cohorts. An estimated 81.5% of the 23-to-32-year-old cohort is expected to receive less than $500 in health benefits during a year for one prototypical high-deductible health plan. Low expected benefits for younger relatively healthy cohorts could increase the number of younger individuals who eschew health coverage. Age-rated premiums are probably the most straightforward way to stimulate demand for high-deductible health plans among younger healthier individuals. Journal: North American Actuarial Journal Pages: 292-298 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597522 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597522 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:292-298 Template-Type: ReDIF-Article 1.0 Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: Author’s Reply: On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals - Discussion by Professor Elias Shiu, April 2008 Journal: North American Actuarial Journal Pages: 341-342 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597527 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597527 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:341-342 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Edited by Geoffrey Poitras with Franck Jovanovic Journal: North American Actuarial Journal Pages: 343-343 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597528 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597528 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:343-343 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Title: “Recursive Calculation of the Dividend Moments in a Multi-Threshold Risk Model,” Andrei Badescu and David Landriault, January 2008 Journal: North American Actuarial Journal Pages: 336-340 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597525 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597525 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:336-340 Template-Type: ReDIF-Article 1.0 Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: Author’s Reply: The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model - Discussion by Shuanming Li, July 2007 Journal: North American Actuarial Journal Pages: 341-341 Issue: 3 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597526 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597526 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:3:p:341-341 Template-Type: ReDIF-Article 1.0 Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: The Tail Stein's Identity with Applications to Risk Measures Abstract: In this article, we examine a generalized version of an identity made famous by Stein, who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works followed to extend the lemma to the larger class of elliptical distributions. The lemma has had many applications in statistics, finance, insurance, and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is very important in actuarial science and insurance. Our article therefore introduces the concept of the “tail Stein's identity” to the case of any random variable defined on an appropriate probability space with a Lebesgue density function satisfying certain regularity conditions. We also examine this “tail Stein's identity” to the class of discrete distributions. This extended identity allows us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This holds a large promise for applications in risk management. Journal: North American Actuarial Journal Pages: 313-326 Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1237879 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1237879 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:313-326 Template-Type: ReDIF-Article 1.0 Author-Name: David L. Eckles Author-X-Name-First: David L. Author-X-Name-Last: Eckles Author-Name: David G. McCarthy Author-X-Name-First: David G. Author-X-Name-Last: McCarthy Author-Name: Xudong Zeng Author-X-Name-First: Xudong Author-X-Name-Last: Zeng Title: The Theory of Optimal Stochastic Control as Applied to Insurance Underwriting Cycles Abstract: We use the theories of optimal stochastic control and engineering process control to analyze the well-known phenomenon of insurance underwriting cycles in continuous time. We show in a continuous time framework that underwriting cycles can be explained with a model where premiums are set rationally, but where there are various reporting and regulatory lags. We find that the observed cycle length depends on the length of these underlying lags. Our result can be seen as consistent with previous empirical work showing underwriting cycles varying across countries and lines of insurance. In the event that no lags exist, our result is also consistent with more recent literature suggesting that insurance cycles may not exist. Journal: North American Actuarial Journal Pages: 327-340 Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1179122 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1179122 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:327-340 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Stallard Author-X-Name-First: Eric Author-X-Name-Last: Stallard Title: Compression of Morbidity and Mortality: New Perspectives Abstract: Compression of morbidity is a reduction over time in the total lifetime days of chronic disability, reflecting a balance between (1) morbidity incidence rates and (2) case-continuance rates, generated by case-fatality and case-recovery rates. Chronic disability includes limitations in activities of daily living and cognitive impairment, which can be covered by long-term-care insurance. Morbidity improvement can lead to a compression of morbidity if the reductions in age-specific prevalence rates are sufficiently large to overcome the increases in lifetime disability due to concurrent mortality improvements and progressively higher disability prevalence rates with increasing age. Compression of mortality is a reduction over time in the variance of age at death. Such reductions are generally accompanied by increases in the mean age at death; otherwise, for the variances to decrease, the death rates above the mean age at death would need to increase, and this has rarely been the case. Mortality improvement is a reduction over time in the age-specific death rates and a corresponding increase in the cumulative survival probabilities and age-specific residual life expectancies. Mortality improvement does not necessarily imply concurrent compression of mortality. This article reviews these concepts, describes how they are related, shows how they apply to changes in mortality over the past century and to changes in morbidity over the past 30 years, and discusses their implications for future changes in the United States. The major findings of the empirical analyses are the substantial slowdowns in the degree of mortality compression over the past half century and the unexpectedly large degree of morbidity compression that occurred over the morbidity/disability study period 1984–2004; evidence from other published sources suggests that morbidity compression may be continuing. Journal: North American Actuarial Journal Pages: 341-354 Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1227269 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1227269 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:341-354 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: Obesity, Mortality, and the Obesity Paradox Abstract: The percentage of the population who are obese has grown dramatically on a worldwide basis over the last several decades, although the growth in the prevalence of obesity has slowed recently at a high level in the United States. Although there have been numerous studies of the effect of this trend on mortality, the findings have been inconsistent and controversial, in part because of methodological differences and the complexity of the relationships between obesity and mortality. The objective of this article is to discuss the issues surrounding these relationships and to shed light on the likely effects of the obesity epidemic on mortality. Of particular interest is the so-called obesity-mortality paradox, where mortality experience is lower for overweight and in some cases obese individuals than for those of normal weight. Although more recent studies of the relationship between mortality and obesity seem to indicate those who are obese have experienced a reduced percentage of additional mortality, this may in part be due to the shorter average time those currently obese have been exposed to their condition, the heterogeneity of the normal and obese populations, measurement issues including treatment of smokers and those who are ill, and study design limitations. An increased number of premature deaths may arise as more individuals who are obese are exposed for a longer period to excess adiposity. Although public policy issues surrounding obesity are being addressed with a great deal of activity and publicity, they have and will continue to prove quite challenging for both individuals and society to manage and overcome. The prevalence of obesity has had and will continue to have a significant effect on the mortality experience in most areas of actuarial practice. As a result, it is important for actuaries to enhance their understanding of these effects. Journal: North American Actuarial Journal Pages: 355-403 Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1241183 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1241183 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:355-403 Template-Type: ReDIF-Article 1.0 Author-Name: Ian Duncan Author-X-Name-First: Ian Author-X-Name-Last: Duncan Author-Name: Stéphane Guerrier Author-X-Name-First: Stéphane Author-X-Name-Last: Guerrier Title: Member Plan Choice and Migration in Response to Changes in Member Premiums after Massachusetts Health Insurance Reform Abstract: In 2006 Massachusetts implemented a substantial reform of its health insurance market that included a new program for uninsured individuals with income between 100% of Federal Poverty (the upper limit for state Medicaid benefits) and 300% of Federal Poverty. Enrollment was compulsory for all citizens because of a mandate. Consumers who enrolled in this program, which offered generous benefits with low copays, received graduated subsidies depending on their income. Five insurers were contracted to underwrite the program, and consumers were able to choose their insurer. Insurers bid annually, and the member contribution was set according to an affordability schedule for the lowest-bidding insurer. Consumers could choose from the range of insurers, but if they chose a plan other than the lowest cost, their contributions reflected the difference. Premiums were changed annually at July 1, and members were eligible to move to a different plan at this date; a number of members migrated each year. This study aims to quantify the effect of this premium-induced switching behavior. Prior studies of member switching behavior have looked at employer plans and estimated the elasticity of response to changes in member contributions. The Massachusetts environment is unique in that there is a mandate (so being uninsured is not an option) and members may choose insurer but not benefit plan. Thus a study of migration in Massachusetts is uniquely able to quantify the effect of price (contribution rates) on member switching behavior. We find elasticity averaging −0.21 for 2013 (the last year of the study) to be somewhat lower (in absolute value) than previous studies of employer populations. Elasticity has also been significantly increasing with time and appeared to have at least doubled over the studied period (i.e., 2008–2013). Prior studies have estimated higher elasticities in the range −0.3 to −0.6. We found that the data contained many outliers in terms of both changes in contributions and percentage of members switching plans. The effect of outliers was moderated by the choice of robust regression models, leading us to question whether other studies may have been affected by outliers, leading to overestimates of the elasticities. Journal: North American Actuarial Journal Pages: 404-419 Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1200991 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1200991 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:404-419 Template-Type: ReDIF-Article 1.0 Author-Name: César Neves Author-X-Name-First: César Author-X-Name-Last: Neves Author-Name: Eduardo Fraga L. de Melo Author-X-Name-First: Eduardo Fraga L. Author-X-Name-Last: de Melo Title: Evaluating the Technical Provisions for Traditional Brazilian Annuity Plans: Continuous-Time Stochastic Approach Based on Solvency Principles Abstract: This article presents an approach for evaluating the liabilities of traditional Brazilian annuity plans, using a continuous-time stochastic approach based on modern solvency principles. The technical provisions are obtained by means of conditional expectation, under a real-world measure and considering the peculiar characteristics of each plan and the financial guarantees and profit participations (bonus and dividend plans) embedded in the annuity plans. We assume that policyholder behavior is not optimal, but we also illustrate a calculation of provision assuming optimal policyholder behavior to show the differences between both assumptions. In this article all explicit provisions formulas are derived, and several relevant conclusions about the values of these provisions are discussed. Journal: North American Actuarial Journal Pages: 420-436 Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1192476 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1192476 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:420-436 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board EOV Journal: North American Actuarial Journal Pages: ebi-ebi Issue: 4 Volume: 20 Year: 2016 Month: 10 X-DOI: 10.1080/10920277.2016.1267527 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1267527 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: Daniel H. Alai Author-X-Name-First: Daniel H. Author-X-Name-Last: Alai Author-Name: Séverine Arnold (-Gaille) Author-X-Name-First: Séverine Author-X-Name-Last: Arnold (-Gaille) Author-Name: Madhavi Bajekal Author-X-Name-First: Madhavi Author-X-Name-Last: Bajekal Author-Name: Andrés M. Villegas Author-X-Name-First: Andrés M. Author-X-Name-Last: Villegas Title: Mind the Gap: A Study of Cause-Specific Mortality by Socioeconomic Circumstances Abstract: Socioeconomic groups may be exposed to varying levels of mortality; this is certainly the case in the United Kingdom, where the gaps in life expectancy, differentiated by socioeconomic circumstances, are widening. The reasons for such diverging trends are yet unclear, but a study of cause-specific mortality may provide rich insight into this phenomenon. Therefore, we investigate the relationship between socioeconomic circumstances and cause-specific mortality using a unique dataset obtained from the U.K. Office for National Statistics. We apply a multinomial logistic framework; the reason is twofold. First, covariates such as socioeconomic circumstances are readily incorporated, and, second, the framework is able to handle the intrinsic dependence amongst the competing causes. As a consequence of the dataset and modeling framework, we are able to investigate the impact of improvements in cause-specific mortality by socioeconomic circumstances. We assess the impact using (residual) life expectancy, a measure of aggregate mortality. Of main interest are the gaps in life expectancy among socioeconomic groups, the trends in these gaps over time, and the ability to identify the causes most influential in reducing these gaps. This analysis is performed through the investigation of different scenarios: first, by eliminating one cause of death at a time; second, by meeting a target set by the World Health Organization (WHO), called WHO 25 × 25; and third, by developing an optimal strategy to increase life expectancy and reduce inequalities. Journal: North American Actuarial Journal Pages: 161-181 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1377621 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1377621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:161-181 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Target-Bequest Investment and Insurance Fund Abstract: We propose a new type of investment fund, a Target-Bequest Fund (TBF), for which the manager of the fund invests to maximize the probability of reaching a bequest goal, specified by the investor. We assume the fund pays dividends at a rate proportional to the value of the fund, with the proportion also specified by the investor. In addition to considering this basic fund, we propose two extensions. The first extension is to impose a no-borrowing constraint. Indeed, unless the investment fund is a hedge fund, it will likely not allow the manager to invest more in the risky asset than is available in the fund, so this constraint is a realistic one. The second extension is to allow the fund manager to buy life insurance to help reach the bequest goal. We consider both extensions in the special case for which the proportional dividend rate is less than or equal to the riskless rate of return. Our focus is to obtain explicit solutions in a simplified market and insurance setting to give actuaries implementing this fund design some rules-of-thumb for investing in a financial market and buying life insurance in more realistic settings. We fully expect these rules-of-thumb to be generally valid in those more realistic settings. Journal: North American Actuarial Journal Pages: 182-197 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1381030 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1381030 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:182-197 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Bauer Author-X-Name-First: Daniel Author-X-Name-Last: Bauer Author-Name: Michael V. Fasano Author-X-Name-First: Michael V. Author-X-Name-Last: Fasano Author-Name: Jochen Russ Author-X-Name-First: Jochen Author-X-Name-Last: Russ Author-Name: Nan Zhu Author-X-Name-First: Nan Author-X-Name-Last: Zhu Title: Evaluating Life Expectancy Evaluations Abstract: The quality of life expectancy estimates is one key consideration for an investor in life settlements. The predominant metric for assessing this quality is the so-called A-to-E ratio, which relies on a comparison of the actual to the predicted number of deaths. In this article, we explain key issues with this metric: In the short run, it is subject to estimation uncertainty for small and moderately sized portfolios; and, more critically, in the long run, it converges to 100% even if the underwriting is systematically biased. As an alternative, we propose and discuss a set of new metrics based on the difference in (temporary) life expectancies. We examine the underwriting quality of a leading U.S. life expectancy provider based on this new methodology. Journal: North American Actuarial Journal Pages: 198-209 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1381031 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1381031 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:198-209 Template-Type: ReDIF-Article 1.0 Author-Name: Doug Andrews Author-X-Name-First: Doug Author-X-Name-Last: Andrews Author-Name: Jaideep Oberoi Author-X-Name-First: Jaideep Author-X-Name-Last: Oberoi Author-Name: Tony Wirjanto Author-X-Name-First: Tony Author-X-Name-Last: Wirjanto Author-Name: Chenggang Zhou Author-X-Name-First: Chenggang Author-X-Name-Last: Zhou Title: Demography and Inflation: An International Study Abstract: Changes in the relative share of different age groups in the population may present inflationary, disinflationary, or even deflationary tendencies. We find evidence that increases in the share of the very old (age 80 and older) may be associated with deflation. The analysis is based on an international dataset over a long period. Classifying age groups into young, working, younger old, and older old, we find that the shares of the young and the younger old groups are inflationary, while those of the working group are disinflationary and those of the very old group seemingly deflationary. Journal: North American Actuarial Journal Pages: 210-222 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1387572 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1387572 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:210-222 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Shui Feng Author-X-Name-First: Shui Author-X-Name-Last: Feng Author-Name: David Melkuev Author-X-Name-First: David Author-X-Name-Last: Melkuev Author-Name: Shuai Yang Author-X-Name-First: Shuai Author-X-Name-Last: Yang Author-Name: Johnew Zhang Author-X-Name-First: Johnew Author-X-Name-Last: Zhang Title: Short Positions in the First Principal Component Portfolio Abstract: Insurance companies and pension plans typically hold well-diversified equity portfolios. These institutions are also often restricted from taking short positions. The diversification requirement operates on the portfolio level, while the short sale constraint is at the individual security level. We examine an investment strategy that exposes a tension between these two requirements. This strategy uses the first principal component to construct the portfolio and by design meets the first requirement. Empirical portfolios based on the first principal component do an excellent job of capturing market exposure and minimizing diversifiable risk. However, in practice such portfolios sometimes contain a few short positions. So this strategy does not always meet the second requirement. We examine which features of stock returns give rise to short positions when a portfolio is based on the first principal component, and we are able to identify the characteristics of the stocks that are responsible for the short positions. These stocks tend to have negative correlations with the majority of other stocks. In contrast such stocks would typically be held long in a Markowitz portfolio. We discuss and explain this puzzle. Journal: North American Actuarial Journal Pages: 223-251 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1387573 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1387573 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:223-251 Template-Type: ReDIF-Article 1.0 Author-Name: Kyeonghee Kim Author-X-Name-First: Kyeonghee Author-X-Name-Last: Kim Author-Name: Marjorie A. Rosenberg Author-X-Name-First: Marjorie A. Author-X-Name-Last: Rosenberg Title: The Role of Unhealthy Behaviors on an Individual's Self-Reported Perceived Health Status Abstract: Many health plans and employers gather information about their enrollees in the form of self-reported surveys. This information is useful in assessing the risk pool of the population, targeting disease or case management programs to affected personnel, and developing/assessing wellness/incentive programs to lower medical costs and improve quality of life. The purpose of our study is to explore the role of individual-level unhealthy behaviors in influencing self-reported perceived health status. We extend prior research to estimate the effects of unhealthy behaviors on subsequent perceived health status using longitudinal data for the noninstitutional civilian adult population in the United States. We link data from two sources, the National Health Interview Survey (NHIS) and the longitudinal form of the Medical Expenditure Panel Survey (MEPS). Both the NHIS and MEPS data were collected using a complex survey design, enabling our results to be representative of the U.S. noninstitutionalized civilian population. We find that an increase in the number of unhealthy behaviors reduces the likelihood of individuals perceiving their health status as Excellent. In contrast, the likelihood of individuals perceiving their health status as Poor increases as the number of unhealthy behaviors increases, with a more pronounced effect for individuals with medically diagnosed conditions or perceived functional limitations. Journal: North American Actuarial Journal Pages: 252-269 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1387574 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1387574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:252-269 Template-Type: ReDIF-Article 1.0 Author-Name: Fabio Baione Author-X-Name-First: Fabio Author-X-Name-Last: Baione Author-Name: Susanna Levantesi Author-X-Name-First: Susanna Author-X-Name-Last: Levantesi Title: Pricing Critical Illness Insurance from Prevalence Rates: Gompertz versus Weibull Abstract: The pricing of critical illness insurance requires specific and detailed insurance data on healthy and ill lives. However, where the critical illness insurance market is small or national commercial insurance data needed for premium estimates are unavailable, national health statistics can be a viable starting point for insurance ratemaking purposes, even if such statistics cover the general population, are aggregate, and are reported at irregular intervals. To develop a critical illness insurance pricing model structured on a multiple state continuous and time-inhomogeneous Markov chain and based on national statistics, we do three things: First, assuming that the mortality intensity of healthy and ill lives is modeled by two parametrically different Weibull hazard functions, we provide closed formulas for transition probabilities involved in the multiple state model we propose. Second, we use a dataset that allows us to assess the accuracy of our multiple state model as a good estimator of incidence rates under the Weibull assumption applied to mortality rates. Third, the Weibull results are compared to corresponding results obtained by substituting two parametrically different Gompertz models for the Weibull models of mortality rates, as proposed previously. This enables us to assess which of the two parametric models is the superior tool for accurately calculating the multiple state model transition probabilities and assessing the comparative efficiency of Weibull and Gompertz as methods for pricing critical illness insurance. Journal: North American Actuarial Journal Pages: 270-288 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1397524 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1397524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:270-288 Template-Type: ReDIF-Article 1.0 Author-Name: Sebastain N. Awondo Author-X-Name-First: Sebastain N. Author-X-Name-Last: Awondo Author-Name: Octavio A. Ramirez Author-X-Name-First: Octavio A. Author-X-Name-Last: Ramirez Author-Name: Gauri S. Datta Author-X-Name-First: Gauri S. Author-X-Name-Last: Datta Author-Name: Gregory Colson Author-X-Name-First: Gregory Author-X-Name-Last: Colson Author-Name: Esendugue G. Fonsah Author-X-Name-First: Esendugue G. Author-X-Name-Last: Fonsah Title: Estimation of Crop Yields and Insurance Premiums Using a Shrinkage Estimator Abstract: We explore the estimation of crop yields and insurance premiums using a hierarchical Bayes small area estimator. The estimator is evaluated for Area Yield Production (AYP) policy using quasi-simulated corn yields in the United States. Its performance in producing reliable mean county yield and premium estimates is compared to that of a naive estimator. We also investigate the impact of these efficiency improvements on the residual losses between a farm-level policy and AYP. The proposed estimator is found to be substantially more efficient and less biased than the naive estimator. Journal: North American Actuarial Journal Pages: 289-308 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2017.1404477 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1404477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:289-308 Template-Type: ReDIF-Article 1.0 Author-Name: Min-Ming Wen Author-X-Name-First: Min-Ming Author-X-Name-Last: Wen Author-Name: H. J. Abraham Lin Author-X-Name-First: H. J. Abraham Author-X-Name-Last: Lin Author-Name: Patricia H. Born Author-X-Name-First: Patricia H. Author-X-Name-Last: Born Author-Name: Charles Yang Author-X-Name-First: Charles Author-X-Name-Last: Yang Author-Name: Chun Wang Author-X-Name-First: Chun Author-X-Name-Last: Wang Title: Cash Flow Risk Management in the Property/Liability Insurance Industry: A Dynamic Factor Modeling Approach Abstract: This study proposes and demonstrates a dynamic factor model that can be empirically carried out by the utilization of a factor-augmented autoregressive technique to explain and forecast the time-varying patterns of cash flows of insurance companies in the United States. A principal component approach is employed in the Factor-Augmented Autoregressive Model (FAARM) to capture the augmented factors that are to be utilized for forecasting. We describe the cash flow statistical model by a dimension-reduction technique that can depict the dynamic patterns of the cash flows of insurance firms and then measure the FAARM model. Results from the first step (principal component analysis) help capture the macroeconomic variables and the variables pertaining to insurance companies' cash flows, namely, cash flows from investment, underwriting, and risk management activities. Results from the second step offer evidence supporting that the FAARM improves the out-of-sample forecasting accuracy assessed by a forecasted root-mean-squared error (FRMSE). This article presents a set of feasible FAAR models from which an insurance firm can choose one that can be a better fit to the firm corresponding to its specific firm characteristics, such as firm size. Consequently, the chosen FAARM(s) can improve the accuracy of cash flow forecasting and thus can help insurers to manage risk via cash-flow–matching techniques. Journal: North American Actuarial Journal Pages: 309-322 Issue: 2 Volume: 22 Year: 2018 Month: 4 X-DOI: 10.1080/10920277.2018.1423994 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1423994 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:2:p:309-322 Template-Type: ReDIF-Article 1.0 Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Title: A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks Abstract: This paper proposes a computationally efficient algorithm for quantifying the impact of interestrate risk and longevity risk on the distribution of annuity values in the distant future. The algorithm simulates the state variables out to the end of the horizon period and then uses a Taylor series approximation to compute approximate annuity values at the end of that period, thereby avoiding a computationally expensive “simulation-within-simulation” problem. Illustrative results suggest that annuity values are likely to rise considerably but are also quite uncertain. These findings have some unpleasant implications both for defined contribution pension plans and for defined benefit plan sponsors considering using annuities to hedge their exposure to these risks at some point in the future. Journal: North American Actuarial Journal Pages: 237-247 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597619 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597619 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:237-247 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Tsai Author-X-Name-First: Jeffrey Author-X-Name-Last: Tsai Author-Name: Larry Tzeng Author-X-Name-First: Larry Author-X-Name-Last: Tzeng Author-Name: Jennifer Wang Author-X-Name-First: Jennifer Author-X-Name-Last: Wang Title: Hedging Longevity Risk When Interest Rates are Uncertain Abstract: This paper proposes an asset liability management strategy to hedge the aggregate risk of annuity providers under the assumption that both the interest rate and mortality rate are stochastic. We assume that annuity providers can invest in longevity bonds, long-term coupon bonds, and shortterm zero-coupon bonds to immunize themselves from the risks of the annuity for the equity holders subject to a required profit. We demonstrate that the optimal allocation strategy can lead to the lowest risk under different yield curves and mortality rate assumptions. The longevity bond can also be regarded as an effective hedging vehicle that significantly reduces the aggregate risk of the annuity providers. Journal: North American Actuarial Journal Pages: 201-211 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597617 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597617 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:201-211 Template-Type: ReDIF-Article 1.0 Author-Name: Andreas Richter Author-X-Name-First: Andreas Author-X-Name-Last: Richter Author-Name: Frederik Weber Author-X-Name-First: Frederik Author-X-Name-Last: Weber Title: Mortality-Indexed Annuities Managing Longevity Risk Via Product Design Abstract: Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries. In its aggregate form, the systematic risk of changes to general mortality patterns, it has the potential for causing large cumulative losses for insurers. Since obvious risk management tools, such as (re)insurance or hedging, are less suited for managing an annuity provider’s exposure to this risk, we propose a type of life annuity with benefits contingent on actual mortality experience.Similar adaptations to conventional product design exist with investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience can be found in German private health insurance. By effectively sharing systematic longevity risk with policyholders, insurers may avoid cumulative losses.Policyholders also gain in comparison with a comparable conventional annuity product: Using a Monte Carlo simulation, we identify a significant upside potential for policyholders while downside risk is limited. Journal: North American Actuarial Journal Pages: 212-236 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597618 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597618 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:212-236 Template-Type: ReDIF-Article 1.0 Author-Name: Andreas Milidonis Author-X-Name-First: Andreas Author-X-Name-Last: Milidonis Author-Name: Yijia Lin Author-X-Name-First: Yijia Author-X-Name-Last: Lin Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Title: Mortality Regimes and Pricing Abstract: Mortality dynamics are characterized by changes in mortality regimes. This paper describes a Markov regime-switching model that incorporates mortality state switches into mortality dynamics. Using the 1901-2005 U.S. population mortality data, we illustrate that regime-switching models can perform better than well-known models in the literature. Furthermore, we extend the 1992 Lee-Carter model in such a way that the time-series common risk factor to all cohorts has distinct mortality regimes with different means and volatilities. Finally, we show how to price mortality securities with this model. Journal: North American Actuarial Journal Pages: 266-289 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597621 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:266-289 Template-Type: ReDIF-Article 1.0 Author-Name: Leslie Mayhew Author-X-Name-First: Leslie Author-X-Name-Last: Mayhew Author-Name: David Smith Author-X-Name-First: David Author-X-Name-Last: Smith Title: Human Survival at Older Ages and the Implications for Longevity Bond Pricing Abstract: Governments are concerned about the future of pension plans, for which increasing longevity is judged to be an important risk to their future viability. We focus on human survival at age 65, the starting age point for many pension products. Using a simple model, we link basic measures of life expectancy to the shape of the human survival function and consider its various forms. The model is then used as the basis for investigating actual survival in England and Wales. We find that life expectancy is increasing at a faster rate than at any time in history, with no evidence of this trend slowing or any upper age limit. With interest growing in the use of longevity bonds as a way to transfer longevity risks from pension providers to the capital markets, we seek to understand how longevity drift affects pension liabilities based on mortality rates at the point of annuitization, versus what actually happens as a cohort ages. The main findings are that longevity bonds are an effective hedge against longevity risk; however, it is not only the oldest old that are driving risk, but also more 65-year-olds reaching less extreme ages such as 80. In addition, we find that the possibility of future inflation and interest rates could be as an important a risk to annuities as longevity itself. Journal: North American Actuarial Journal Pages: 248-265 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597620 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597620 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:248-265 Template-Type: ReDIF-Article 1.0 Author-Name: Valeria D’Amato Author-X-Name-First: Valeria Author-X-Name-Last: D’Amato Author-Name: Emilia Di Lorenzo Author-X-Name-First: Emilia Author-X-Name-Last: Di Lorenzo Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Maria Russolillo Author-X-Name-First: Maria Author-X-Name-Last: Russolillo Author-Name: Marilena Sibillo Author-X-Name-First: Marilena Author-X-Name-Last: Sibillo Title: The Poisson Log-Bilinear Lee-Carter Model Abstract: Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. Recent work on the latter has focused on modeling the trend in mortality as a stochastic process. A popular method for modeling death rates is the Lee-Carter model. This methodology has become widely used, and various extensions and modifications have been proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their solvency capital requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company’s financial position, expressing the degree to which the liabilities are covered by the assets. Journal: North American Actuarial Journal Pages: 315-333 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597623 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597623 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:315-333 Template-Type: ReDIF-Article 1.0 Author-Name: Katja Hanewald Author-X-Name-First: Katja Author-X-Name-Last: Hanewald Title: Explaining Mortality Dynamics Abstract: Using data for six OECD countries over the period 1950–2006, this paper studies the impact of macroeconomic fluctuations and cause of death trends on mortality dynamics in the Lee-Carter mortality forecasting model. The key results of this study are the following: (1) Periods can be identified in which the Lee-Carter mortality index kt correlates significantly with macroeconomic fluctuations. (2) A few causes of death such as diseases of the circulatory system, influenza and pneumonia, and diabetes mellitus account for a large fraction of the variations in the Lee-Carter mortality index kt. (3) Most cause-specific mortality rates show pronounced trends over the last few decades. These trends change the composition of deaths and alter how total mortality reacts to external factors such as macroeconomic fluctuations. Journal: North American Actuarial Journal Pages: 290-314 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597622 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597622 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:290-314 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Measuring Basis Risk in Longevity Hedges Abstract: In examining basis risk in index longevity hedges, it is important not to ignore the dependence between the population underlying the hedging instrument and the population being hedged. We consider four extensions to the Lee-Carter model that incorporate such dependence: Both populations are jointly driven by the same single time-varying index, the two populations are cointegrated, the populations depend on a common age factor, and there is an augmented common factor model in which a population-specific time-varying index is added to the common factor model with the property that it will tend toward a certain constant level over time. Using data from the female populations of Canada and the United States, we show the augmented common factor model is preferred in terms of both goodness-of-fit and ex post forecasting performance. This model is then used to quantify the basis risk in a longevity hedge of 65-year old Canadian females structured using a portfolio of q-forward contracts predicated on U.S. female population mortality. The hedge effectiveness is estimated at 56% on the basis of longevity value-at-risk and 81.61% on the basis of longevity risk reduction. Journal: North American Actuarial Journal Pages: 177-200 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597616 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597616 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:177-200 Template-Type: ReDIF-Article 1.0 Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Guy Coughlan Author-X-Name-First: Guy Author-X-Name-Last: Coughlan Author-Name: Marwa Khalaf-Allah Author-X-Name-First: Marwa Author-X-Name-Last: Khalaf-Allah Title: A Gravity Model of Mortality Rates for Two Related Populations Abstract: The mortality rate dynamics between two related but different-sized populations are modeled consistently using a new stochastic mortality model that we call the gravity model. The larger population is modeled independently, and the smaller population is modeled in terms of spreads (or deviations) relative to the evolution of the former, but the spreads in the period and cohort effects between the larger and smaller populations depend on gravity or spread reversion parameters for the two effects. The larger the two gravity parameters, the more strongly the smaller population’s mortality rates move in line with those of the larger population in the long run. This is important where it is believed that the mortality rates between related populations should not diverge over time on grounds of biological reasonableness. The model is illustrated using an extension of the Age-Period-Cohort model and mortality rate data for English and Welsh males representing a large population and the Continuous Mortality Investigation assured male lives representing a smaller related population. Journal: North American Actuarial Journal Pages: 334-356 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597624 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597624 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:334-356 Template-Type: ReDIF-Article 1.0 Author-Name: Guy Coughlan Author-X-Name-First: Guy Author-X-Name-Last: Coughlan Author-Name: Marwa Khalaf-Allah Author-X-Name-First: Marwa Author-X-Name-Last: Khalaf-Allah Author-Name: Yijing Ye Author-X-Name-First: Yijing Author-X-Name-Last: Ye Author-Name: Sumit Kumar Author-X-Name-First: Sumit Author-X-Name-Last: Kumar Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Title: Longevity Hedging 101 Abstract: Basis risk is an important consideration when hedging longevity risk with instruments based on longevity indices, since the longevity experience of the hedged exposure may differ from that of the index. As a result, any decision to execute an index-based hedge requires a framework for (1) developing an informed understanding of the basis risk, (2) appropriately calibrating the hedging instrument, and (3) evaluating hedge effectiveness. We describe such a framework and apply it to a U.K. case study, which compares the population of assured lives from the Continuous Mortality Investigation with the England and Wales national population. The framework is founded on an analysis of historical experience data, together with an appreciation of the contextual relationship between the two related populations in social, economic, and demographic terms. Despite the different demographic profiles, the case study provides evidence of stable long-term relationships between the mortality experiences of the two populations. This suggests the important result that high levels of hedge effectiveness should be achievable with appropriately calibrated, static, index-based longevity hedges. Indeed, this is borne out in detailed calculations of hedge effectiveness for a hypothetical pension portfolio where the basis risk is based on the case study. A robustness check involving populations from the United States yields similar results. Journal: North American Actuarial Journal Pages: 150-176 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597615 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597615 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:150-176 Template-Type: ReDIF-Article 1.0 Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Pat Brockett Author-X-Name-First: Pat Author-X-Name-Last: Brockett Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Author-Name: Richard MacMinn Author-X-Name-First: Richard Author-X-Name-Last: MacMinn Title: Longevity Risk and Capital Markets Journal: North American Actuarial Journal Pages: 141-149 Issue: 2 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597614 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597614 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:141-149 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: A Logical, Simple Method for Solving the Problem of Properly Indexing Social Security Benefits Journal: North American Actuarial Journal Pages: 113-116 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595740 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595740 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:113-116 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: Author’s Reply: A Logical, Simple Method for Solving the Problem of Properly Indexing Social Security Benefits - Discussion by Robert L. Brown Journal: North American Actuarial Journal Pages: 117-117 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595742 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595742 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:117-117 Template-Type: ReDIF-Article 1.0 Author-Name: Hangsuck Lee Author-X-Name-First: Hangsuck Author-X-Name-Last: Lee Title: “Utility Functions: From Risk Theory to Finance”, Hans U. Gerber and Gérard Pafum, July 1998 Journal: North American Actuarial Journal Pages: 91-91 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595729 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595729 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:91-91 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: “A Logical, Simple Method for Solving the Problem of Properly Indexing Social Security Benefits”, Robert J. Myers, July 1998 Journal: North American Actuarial Journal Pages: 116-116 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595741 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595741 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:116-116 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Gérard Pafum Author-X-Name-First: Gérard Author-X-Name-Last: Pafum Title: Utility Functions Abstract: This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility function). The postulate of equivalent expected utility can be used to replace a random gain by a fixed amount and to determine a fair premium for claims to be insured, even if the insurer’s wealth without the new contract is a random variable itself. Then n companies (or economic agents) with random wealth are considered. They are interested in exchanging wealth to improve their expected utility. The family of Pareto optimal risk exchanges is characterized by the theorem of Borch. Two specific solutions are proposed. The first, believed to be new, is based on the synergy potential; this is the largest amount that can be withdrawn from the system without hurting any company in terms of expected utility. The second is the economic equilibrium originally proposed by Borch. As by-products, the option-pricing formula of Black-Scholes can be derived and the Esscher method of option pricing can be explained. Journal: North American Actuarial Journal Pages: 74-91 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595728 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595728 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:74-91 Template-Type: ReDIF-Article 1.0 Author-Name: Cecil Nesbitt Author-X-Name-First: Cecil Author-X-Name-Last: Nesbitt Title: “Reserves for Policies with Nonannual Premiums”, Keith P. Sharp, July 1998 Journal: North American Actuarial Journal Pages: 125-126 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595744 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595744 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:125-126 Template-Type: ReDIF-Article 1.0 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Title: Author’s Reply: On a Class of Renewal Risk Processes - Discussion by F. Etienne De Vylder; Marc J. Goovaerts; Vladimir Kalashnikov; Changki Kim Journal: North American Actuarial Journal Pages: 72-73 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595727 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:72-73 Template-Type: ReDIF-Article 1.0 Author-Name: Keith Sharp Author-X-Name-First: Keith Author-X-Name-Last: Sharp Title: Reserves for Policies with Nonannual Premiums Abstract: Actuaries use a variety of approximations in calculating reserves. Among the methods used by actuaries for policies with modal premiums are fully discrete reserves, fully continuous reserves, discounted continuous reserves (equivalent to the apportionable premium case), and semicontinuous reserves. In this paper I discuss the relationships between these methods. I also examine the practical approximations commonly used and the way in which unearned premiums and deferred premiums are incorporated into this framework. Journal: North American Actuarial Journal Pages: 118-125 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595743 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595743 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:118-125 Template-Type: ReDIF-Article 1.0 Author-Name: Changki Kim Author-X-Name-First: Changki Author-X-Name-Last: Kim Title: “On a Class of Renewal Risk Processes”, David C.M. Dickson, July 1998 Journal: North American Actuarial Journal Pages: 72-72 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595726 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:72-72 Template-Type: ReDIF-Article 1.0 Author-Name: Keith Sharp Author-X-Name-First: Keith Author-X-Name-Last: Sharp Title: Author’s Reply: Reserves for Policies with Nonannual Premiums - Discussion by Cecil Nesbitt; Elias S.W. Shiu; Serena Tiong Journal: North American Actuarial Journal Pages: 127-127 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595746 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595746 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:127-127 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Kalashnikov Author-X-Name-First: Vladimir Author-X-Name-Last: Kalashnikov Title: “On a Class of Renewal Risk Processes”, David C.M. Dickson, July 1998 Journal: North American Actuarial Journal Pages: 70-71 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595725 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595725 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:70-71 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Author-Name: Serena Tiong Author-X-Name-First: Serena Author-X-Name-Last: Tiong Title: “Reserves for Policies with Nonannual Premiums”, Keith P. Sharp, July 1998 Journal: North American Actuarial Journal Pages: 126-127 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595745 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595745 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:126-127 Template-Type: ReDIF-Article 1.0 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Title: On a Class of Renewal Risk Processes Abstract: In this paper I show how methods that have been applied to derive results for the classical risk process can be adapted to derive results for a class of risk processes in which claims occur as a renewal process. In particular, claims occur as an Erlang process. I consider the problem of finding the survival probability for such risk processes and then derive expressions for the probability and severity of ruin and for the probability of absorption by an upper barrier. Finally, I apply these results to consider the problem of finding the distribution of the maximum deficit during the period from ruin to recovery to surplus level 0. Journal: North American Actuarial Journal Pages: 60-68 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595723 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595723 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:60-68 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: The Actuary’s Role in Managed Care Abstract: Financial risk is moving to center stage in the $1-trillion U.S. health-care market. The growth of managed care has created new forms of risk and has shifted this risk from insurance companies, which have long dealt with it successfully, to health-care providers and other organizations that have not traditionally accepted the same type and amount of risk. Health-care actuaries have the expertise to help these institutions, and the nation, protect their financial well-being.Actuaries specialize in the evaluation, quantification, and management of risk. Actuarial models of health-care costs, which help evaluate risk, offer management a window to the managed care world. With these models and other tools, health-care actuaries help organizations succeed in today’s health-care environment by showing how the financial and functional elements of an organization relate to risk.This report discusses the evolution of the health-care industry and the role that the healthcare actuary has played in that evolution. Eight case studies outline actuarial approaches to assessing risk in the era of managed care by discussing situations affecting five groups: providers, employers, regulators, public policy organizations, and HMOs. Built on experience gained in hundreds of cases, these studies show the range of tasks encountered by managed care actuaries and outline approaches that can help balance risks in today’s health-care system. Journal: North American Actuarial Journal Pages: 128-136 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595747 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595747 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:128-136 Template-Type: ReDIF-Article 1.0 Author-Name: F. De Vylder Author-X-Name-First: F. Author-X-Name-Last: De Vylder Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Title: “On a Class of Renewal Risk Processes”, David C.M. Dickson, July 1998 Journal: North American Actuarial Journal Pages: 68-70 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595724 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595724 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:68-70 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Title: “Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results,” Edward L. Robbins, Samuel H. Cox, and Richard D. Phillips, April 1998 Journal: North American Actuarial Journal Pages: 141-143 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595748 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595748 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:141-143 Template-Type: ReDIF-Article 1.0 Author-Name: Jacques Carriere Author-X-Name-First: Jacques Author-X-Name-Last: Carriere Author-Name: Kevin Shand Author-X-Name-First: Kevin Author-X-Name-Last: Shand Title: Authors’ Reply: New Salary Functions for Pension Valuations - Discussion by Arnold F. Shapiro Journal: North American Actuarial Journal Pages: 27-28 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595721 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595721 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:27-28 Template-Type: ReDIF-Article 1.0 Author-Name: Christian Genest Author-X-Name-First: Christian Author-X-Name-Last: Genest Author-Name: Kilani Ghoudi Author-X-Name-First: Kilani Author-X-Name-Last: Ghoudi Author-Name: Louis-Paul Rivest Author-X-Name-First: Louis-Paul Author-X-Name-Last: Rivest Title: “Understanding Relationships Using Copulas,” by Edward Frees and Emiliano Valdez, January 1998 Journal: North American Actuarial Journal Pages: 143-149 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595749 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595749 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:143-149 Template-Type: ReDIF-Article 1.0 Author-Name: Sarah Christiansen Author-X-Name-First: Sarah Author-X-Name-Last: Christiansen Title: Representative Interest Rate Scenarios Abstract: This paper suggests a possible flexible solution to the time and resource problems of running a large number of stochastic interest rate scenarios, that is, selecting a representative subset. Each interest rate scenario consists of 30 future spot yield curves, in which 12 points are specified on each curve. The distribution of the scenarios is approximated by the subset, and each scenario in the subset has equal weight. The method is independent of the interest rate generator used. Modeling research may be more similar to experimental or laboratory science than to a mathematical science. This paper presents a new tool to evaluate. Journal: North American Actuarial Journal Pages: 29-44 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595722 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595722 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:29-44 Template-Type: ReDIF-Article 1.0 Author-Name: Arnold Shapiro Author-X-Name-First: Arnold Author-X-Name-Last: Shapiro Title: “New Salary Functions for Pension Valuations”, Jacques F. Carriere and Kevin J. Shand, July 1998 Journal: North American Actuarial Journal Pages: 26-27 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595720 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595720 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:26-27 Template-Type: ReDIF-Article 1.0 Author-Name: Jacques Carriere Author-X-Name-First: Jacques Author-X-Name-Last: Carriere Author-Name: Kevin Shand Author-X-Name-First: Kevin Author-X-Name-Last: Shand Title: New Salary Functions for Pension Valuations Abstract: This paper investigates salary functions as used in the valuation of pension plans. Pension actuaries as well as researchers in actuarial science may find many of the ideas in this article useful. The main conclusion of this paper is that salary functions, as derived from the parametric models, yield gains and losses that can be quite small and, in some cases, less variable than nonparametric methods. This paper starts by defining the salary function as an accumulation function based on inflation and merit. Next, we investigate traditional estimation methods in the context of this definition. We then present a parametric age-based model for the salary function and compare it with a parametric service-based model. Finally, we apply real pension plan data to derive age-and service-based salary functions and, through the use of two funding methods, investigate how these salary functions affect salary gains and losses. Journal: North American Actuarial Journal Pages: 18-26 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595719 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595719 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:18-26 Template-Type: ReDIF-Article 1.0 Author-Name: Heinz Müller Author-X-Name-First: Heinz Author-X-Name-Last: Müller Title: “Utility Functions: From Risk Theory to Finance”, Hans U. Gerber and Gérard Pafum, July 1998 Journal: North American Actuarial Journal Pages: 92-94 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595731 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595731 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:92-94 Template-Type: ReDIF-Article 1.0 Author-Name: David Babbel Author-X-Name-First: David Author-X-Name-Last: Babbel Author-Name: Craig Merrill Author-X-Name-First: Craig Author-X-Name-Last: Merrill Title: Authors’ Reply: Economic Valuation Models for Insurers - Discussion by Jacques F. Carriere Journal: North American Actuarial Journal Pages: 16-17 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595718 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595718 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:16-17 Template-Type: ReDIF-Article 1.0 Author-Name: Alastair Longley-Cook Author-X-Name-First: Alastair Author-X-Name-Last: Longley-Cook Title: “Utility Functions: From Risk Theory to Finance”, Hans U. Gerber and Gérard Pafum, July 1998 Journal: North American Actuarial Journal Pages: 92-92 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595730 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595730 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:92-92 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Gérard Pafumi Author-X-Name-First: Gérard Author-X-Name-Last: Pafumi Title: Authors’ Reply: Utility Functions: From Risk Theory to Finance - Discussion by Hangsuck Lee; Alastair G. Longley-Cook; Heinz H. Müller; Stanley R. Pliska; Elias S.W. Shiu; Virginia R. Young Journal: North American Actuarial Journal Pages: 96-100 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595735 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595735 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:96-100 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: “Utility Functions”, Hans U. Gerber and Gérard Pafum, July 1998 Journal: North American Actuarial Journal Pages: 95-96 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595734 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595734 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:95-96 Template-Type: ReDIF-Article 1.0 Author-Name: Jacques Carriere Author-X-Name-First: Jacques Author-X-Name-Last: Carriere Title: “Economic Valuation Models for Insurers”, David F. Babbel and Craig Merrill, July 1998 Journal: North American Actuarial Journal Pages: 15-16 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595717 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595717 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:15-16 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Utility Functions: From Risk Theory to Finance”, Hans U. Gerber and Gérard Pafum, July 1998 Journal: North American Actuarial Journal Pages: 94-95 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595733 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595733 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:94-95 Template-Type: ReDIF-Article 1.0 Author-Name: David Babbel Author-X-Name-First: David Author-X-Name-Last: Babbel Author-Name: Craig Merrill Author-X-Name-First: Craig Author-X-Name-Last: Merrill Title: Economic Valuation Models for Insurers Abstract: Recently much attention has been given to the approaches insurers undertake in valuing their liabilities and assets. For example, in 1994 the American Academy of Actuaries created a Fair Valuation of Liabilities Task Force to address the issue [see Doll et al. (1998), Reitano (1997), Babbel (1997, 1998b), Babbel and Merrill (1996), and Merrill (1997)]. In 1997, the Academy established a Valuation Law Task Force and a Valuation Tools Working Group to investigate the various valuation approaches extant and to recommend the models best suited to the task.Much of the literature on valuation has focused on the strengths and shortcomings of the various models. Some of the work has addressed larger questions, but in our view it is useful and necessary to provide a taxonomy of approaches and evaluate them in a systematic way in accordance with how well they achieve their aims.In this paper we focus primarily on the economic valuation of insurance liabilities, although we do address some valuation issues for assets. We begin by defining insurance liabilities in Section I. Next, in Section II we discuss the criteria for a good economic valuation model and provide a taxonomy of valuation models in Section III. In Section IV, we examine insurance liabilities in the context of this taxonomy and identify the minimum requirements of an economic valuation approach that purports to value them adequately. An illustration of the application of a modern valuation model is given in Section V. We conclude in Section VI by discussing some limitations of our analysis and offer some recommendations for implementation. Journal: North American Actuarial Journal Pages: 1-15 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595716 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595716 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:1-15 Template-Type: ReDIF-Article 1.0 Author-Name: Stanley Pliska Author-X-Name-First: Stanley Author-X-Name-Last: Pliska Title: “Utility Functions: From Risk Theory to Finance”, Hans U. Gerber and Gérard Pafum, July 1998 Journal: North American Actuarial Journal Pages: 94-94 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595732 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595732 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:94-94 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaolan Zhang Author-X-Name-First: Xiaolan Author-X-Name-Last: Zhang Title: “Pricing Perpetual Options for Jump Processes”, Hans U. Gerber and Elias S.W. Shiu, July 1998 Journal: North American Actuarial Journal Pages: 109-111 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595738 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595738 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:109-111 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Authors’ Reply: Pricing Perpetual Options for Jump Processes - Discussion by X. Sheldon Lin; Xiaolan Zhang Journal: North American Actuarial Journal Pages: 112-112 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595739 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595739 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:112-112 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Pricing Perpetual Options for Jump Processes Abstract: We consider two models in which the logarithm of the price of an asset is a shifted compound Poisson process. Explicit results are obtained for prices and optimal exercise strategies of certain perpetual American options on the asset, in particular for the perpetual put option. In the first model in which the jumps of the asset price are upwards, the results are obtained by the martingale approach and the smooth junction condition. In the second model in which the jumps are downwards, we show that the value of the strategy corresponding to a constant option-exercise boundary satisfies a certain renewal equation. Then the optimal exercise strategy is obtained from the continuous junction condition. Furthermore, the same model can be used to price certain reset options. Finally, we show how the classical model of geometric Brownian motion can be obtained as a limit and also how it can be integrated in the two models. Journal: North American Actuarial Journal Pages: 101-107 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595736 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595736 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:101-107 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheldon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheldon Lin Title: “Pricing Perpetual Options for Jump Processes”, Hans U. Gerber and Elias S.W. Shiu, July 1998 Journal: North American Actuarial Journal Pages: 108-109 Issue: 3 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595737 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595737 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:108-109 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rappaport Author-X-Name-First: Anna Author-X-Name-Last: Rappaport Title: Author’s Reply: Reaching Out to Make a Difference (Guest Editorial) - Discission by Caterina Lindman Journal: North American Actuarial Journal Pages: 115-115 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595887 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595887 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:115-115 Template-Type: ReDIF-Article 1.0 Author-Name: Caterina Lindman Author-X-Name-First: Caterina Author-X-Name-Last: Lindman Title: “Reaching Out to Make a Difference” (Guest Editorial), Anna M. Rappaport, April 1999 Journal: North American Actuarial Journal Pages: 114-115 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595886 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595886 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:114-115 Template-Type: ReDIF-Article 1.0 Author-Name: Philippe Artzner Author-X-Name-First: Philippe Author-X-Name-Last: Artzner Title: Author’s Reply: Application of Coherent Risk Measures to Capital Requirements in Insurance - Discussion by Elias S.W. Shiu Journal: North American Actuarial Journal Pages: 116-116 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595889 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595889 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:116-116 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Application of Coherent Risk Measures to Capital Requirements in Insurance,” Philippe Artzner, April 1999 Journal: North American Actuarial Journal Pages: 115-116 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595888 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595888 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:115-116 Template-Type: ReDIF-Article 1.0 Author-Name: Juha Alho Author-X-Name-First: Juha Author-X-Name-Last: Alho Title: “The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications“, Ronald Lee, January 2000 Journal: North American Actuarial Journal Pages: 91-93 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595883 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595883 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:91-93 Template-Type: ReDIF-Article 1.0 Author-Name: Ronald Lee Author-X-Name-First: Ronald Author-X-Name-Last: Lee Title: The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications Abstract: In 1992, Lee and Carter published a new method for long-run forecasts of the level and age pattern of mortality, based on a combination of statistical time series methods and a simple approach to dealing with the age distribution of mortality. The method describes the log of a time series of age-specific death rates as the sum of an age-specific component that is independent of time and another component that is the product of a time-varying parameter reflecting the general level of mortality, and an age-specific component that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. This model is fit to historical data. The resulting estimate of the time-varying parameter is then modeled and forecast as a stochastic time series using standard methods. From this forecast of the general level of mortality, the actual age-specific rates are derived using the estimated age effects. The forecasts of the various life table functions have probability distributions, so probability intervals can be calculated for each variable and for summary measures such as life expectancy. The projected gain in life expectancy from 1989 to 1997 matches the actual gain very closely and is nearly twice the gain projected by the Social Security Administration’s Office of the Actuary. This paper describes the basic Lee-Carter method and discusses the forecasts to which it has led. It then discusses extensions, applications, and methodological improvements that have been made in recent years; considers shortcomings of the method; and briefly describes how it has been used as a component of more general stochastic population projections and stochastic forecasts of the finances of the U.S. Social Security system. Journal: North American Actuarial Journal Pages: 80-91 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595882 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595882 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:80-91 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Ballantyne Author-X-Name-First: Harry Author-X-Name-Last: Ballantyne Title: “Social Security—Adequacy, Equity, and Progressiveness: A Review of Criteria Based on Experience In Canada and the United States”, Robert L. Brown, January 2000 Journal: North American Actuarial Journal Pages: 17-17 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595867 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595867 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:17-17 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Author-Name: F. De Vylder Author-X-Name-First: F. Author-X-Name-Last: De Vylder Title: Credibility in Favor of Unlucky Insureds Abstract: The classical Bühlmann credibility formula estimates the hypothetical mean of a particular insured, or risk, by a weighted average of the grand mean of the collection of risks with the sample mean of the given insured. If the insured is unfortunate enough to have had large claims in the previous policy period(s), then the estimate of future claims for that risk will also be large. In this paper we provide actuaries with a method for not overly penalizing an unlucky insured while still targeting the goal of accuracy in the estimate. We propose a credibility estimator that minimizes the expectation of a linear combination of a squared-error term and a first-derivative term. The squared-error term measures the accuracy of the estimator, while the first-derivative term constrains the estimator to be close to constant. Journal: North American Actuarial Journal Pages: 107-113 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595885 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:107-113 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Jeffrey Ip Author-X-Name-First: Jeffrey Author-X-Name-Last: Ip Title: Social Security—Adequacy, Equity, and Progressiveness Abstract: This paper reviews and compares the Canadian and U.S. social security systems, based on criteria defined in a paper by Knox and Cornish, as to their adequacy, equity, and progressiveness. It concludes that the Canadian system provides larger minimum benefits and, thus, greater adequacy for the poor than does the U.S. system. On the other hand, the analysis indicates more emphasis on equity in the U.S. system (in total) than in the Canadian. Finally, both systems are shown to be highly progressive in that lower-wage earners get larger benefits per dollar of contribution than do higher-wage earners.The paper also studies the Seniors Benefit recently proposed in Canada that would have replaced the Old Age Security and the Guaranteed Income Supplement. The proposal was rescinded in July, 1998. Its failure points out the need for a further criterion for optimal social security design beyond those listed by Knox and Cornish.We conclude by noting that the social security systems in both Canada and the U.S. achieve the basic criteria defined in the paper despite having remarkably different actuarial formulas for determining benefits and remarkably different structures. Journal: North American Actuarial Journal Pages: 1-17 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595866 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595866 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:1-17 Template-Type: ReDIF-Article 1.0 Author-Name: Louis Lombardi Author-X-Name-First: Louis Author-X-Name-Last: Lombardi Title: Managing The Volatility Of Gaap Earnings Abstract: The adoption of Statement of Financial Accounting Standards No. 97 (SFAS 97) eliminated the “lock-in” concept introduced in SFAS 60. Since many of the actuarial assumptions used in the calculation of the deferred acquisition cost (DAC) asset are difficult to predict over an extended period of time, “dynamic unlocking” was a sensible solution. Although this “dynamic unlocking” keeps the assumptions in line with recent experience, it comes at a cost—increased volatility of GAAP earnings. Some of the causes of this volatility are warranted since it accentuates the effects on earnings due to certain changes in the underlying experience. Other causes of this volatility may be unwarranted because of a misapplication of the principles underlying SFAS 97 and SFAS 120 or the manner in which changes in experience were reflected. In addition, most analysts expect the amortization of deferred acquisition costs to increase when earnings are better than expected. Conversely, analysts expect the amortization of deferred acquisition costs to decrease when earnings are worse than expected. Often the amortization of deferred acquisition costs behaves in a manner contrary to their expectations. This article analyzes what causes this volatility, explains why the amortization can behave contrary to expectations, and suggests several techniques for minimizing these unwarranted results. Journal: North American Actuarial Journal Pages: 94-106 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595884 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595884 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:94-106 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sze Author-X-Name-First: Michael Author-X-Name-Last: Sze Title: “A Retirement Plan Based on Fixed Accumulation and Variable Accrual”, M. Zaki Khorasanee and Ho Kuen Ng, January 2000 Journal: North American Actuarial Journal Pages: 78-79 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595881 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595881 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:78-79 Template-Type: ReDIF-Article 1.0 Author-Name: Keith Sharp Author-X-Name-First: Keith Author-X-Name-Last: Sharp Title: “A Retirement Plan Based on Fixed Accumulation and Variable Accrual”, M. Zaki Khorasanee and Ho Kuen Ng, January 2000 Journal: North American Actuarial Journal Pages: 78-78 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595880 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595880 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:78-78 Template-Type: ReDIF-Article 1.0 Author-Name: Malcolm Hamilton Author-X-Name-First: Malcolm Author-X-Name-Last: Hamilton Title: “Social Security—Adequacy, Equity, and Progressiveness: A Review of Criteria Based on Experience In Canada and the United States”, Robert L. Brown, January 2000 Journal: North American Actuarial Journal Pages: 18-19 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595868 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595868 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:18-19 Template-Type: ReDIF-Article 1.0 Author-Name: P. W. A. Dayananda Author-X-Name-First: P. W. A. Author-X-Name-Last: Dayananda Title: Executive Stock Options Abstract: As a part of the compensation package many companies provide executives with executive stock options, which are call options with additional restrictions. They provide some financial advantages to the executives and help the company retain the service of the executives who improve the company’s earnings and management.Until recently the values of the executive stock options were not required to be disclosed in the company�s financial reports. But recent statements from the Financial Accounting Standards Board (FASB) have made it necessary to value these executive stock options. The valuation of executive stock options is also required for investors and financial practitioners. This paper considers the award of performance-based executive stock options when the stock price at the time of stock option award exceeds a given preassigned value. It is assumed that the stock price follows a geometric Brownian motion, and that the number of stock options awarded at any time depends on the stock price at that time.A valuation formula is derived using the method of Esscher transforms for a multiyear award plan. The closed-form formula derived is similar to the Black-Scholes formula for options and utilizes the standard bivariate normal distribution function, which is available in statistical software. In this paper the number of stock options awarded is assumed to be in a specific form, but the theory presented can be modified to suit other forms of award structure. Moreover, by suitable choice of parameters, a valuation formula is also presented for the award of fixed-value executive stock options grants; this formula is also in a closed form and involves cumulative distribution values of the standard normal random variable. Numerical illustrations of the use of the valuation formulas are presented. Journal: North American Actuarial Journal Pages: 20-30 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595869 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595869 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:20-30 Template-Type: ReDIF-Article 1.0 Author-Name: Yuan Chang Author-X-Name-First: Yuan Author-X-Name-Last: Chang Title: “A Retirement Plan Based on Fixed Accumulation and Variable Accrual”, M. Zaki Khorasanee and Ho Kuen Ng, January 2000 Journal: North American Actuarial Journal Pages: 76-77 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595878 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595878 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:76-77 Template-Type: ReDIF-Article 1.0 Author-Name: M. Khorasanee Author-X-Name-First: M. Author-X-Name-Last: Khorasanee Author-Name: Ho Ng Author-X-Name-First: Ho Author-X-Name-Last: Ng Title: A Retirement Plan Based on Fixed Accumulation and Variable Accrual Abstract: We propose a new type of retirement plan, aimed at achieving a compromise between stability in cost for the plan sponsor and guaranteed accumulation for the participants. The behavior of the plan is compared with that of a money purchase plan for both deterministic and stochastic investment scenarios. The proposed plan is shown to provide more stable and predictable benefits than a money purchase plan. Obstacles to the establishment of such a plan, from the perspective of U.S. pensions legislation, are considered. Journal: North American Actuarial Journal Pages: 63-76 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595877 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595877 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:63-76 Template-Type: ReDIF-Article 1.0 Author-Name: Luke Girard Author-X-Name-First: Luke Author-X-Name-Last: Girard Title: Author’s Reply: Market Value Of Insurance Liabilities: Reconciling the Actuarial Appraisal and Option Pricing Methods - Discussion by Thomas S. Y. Ho; Joe Koltisko; Thomas J. Merfeld; Marsha Wallace Journal: North American Actuarial Journal Pages: 60-62 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595876 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:60-62 Template-Type: ReDIF-Article 1.0 Author-Name: Marsha Wallace Author-X-Name-First: Marsha Author-X-Name-Last: Wallace Title: “Market Value Of Insurance Liabilities: Reconciling the Actuarial Appraisal and Option Pricing Methods”, Luke N. Girard, January 2000 Journal: North American Actuarial Journal Pages: 57-60 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595875 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595875 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:57-60 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Leap of Faith Journal: North American Actuarial Journal Pages: iii-iii Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595891 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595891 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Merfeld Author-X-Name-First: Thomas Author-X-Name-Last: Merfeld Title: “Market Value Of Insurance Liabilities: Reconciling the Actuarial Appraisal and Option Pricing Methods”, Luke N. Girard, January 2000 Journal: North American Actuarial Journal Pages: 56-57 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595874 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595874 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:56-57 Template-Type: ReDIF-Article 1.0 Author-Name: Joe Koltisko Author-X-Name-First: Joe Author-X-Name-Last: Koltisko Title: “Market Value Of Insurance Liabilities: Reconciling the Actuarial Appraisal and Option Pricing Methods”, Luke N. Girard, January 2000 Journal: North American Actuarial Journal Pages: 55-56 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595873 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595873 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:55-56 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Ho Author-X-Name-First: Thomas Author-X-Name-Last: Ho Title: “Market Value Of Insurance Liabilities: Reconciling the Actuarial Appraisal and Option Pricing Methods”, Luke N. Girard, January 2000 Journal: North American Actuarial Journal Pages: 50-55 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595872 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595872 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:50-55 Template-Type: ReDIF-Article 1.0 Author-Name: Luke Girard Author-X-Name-First: Luke Author-X-Name-Last: Girard Title: Market Value Of Insurance Liabilities Abstract: With Statement of Financial Accounting Standards 115 (FASB 1993), insurers are now in the awkward situation that almost half of the balance sheet is marked to market. This has created a material inconsistency with the way liabilities are reported, thus diminishing the usefulness of financial reporting to shareholders and potential new investors. Discussion has emerged in the industry about the process of market valuing liabilities. The American Academy of Actuaries has formed a “Fair Valuation of Liabilities” task force to compare and review various alternative methodologies. During 1995 the Society of Actuaries and New York University jointly sponsored a conference on “Fair Value of Insurance Liabilities.” Motivated by the conference, this paper attempts to bridge the gap between option pricing and actuarial appraisal methodologies. The author suggests we refocus attention toward the assumption-setting process, which is the key driver of a fair valuation. In this regard, this paper attempts to advance practice and methodology with respect to life insurance company valuation. Journal: North American Actuarial Journal Pages: 31-49 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595871 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595871 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:31-49 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Enterprise Risk and return Management for Financial Institutions,” Mark Griffin and Rick Boomgaardt, April 1999 Journal: North American Actuarial Journal Pages: 116-117 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595890 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595890 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:116-117 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Executive Stock Options: Valuation Based on Targeted Performance”, P. W. A. Dayananda, January 2000 Journal: North American Actuarial Journal Pages: 30-30 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595870 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595870 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:30-30 Template-Type: ReDIF-Article 1.0 Author-Name: Cecil Nesbitt Author-X-Name-First: Cecil Author-X-Name-Last: Nesbitt Title: “A Retirement Plan Based on Fixed Accumulation and Variable Accrual”, M. Zaki Khorasanee and Ho Kuen Ng, January 2000 Journal: North American Actuarial Journal Pages: 77-77 Issue: 1 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595879 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595879 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:77-77 Template-Type: ReDIF-Article 1.0 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Author-Name: Shuai Yang Author-X-Name-First: Shuai Author-X-Name-Last: Yang Title: A Linear Regression Approach to Modeling Mortality Rates of Different Forms Abstract: In this article, we propose a linear regression approach to modeling mortality rates of different forms. First, we repeat to fit a mortality sequence for each of K years (called the fitting years) with another mortality sequence of equal length for some year (called the base year) differing by tj years (j = 1, …, K) using a simple linear regression. Then we fit the sequences of the estimated slope and intercept parameters of length K, respectively, with the sequence of {tj} by each of the simple linear regression and random walk with drift models. The sequences of the fitted slope and intercept parameters can be used for forecasting deterministic and stochastic mortality rates. Forecasting performances are compared among these two approaches and the Lee-Carter model. The CBD model is also included for comparisons for an elderly age group. Moreover, we give a central-death-rate–linked security to hedge mortality/longevity risks. Optimal units, purchased from the special purpose vehicle, which maximize the hedge effectiveness for life insurers and annuity providers, respectively, are derived and can be expressed in terms of the cumulative distribution function of the standard normal random variable. A measure with hedge cost involved, called hedge effectiveness rate, for comparing risk reduction amount per dollar spent among mortality models is proposed. Finally, numerical examples are presented for illustrations. Journal: North American Actuarial Journal Pages: 1-23 Issue: 1 Volume: 19 Year: 2015 Month: 1 X-DOI: 10.1080/10920277.2014.975252 File-URL: http://hdl.handle.net/10.1080/10920277.2014.975252 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:1-23 Template-Type: ReDIF-Article 1.0 Author-Name: Ruodu Wang Author-X-Name-First: Ruodu Author-X-Name-Last: Wang Author-Name: Liang Peng Author-X-Name-First: Liang Author-X-Name-Last: Peng Author-Name: Jingping Yang Author-X-Name-First: Jingping Author-X-Name-Last: Yang Title: CreditRisk Model with Dependent Risk Factors Abstract: The CreditRisk+ model is widely used in industry for computing the loss of a credit portfolio. The standard CreditRisk+ model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors. Journal: North American Actuarial Journal Pages: 24-40 Issue: 1 Volume: 19 Year: 2015 Month: 1 X-DOI: 10.1080/10920277.2014.976311 File-URL: http://hdl.handle.net/10.1080/10920277.2014.976311 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:24-40 Template-Type: ReDIF-Article 1.0 Author-Name: Joelle H. Fong Author-X-Name-First: Joelle H. Author-X-Name-Last: Fong Author-Name: Adam W. Shao Author-X-Name-First: Adam W. Author-X-Name-Last: Shao Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Multistate Actuarial Models of Functional Disability Abstract: Long-term-care (LTC) costs are expected to significantly increase over the coming decades as the Baby Boom generation nears retirement. Recent policy discussions in the United State have focused on expanding the private LTC insurance market so as to alleviate some of the pressure on public programs. An important and fundamental input to the pricing of LTC insurance products is a set of age- and sex-specific functional status transition rates that can flexibly take into account alternative benefit trigger specifications. We apply generalized linear models to evaluate disability transitions for individuals in old age based on a large sample of U.S. elderly. We estimate a multistate model for LTC insurance applications and find significant differences in disability rate patterns and levels between our set of estimates and those separately estimated using an earlier approach developed by the Society of Actuaries. Our results suggest that the elderly face a 10% chance of becoming LTC disabled only at ages past 90, rather than in their 80s. Furthermore, age patterns of recovery are found to differ significantly between the sexes. We also show that these estimates of transition probability are sensitive to the definition of “LTC disability,” which has implications for the design of benefit triggers for private and public LTC insurance programs. Journal: North American Actuarial Journal Pages: 41-59 Issue: 1 Volume: 19 Year: 2015 Month: 1 X-DOI: 10.1080/10920277.2014.978025 File-URL: http://hdl.handle.net/10.1080/10920277.2014.978025 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:41-59 Template-Type: ReDIF-Article 1.0 Author-Name: H. E. Frech Author-X-Name-First: H. E. Author-X-Name-Last: Frech Author-Name: Michael P. Smith Author-X-Name-First: Michael P. Author-X-Name-Last: Smith Title: Anatomy of a Slow-Motion Health Insurance Death Spiral Abstract: Adverse selection death spirals in health insurance are dramatic and, so far, exotic economic events. The possibility of death spirals has garnered recent policy and popular attention because the pricing regulations in the Affordable Care Act (ACA) of 2010 make health plans more vulnerable to them (though some other aspects of the ACA limit them). Most death spirals tracked in the literature have involved selection against a group health plan that was dropped quickly by the employer. In this article, we empirically document a death spiral in individual health insurance that was apparently triggered by a block closure in 1981 and developed slowly because the insurer partially subsidized the block. We show that premiums rose dramatically from around the time of the block closure to at least 2009 (the last year of available data). By 2009, some, but very few, policyholders remained in the block, and premiums were roughly seven times that of a yardstick we developed. The history of this slow-moving event is directly relevant to current policy discussions because of both adverse selection in general and the particular problems induced by closing a block. Journal: North American Actuarial Journal Pages: 60-72 Issue: 1 Volume: 19 Year: 2015 Month: 1 X-DOI: 10.1080/10920277.2014.982871 File-URL: http://hdl.handle.net/10.1080/10920277.2014.982871 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:60-72 Template-Type: ReDIF-Article 1.0 Author-Name: H. P. Keeler Author-X-Name-First: H. P. Author-X-Name-Last: Keeler Author-Name: P. G. Taylor Author-X-Name-First: P. G. Author-X-Name-Last: Taylor Title: Discussion on “On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals,” by Jiandong Ren, Volume 12(2) Journal: North American Actuarial Journal Pages: 73-77 Issue: 1 Volume: 19 Year: 2015 Month: 1 X-DOI: 10.1080/10920277.2014.977453 File-URL: http://hdl.handle.net/10.1080/10920277.2014.977453 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:73-77 Template-Type: ReDIF-Article 1.0 Author-Name: Joshua D. Woodard Author-X-Name-First: Joshua D. Author-X-Name-Last: Woodard Title: Impacts of Weather and Time Horizon Selection on Crop Insurance Ratemaking: A Conditional Distribution Approach Abstract: An important issue in the agricultural risk and actuarial literatures is the extent to which sample period selection affects the accuracy of insurance rating. This is typically more problematic in agriculture than in other types of insurance because of the variation in weather through time. A conditional Weibull distribution approach is developed that explicitly models the interaction of weather, technology, and other variables on probabilistic yield outcomes to address this issue. Results from an application with an extensive producer-level yield dataset representing commercial-scale Illinois firms suggest that the impact of weather heterogeneity on risk estimation across reasonable samples is likely not as great as is often claimed. The results also suggest that yield risk is decreasing significantly through time and indicate the presence of trend acceleration. A rating analysis indicates that violations in the risk evolution assumptions of the rating approaches used in the Federal Crop Insurance Program—which implicitly assume increasing yield risk through time when yields trend—result in severely biased rates, with typical overstatements of 200% to 400% for Midwest corn. Journal: North American Actuarial Journal Pages: 279-293 Issue: 2 Volume: 18 Year: 2014 Month: 4 X-DOI: 10.1080/10920277.2014.887476 File-URL: http://hdl.handle.net/10.1080/10920277.2014.887476 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:2:p:279-293 Template-Type: ReDIF-Article 1.0 Author-Name: M. R. Hardy Author-X-Name-First: M. R. Author-X-Name-Last: Hardy Author-Name: D. Saunders Author-X-Name-First: D. Author-X-Name-Last: Saunders Author-Name: X. Zhu Author-X-Name-First: X. Author-X-Name-Last: Zhu Title: Market-Consistent Valuation and Funding of Cash Balance Pensions Abstract: Cash balance pension benefits are accumulated at guaranteed crediting rates, usually based on yields on government securities. Viewed as a financial liability, the benefit is a form of interest rate derivative, which can be valued using financial models and theory. In this article, we derive the market value for a range of commonly used crediting rates, assuming the accrued benefit liability comprises the past contributions, allowing for full interest credits up to a known future retirement date. We use the Hull-White interest rate model to determine crediting rates and to determine the market value. We explore the risks associated with different crediting rate choices by evaluating the liability using market data from 1998 to 2013. We propose two other approaches to the accrued benefit. The first approach assumes the accrued benefit comprises past contributions with interest up to the valuation date, but no future interest credits. Future credits on past contributions are assumed funded through future contributions. The second method projects all contributions and interest to retirement and assumes equal units of accrual of this projected benefit in each year of service. We compare the three approaches through numerical examples. Journal: North American Actuarial Journal Pages: 294-314 Issue: 2 Volume: 18 Year: 2014 Month: 4 X-DOI: 10.1080/10920277.2014.906154 File-URL: http://hdl.handle.net/10.1080/10920277.2014.906154 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:2:p:294-314 Template-Type: ReDIF-Article 1.0 Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Title: Empirical Approach for Optimal Reinsurance Design Abstract: This article proposes a novel and practical approach of addressing optimal reinsurance via an empirical approach. This method formulates reinsurance models using the observed data directly and has advantages including (1) transformation of an infinite dimensional optimization problem to a finite dimension, (2) no required explicit distributional assumption on the underlying risk, and (3) many empirical-based reinsurance models can be solved efficiently using the second-order conic programming. This allows insurers to incorporate many desirable objective functions and constraints while still retaining the ease of obtaining optimal reinsurance strategies. Numerical examples, including applications to actual Danish fire loss data, are provided to highlight the efficiency and the practicality of the proposed empirical models. The stability and consistency of the empirical-based solutions are also analyzed numerically. Journal: North American Actuarial Journal Pages: 315-342 Issue: 2 Volume: 18 Year: 2014 Month: 4 X-DOI: 10.1080/10920277.2014.888008 File-URL: http://hdl.handle.net/10.1080/10920277.2014.888008 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:2:p:315-342 Template-Type: ReDIF-Article 1.0 Author-Name: César Neves Author-X-Name-First: César Author-X-Name-Last: Neves Author-Name: Cristiano Fernandes Author-X-Name-First: Cristiano Author-X-Name-Last: Fernandes Author-Name: Eduardo Melo Author-X-Name-First: Eduardo Author-X-Name-Last: Melo Title: Forecasting Surrender Rates Using Elliptical Copulas and Financial Variables Abstract: A multistage stochastic model to forecast surrender rates for life insurance and pension plans is proposed. Surrender rates are forecasted by means of Monte Carlo simulation after a sequence of GLM, ARMA-GARCH, and copula fitting is executed. The model is illustrated by applying it to age-specific time series of surrender rates derived from pension plans with annuity payments of a Brazilian insurer. In the GLM process, the only macroeconomic variable used as an explanatory variable is the Brazilian real short-term interest rate. The advantage of such a variable is that we can take future market expectation through the current term structure of interest rates. The GLM residuals of each age/gender group are then modeled by ARMA-GARCH processes to generate i.i.d. residuals. The dependence among these residuals is then modeled by multivariate Gaussian and Student's t copulas. To produce a conditional forecast on a stock market index, in our application we used the residuals of an ARMA-GARCH model fitted to the Brazilian stock market index (Ibovespa) returns, which generates one of the marginal distributions used in the dependence modeling through copulas. This strategy is adopted to explain the high and uncommon surrender rates observed during the recent economic crisis. After applying known simulation methods for elliptical copulas, we proceeded backwards to obtain the forecasted distributions of surrender rates by application, in the sequel, of ARMA-GARCH and GLM models. Additionally, our approach produced an algorithm able to simulate multivariate elliptical copulas conditioned on a marginal distribution. Using this algorithm, surrender rates can be simulated conditioned on stock index residuals (in our case, the residuals of the Ibovespa returns), which allows insurers and pension funds to simulate future surrender rates assuming a financial stress scenario with no need to predict the stock market index. Journal: North American Actuarial Journal Pages: 343-362 Issue: 2 Volume: 18 Year: 2014 Month: 4 X-DOI: 10.1080/10920277.2014.888315 File-URL: http://hdl.handle.net/10.1080/10920277.2014.888315 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:2:p:343-362 Template-Type: ReDIF-Article 1.0 Author-Name: Miguel de Carvalho Author-X-Name-First: Miguel Author-X-Name-Last: de Carvalho Author-Name: Filipe Marques Author-X-Name-First: Filipe Author-X-Name-Last: Marques Title: Jackknife Euclidean Likelihood-Based Inference for Spearman's Rho Abstract: We discuss jackknife Euclidean likelihood-based inference methods, with a special focus on the construction of confidence intervals for Spearman's rho. We show that a Wilks's theorem holds for jackknife Euclidean likelihood, and based on it we construct confidence intervals for Spearman's rho. In a simulation study we examine the performance of our method, and a fire insurance claims database is used for its illustration. Journal: North American Actuarial Journal Pages: 487-492 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597644 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597644 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:487-492 Template-Type: ReDIF-Article 1.0 Author-Name: Yuliya Mishura Author-X-Name-First: Yuliya Author-X-Name-Last: Mishura Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: Dividend Barrier Strategies in A Renewal Risk Model with Generalized Erlang Interarrival Times Abstract: We consider a renewal risk model with generalized Erlang distributed interarrival times. We assume that the phases of the interarrival time can be observed. In order to solve de Finetti's dividend problem, we first consider phasewise barrier strategies and look for the optimal barriers when the initial capital is 0. For exponentially distributed claim sizes, we show that the barrier strategy is optimal among all admissible strategies. For the special case of Erlang(2) interarrival times, we calculate the value function and the optimal barriers. Journal: North American Actuarial Journal Pages: 493-512 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597645 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597645 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:493-512 Template-Type: ReDIF-Article 1.0 Author-Name: Zaki Khorasanee Author-X-Name-First: Zaki Author-X-Name-Last: Khorasanee Title: Risk-Sharing and Benefit Smoothing in A Hybrid Pension Plan Abstract: A hybrid pension plan with an explicit formula for sharing risk between the plan sponsor and the members is proposed. The performance of this plan is analyzed using a modified version of the model used by Dufresne (1988). Formulas for the variance of the contribution income and benefit outgo are derived, assuming investment returns are independent and identically distributed. The performance of the hybrid plan is compared with a defined contribution (DC) plan providing the same expected retirement benefit. It is shown that the hybrid plan is more efficient in the control of investment risk, and that this gain in efficiency is greater when “lifestyle” investment strategies are adopted in the DC plan. Modifications to the proposed hybrid benefit structure that might be required for a real plan are suggested. Journal: North American Actuarial Journal Pages: 449-461 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597642 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597642 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:449-461 Template-Type: ReDIF-Article 1.0 Author-Name: Nadine Gatzert Author-X-Name-First: Nadine Author-X-Name-Last: Gatzert Author-Name: Gudrun Schmitt-Hoermann Author-X-Name-First: Gudrun Author-X-Name-Last: Schmitt-Hoermann Author-Name: Hato Schmeiser Author-X-Name-First: Hato Author-X-Name-Last: Schmeiser Title: Optimal Risk Classification with an Application to Substandard Annuities Abstract: Substandard annuities pay higher pensions to individuals with impaired health and thus require special underwriting of applicants. Although such risk classification can substantially increase a company's profitability, these products are uncommon except for the well-established U.K. market. In this paper we comprehensively analyze this issue and make several contributions to the literature. First, we describe enhanced, impaired life, and care annuities, and then we discuss the underwriting process and underwriting risk related thereto. Second, we propose a theoretical model to determine the optimal profit-maximizing risk classification system for substandard annuities. Based on the model framework and for given price-demand dependencies, we formally show the effect of classification costs and costs of underwriting risk on profitability for insurers. Risk classes are distinguished by the average mortality of contained insureds, whereby mortality heterogeneity is included by means of a frailty model. Third, we discuss key aspects regarding a practical implementation of our model as well as possible market entry barriers for substandard annuity providers. Journal: North American Actuarial Journal Pages: 462-486 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597643 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597643 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:462-486 Template-Type: ReDIF-Article 1.0 Author-Name: Shang-Yin Yang Author-X-Name-First: Shang-Yin Author-X-Name-Last: Yang Author-Name: Ya-Wen Hwang Author-X-Name-First: Ya-Wen Author-X-Name-Last: Hwang Author-Name: Shih-Chieh Chang Author-X-Name-First: Shih-Chieh Author-X-Name-Last: Chang Title: The Bankruptcy Cost of the Life Insurance Industry Under Regulatory Forbearance Abstract: In this study the Taiwan Insurance Guaranty Fund (TIGF) is introduced to investigate the ex ante assessment insurance guaranty scheme. We study the bankruptcy cost when a financially troubled life insurer is taken over by TIGF. The pricing formula of the fair premium of TIGF incorporating the regulatory forbearance is derived. The embedded Parisian option due to regulatory forbearance on fair premiums is investigated. The numerical results show that leverage ratio, asset volatility, grace period, and intervention criterion influence the default costs. Asset volatility has a significant effect on the default option, while leverage ratio is shown to aggravate the negative influence from the volatility of risky asset. Furthermore, the numerical analysis concludes that the premium for the insurance guaranty fund is risk sensitive and that a risk-based premium scheme could be implemented, hence, to ease the moral hazard. Journal: North American Actuarial Journal Pages: 513-523 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597646 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597646 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:513-523 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Society of Actuaries Journal: North American Actuarial Journal Pages: 524-524 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597647 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597647 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:524-524 Template-Type: ReDIF-Article 1.0 Author-Name: Anatoliy Yashin Author-X-Name-First: Anatoliy Author-X-Name-Last: Yashin Author-Name: Konstantin Arbeev Author-X-Name-First: Konstantin Author-X-Name-Last: Arbeev Author-Name: Svetlana Ukraintseva Author-X-Name-First: Svetlana Author-X-Name-Last: Ukraintseva Author-Name: Igor Akushevich Author-X-Name-First: Igor Author-X-Name-Last: Akushevich Author-Name: Alexander Kulminski Author-X-Name-First: Alexander Author-X-Name-Last: Kulminski Title: Patterns of Aging-Related Changes on the Way to 100 Abstract: The objective of this paper is to investigate dynamic properties of age trajectories of physiological indices and their effects on mortality risk and longevity using longitudinal data on more than 5,000 individuals collected in biennial examinations of the Framingham Heart Study (FHS) original cohort during about 50 subsequent years of follow-up. We first performed empirical analyses of the FHS longitudinal data. We evaluated average age trajectories of indices describing physiological states for different groups of individuals and established their connections with mortality risk. These indices include body mass index, diastolic blood pressure, pulse pressure, pulse rate, level of blood glucose, hematocrit, and serum cholesterol. To be able to investigate dynamic mechanisms responsible for changes in the aging human organisms using available longitudinal data, we further developed a stochastic process model of human mortality and aging, by including in it the notions of “physiological norms,” “allostatic adaptation and allostatic load,” “stress resistance,” and other characteristics associated with the internal process of aging and the effects of external disturbances. In this model, the persistent deviation of physiological indices from their normal values contributes to an increase in morbidity and mortality risks. We used the stochastic process model in the statistical analyses of longitudinal FHS data. We found that different indices have different average age patterns and different dynamic properties. We also found that age trajectories of long-lived individuals differ from those of the shorter-lived members of the FHS original cohort for both sexes. Using methods of statistical modeling, we evaluated “normal” age trajectories of physiological indices and the dynamic effects of allostatic adaptation. The model allows for evaluating average patterns of aging-related decline in stress resistance. This effect is captured by the narrowing of the U-shaped mortality risk (considered a function of physiological state) with age. We showed that individual indices and their rates of change with age, as well as other measures of individual variability, manifested during the life course are important contributors to mortality risks. The advantages and limitations of the approach are discussed. Journal: North American Actuarial Journal Pages: 403-433 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597640 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597640 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:403-433 Template-Type: ReDIF-Article 1.0 Author-Name: Jack Yue Author-X-Name-First: Jack Author-X-Name-Last: Yue Title: Mortality Compression and Longevity Risk Abstract: Mortality improvements, especially of the elderly, have been a common phenomenon since the end of World War II. The longevity risk becomes a major concern in many countries because of underestimating the scale and speed of prolonged life. In this study we explore the increasing life expectancy by examining the basic properties of survival curves. Specifically, we check if there are signs of mortality compression (i.e., rectangularization of the survival curve) and evaluate what it means to designing annuity products. Based on the raw mortality rates, we propose an approach to verify if there is mortality compression. We then apply the proposed method to the mortality rates of Japan, Sweden, and the United States, using the Human Mortality Database. Unlike previous results using the graduated mortality rates, we found no obvious signs that mortality improvements are slowing down. This indicates that human longevity is likely to increase, and longevity risk should be seriously considered in pricing annuity products. Journal: North American Actuarial Journal Pages: 434-448 Issue: 4 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10597641 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10597641 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:434-448 Template-Type: ReDIF-Article 1.0 Author-Name: Luis Zuluaga Author-X-Name-First: Luis Author-X-Name-Last: Zuluaga Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Title: Improving Skewness of Mean-Variance Portfolios Abstract: The widely accepted belief that asset returns and insurance product line margins are not normally distributed has motivated the use of skewness (or higher than second-order moments) in the context of optimal risk-reward portfolio allocation. Here we propose an optimization-based methodology to substantially improve the skewness of portfolios in the mean-variance efficient frontier. Unlike other related methods, the proposed methodology is very intuitive, noniterative, and simple to implement, and it can be readily and efficiently carried out using state-of-the-art optimization solvers. These characteristics should be very appealing to risk managers. Journal: North American Actuarial Journal Pages: 59-67 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597577 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597577 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:59-67 Template-Type: ReDIF-Article 1.0 Author-Name: Claymore Marshall Author-X-Name-First: Claymore Author-X-Name-Last: Marshall Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: David Saunders Author-X-Name-First: David Author-X-Name-Last: Saunders Title: Valuation of a Guaranteed Minimum Income Benefit Abstract: With a deferred variable annuity the policyholder pays an upfront premium to the insurance company, which is then invested in the financial markets for many years (the accumulation phase) until the policyholder decides to convert their investment (often at retirement age) into a stream of variable annuity payments. A Guaranteed Minimum Income Benefit (GMIB) is an option that may be included at inception of a variable annuity contract that, in exchange for small fees charged by the insurer, gives the policyholder a right to receive a guaranteed minimum level of annuity payments upon annuitization. A GMIB is an attractive option because it protects the policyholder’s investment against poor market performance during the accumulation phase.The value of a GMIB is affected by investment account returns, interest rates, and mortality. The intention of this paper is to value a GMIB in a complete market, focusing on the sensitivity of the GMIB value to the financial variables. Mortality is not incorporated into the valuation. We present a comprehensive sensitivity analysis of the model employed. We decompose a GMIB payoff, which is rather complicated, to analyze what drives the value of a GMIB. Our approach offers a simple but effective way for insurers to measure the value of the GMIBs they offer, and it provides insights into the risk management of GMIBs and other guarantees that provide similar payoffs. Our model suggests that the fee rates charged by insurance companies for the GMIB option may be too low. Journal: North American Actuarial Journal Pages: 38-58 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597576 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597576 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:38-58 Template-Type: ReDIF-Article 1.0 Author-Name: Ruilin Tian Author-X-Name-First: Ruilin Author-X-Name-Last: Tian Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Author-Name: Yijia Lin Author-X-Name-First: Yijia Author-X-Name-Last: Lin Author-Name: Luis Zuluaga Author-X-Name-First: Luis Author-X-Name-Last: Zuluaga Title: Portfolio Risk Management with CVaR-Like Constraints Abstract: A current research stream in the portfolio allocation literature develops models that take into account the asymmetric nature of asset return distributions. Our paper contributes to this research stream by extending the Krokhmal, Palmquist, and Uryasev approach. We add CVaR-like constraints in the traditional portfolio optimization problem to reshape the tails of the portfolio return distribution while not significantly affecting its mean and variance. We illustrate how to apply this approach, called the “MV + CVaR approach,” to manage tail risk of an insurer’s asset-liability portfolio. Finally, we compare the MV + CVaR approach with the traditional Markowitz method and a method recently introduced by Boyle and Ding. Our numerical analysis provides empirical support for the effectiveness of the MV + CVaR approach in controlling downside risk. Moreover, we find that the MV + CVaR approach may improve skewness of mean-variance portfolios, especially for high-variance portfolios. Journal: North American Actuarial Journal Pages: 86-106 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597579 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597579 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:86-106 Template-Type: ReDIF-Article 1.0 Author-Name: Matthew Modisett Author-X-Name-First: Matthew Author-X-Name-Last: Modisett Author-Name: Edgard Maboudou-Tchao Author-X-Name-First: Edgard Author-X-Name-Last: Maboudou-Tchao Title: Significantly Lower Estimates of Volatility Arise from the Use of Open-High-Low-Close Price Data Abstract: This research provides an indication of the possible reduction in insurance liability valuations arising from the reduced volatility estimate of the Yang-Zhang refinement of volatility, when the liabilities are based on historic prices estimates arising from end-of-day prices in a jump-diffusion model. The paper also demonstrates the usefulness of change points.This research compares the standard measure of volatility (standard deviation of the log of close prices) for the total return of the S&P 500 to a recently developed volatility measure by Yang and Zhang that capitalizes on open-high-low-close prices. The latter volatility was developed to be the measure providing the narrowest confidence interval of all estimates satisfying certain desirable features and as such is the most desirable measure from a decision theory standpoint. This research shows that the Yang-Zhang volatility generally provides significantly lower estimates of volatility. This lower volatility estimate should lead to lower valuation levels for insurance products with guarantees, and this paper provides indicative reductions in liability valuations.Both volatility measures assume constant volatility and drift over a period. To accommodate this assumption, change points are employed to divide historical data into regimes of constant drift and volatility. To this end, the theory of change points is briefly introduced.The research shows that standard measure of volatility generally overestimates volatility, and the error increases with the absolute value of the underlying drift. There are several potential technical reasons why the lower volatility could be invalid, but this paper considers and rejects each, to conclude that the lower volatility estimate of Yang-Zhang is in fact the better estimate, not a result of a technical degeneracy. One conclusion is that valuations employing regime-switching generators, especially insurance liability valuations, should use the Yang-Zhang measure of volatility, otherwise any analysis embedded (or free-standing) options could overvalue prices or volatility. The simplicity of the Yang-Zhang calculation and its potentially large impact on valuations should justify its adoption for most companies. Journal: North American Actuarial Journal Pages: 68-85 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597578 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597578 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:68-85 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Ulm Author-X-Name-First: Eric Author-X-Name-Last: Ulm Title: The Effect of Policyholder Transfer Behavior on the Value of Guaranteed Minimum Death Benefits Abstract: Variable annuity contracts frequently include both guaranteed minimum death benefit (GMDB) options and options to transfer funds between fixed and variable accounts. We model the difference between fixed and variable rates as the primary determinant of policyholder transfer behavior. We find that people tend to transfer their money into variable accounts at about 39% of the rate that would be required to maintain constant percentage rebalancing, but with the opposite sign. If these transfers are not taken into account, the GMDB options on the variable accounts will be overvalued and overhedged. Ignoring this effect can have a substantial impact on the size of the futures portfolio needed to hedge this risk and a nonnegligible impact on the earnings of the variable annuity portfolio. Journal: North American Actuarial Journal Pages: 16-37 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597575 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597575 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:16-37 Template-Type: ReDIF-Article 1.0 Author-Name: Louis Lombardi Author-X-Name-First: Louis Author-X-Name-Last: Lombardi Title: Monitoring Changes in Capital and Hedge Effectiveness Under Fair Value Accounting Principles Abstract: In the early 1970s Richard G. Horn established a methodology for analyzing the earnings of a life insurance company that reflected, at that time, the types of products underwritten and the accounting principles that were in effect. This methodology became to be known as a “sources of earnings analysis.”With the exception of term life insurance, most life insurance and annuity products underwritten today have significant equity risk. Furthermore, fair value accounting principles are replacing historical-based accounting principles. Finally, life insurance companies have sophisticated risk management policies and procedures to manage risk.The purpose of this paper is to extend Horn’s “sources of earnings analysis” to reflect the evolution in product design, accounting standards, and risk management practices. In particular, under fair value accounting principles, the capital account becomes the primary focus of attention. Accordingly, this paper develops a methodology to perform an “analysis of the change in capital” that would replace a traditional “sources of earnings analysis.” In addition, most life insurance companies have hedging programs to manage the embedded equity risks in the types of products they have underwritten. Thus, an important focus of this analysis is to monitor the effectiveness of these hedging programs. Journal: North American Actuarial Journal Pages: 1-15 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597574 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:1-15 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Siu Author-X-Name-First: Tak Author-X-Name-Last: Siu Title: “Computation of Multivariate Barrier Crossing Probability and Its Applications in Credit Risk Models,” Joonghee Huh and Adam Kolkiewicz, July 2008 Journal: North American Actuarial Journal Pages: 150-156 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597582 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597582 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:150-156 Template-Type: ReDIF-Article 1.0 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Olivier Le Courtois Author-X-Name-First: Olivier Author-X-Name-Last: Le Courtois Author-Name: François Quittard-Pinon Author-X-Name-First: François Author-X-Name-Last: Quittard-Pinon Title: Protection of a Company Issuing a Certain Class of Participating Policies in a Complete Market Framework Abstract: In this article we examine to what extent policyholders buying a certain class of participating contracts (in which they are entitled to receive dividends from the insurer) can be described as standard bondholders. Our analysis extends the ideas of Biihlmann and sequences the fundamental advances of Merton, Longstaff and Schwartz, and Briys and de Varenne. In particular, we develop a setup where these participating policies are comparable to hybrid bonds but not to standard risky bonds (as done in most papers dealing with the pricing of participating contracts). In this mixed framework, policyholders are only partly protected against default consequences. Continuous and discrete protections are also studied in an early default Black and Cox-type setting. A comparative analysis of the impact of various protection schemes on ruin probabilities and severities of a life insurance company that sells only this class of contracts concludes this work. Journal: North American Actuarial Journal Pages: 131-149 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597581 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597581 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:131-149 Template-Type: ReDIF-Article 1.0 Author-Name: Simon Lee Author-X-Name-First: Simon Author-X-Name-Last: Lee Author-Name: X. Lin Author-X-Name-First: X. Author-X-Name-Last: Lin Title: Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions Abstract: In this paper we suggest the use of mixtures of Erlang distributions with common scale parameter to model insurance losses. A modified expectation-maximization (EM) algorithm for parameter estimation tailored to this class of distributions is presented, and its computation efficiency is discussed. Goodness-of-fit tests are performed for data generated from some common parametric distributions and for catastrophic loss data in the United States. Formulas for value-at-risk and conditional tail expectation are provided for individual and aggregate losses. Journal: North American Actuarial Journal Pages: 107-130 Issue: 1 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597580 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597580 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:107-130 Template-Type: ReDIF-Article 1.0 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: Regression Models for Bivariate Loss Data Abstract: This case study illustrates the analysis of two possible regression models for bivariate claims data. Estimates or forecasts of loss distributions under these two models are developed using two methods of analysis: (1) maximum likelihood estimation and (2) the Bayesian method. These methods are applied to two data sets consisting of 24 and 1,500 paired observations, respectively. The Bayesian analyses are implemented using Markov chain Monte Carlo via WinBUGS, as discussed in Scollnik (2001). A comparison of the analyses reveals that forecasted total losses can be dramatically underestimated by the maximum likelihood estimation method because it ignores the inherent parameter uncertainty. Journal: North American Actuarial Journal Pages: 67-80 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596065 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596065 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:67-80 Template-Type: ReDIF-Article 1.0 Author-Name: Dan Segal Author-X-Name-First: Dan Author-X-Name-Last: Segal Title: An Economic Analysis of Life Insurance Company Expenses Abstract: This study provides an economic analysis of life insurance company expenses and develops a methodology for the construction of benchmark expense factors. These benchmarks can facilitate the pricing of new business, cost control within companies, and expense comparisons among companies. We derive the expense factors by estimating a cost function wherein total general expenses are modeled as a function of input prices and physical outputs, and the physical outputs are proxies for the cost drivers of the different lines of business. This methodology has two important advantages: first, the derived expense factors are independent of the methods that insurers use in allocating total expenses across lines of business. Second, the estimated cost function explicitly accounts for different degrees of economies of scale and consequently in the present value of marginal expenses across insurers. Hence, this study demonstrates that economies of scale and, in turn, size must be considered when constructing an expense table. Journal: North American Actuarial Journal Pages: 81-94 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596066 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596066 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:81-94 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Title: Efficient and Robust Fitting of Lognormal Distributions Abstract: In parametric modeling of loss distributions in actuarial science, a versatile choice with intermediate tail weight is the lognormal distribution. Surprisingly, however, the fitting of this model using estimators that are at once efficient and robust has not been seriously addressed in the extensive literature. Consequently, typical estimators of the lognormal mean and variance fail to be both efficient and robust. In particular, the highly efficient maximum likelihood estimators lack robustness because of their limited sensitivity to outliers in the sample. For the two-parameter lognormal estimation problem, the author considers the problem of efficient and robust joint estimation of the mean and variance of a normal model. He introduces generalized-median-type estimators that yield efficient and robust estimators of various parameters of interest in the lognormal model. The paper provides detailed treatment of the lognormal mean and discusses extension of the approach to the much more complicated problem of estimation for the three-parameter lognormal model. Journal: North American Actuarial Journal Pages: 95-109 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596067 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596067 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:95-109 Template-Type: ReDIF-Article 1.0 Author-Name: Maria Giuseppina Bruno Author-X-Name-First: Maria Giuseppina Author-X-Name-Last: Bruno Author-Name: Emanuela Camerini Author-X-Name-First: Emanuela Author-X-Name-Last: Camerini Author-Name: Alvaro Tomassetti Author-X-Name-First: Alvaro Author-X-Name-Last: Tomassetti Title: “Authors’ Reply: Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications,” Maria Giuseppina Bruno, Emanuela Camerini and Alvaro Tomassetti, October 2000 - Discussion by Fabrizio Cacciafesta Journal: North American Actuarial Journal Pages: 110-113 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596068 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596068 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:110-113 Template-Type: ReDIF-Article 1.0 Author-Name: Jean Lemaire Author-X-Name-First: Jean Author-X-Name-Last: Lemaire Title: Why Do Females Live Longer Than Males? Abstract: In most countries, females live several years longer than males. Many biological and behavioral reasons have been presented in the scientific literature to explain this “female advantage.” A cross-sectional regression study, using 45 explanatory variables and data collected from 169 countries, provides support to the behavioral hypothesis. Four variables, unrelated to biological sex differences, explain over 61% of the variability of the life expectancy differential. One variable (the number of persons per physician) summarizes the degree of economic development of a country. The three other selected variables (the fertility rate, the percentage of Hindus and Buddhists, and Europeans countries of the former Soviet Union) are social/cultural/religious variables. This conclusion is slightly weakened when the presence of spatial autocorrelation in the data is specifically acknowledged. Journal: North American Actuarial Journal Pages: 21-37 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596061 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596061 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:21-37 Template-Type: ReDIF-Article 1.0 Author-Name: Olivia Mitchell Author-X-Name-First: Olivia Author-X-Name-Last: Mitchell Author-Name: David McCarthy Author-X-Name-First: David Author-X-Name-Last: McCarthy Title: Estimating International Adverse Selection in Annuities Abstract: It is well known that purchasers of annuities have lower mortality than the general population. Less widely known is the quantitative extent of this adverse selection and how it varies across countries. This paper proposes and applies several methods for comparing alternative mortality tables and illustrates their impact on annuity valuation for men and women in the U.S. and the U.K. Our results indicate that the relatively lower mortality among older Americans who purchase annuities is equivalent to using a discount rate that is 50–100 basis points below the U.K. rate for compulsory annuitants or 10–20 basis points lower than the U.K. rate for voluntary annuitants. We then draw on the mortality experience of over half a billion lives to estimate mortality differentials due to varying degrees of adverse selection controlling for country, gender, and an allowance for mortality improvements. Results show that adverse selection associated with the purchase of individual annuities reduces mortality rates by at least 25% in the international context. We also find that the system of mortality tables used to value Japanese annuities is quite distinct from international norms.‡ Journal: North American Actuarial Journal Pages: 38-54 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596062 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596062 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:38-54 Template-Type: ReDIF-Article 1.0 Author-Name: S. David Promislow Author-X-Name-First: S. Author-X-Name-Last: David Promislow Title: “Response from: A Re-examination of the Joint Mortality Function,” Heekyung Youn, Arkady Shemyakin, and Edwin Herman,” January 2002 Journal: North American Actuarial Journal Pages: 117-117 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596072 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596072 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:117-117 Template-Type: ReDIF-Article 1.0 Author-Name: Brad Roudebush Author-X-Name-First: Brad Author-X-Name-Last: Roudebush Author-Name: John Klein Author-X-Name-First: John Author-X-Name-Last: Klein Title: Converting Clinical Literature to an Insured Population: A Comparison of Models Using Nhanes Abstract: The use of clinical literature to set risk classification standards for life insurance underwriting stems from the need to set the most accurate standards using the best available information. A necessary hurdle in this process is converting any excess mortality observed in a clinical study to the appropriate rating for use in underwriting. A widely accepted model in the insurance industry, the Excess Death Rate model, treats the excess as additive to the conditional probability of death for an insurance company’s unimpaired class.In this paper we test the validity of that model versus other common predictive models of excess mortality in an insured population. Applying these models to National Health and Nutrition Examination Survey (NHANES) data, we derive estimates for excess mortality from three commonly seen underwriting impairments in what could be considered a clinical population. These estimates are added to an estimate of an insurance company’s unimpaired mortality class and then used to predict deaths in an “insurable” subset of that clinical population.The Excess Death Rate model performed the best of all models, having the smallest cumulative difference of actual to predicted deaths. The use of publicly available data, such as that in NHANES, could help bridge the gap between clinical literature and its application in insurance underwriting if insurable cohorts can be reliably identified from these generally healthy, ambulatory groups. Journal: North American Actuarial Journal Pages: 55-65 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596063 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596063 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:55-65 Template-Type: ReDIF-Article 1.0 Author-Name: Grant Hemphill Author-X-Name-First: Grant Author-X-Name-Last: Hemphill Title: Converting Clinical Literature to an Insured Population: A Comparison of Models Using NHANES Journal: North American Actuarial Journal Pages: 65-66 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596064 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596064 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:65-66 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Donald Jones Author-X-Name-First: Donald Author-X-Name-Last: Jones Title: “A Re-examination of the Joint Mortality Function,” Heekyung Youn, Arkady Shemyakin, and Edwin Herman, January 2002 Journal: North American Actuarial Journal Pages: 113-114 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596069 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596069 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:113-114 Template-Type: ReDIF-Article 1.0 Author-Name: Enrique de Alba Author-X-Name-First: Enrique Author-X-Name-Last: de Alba Title: Bayesian Estimation of Outstanding Claim Reserves Abstract: This paper presents a Bayesian approach to forecasting outstanding claims, either the total number of claims or the total amount, that is used for claims reserving. The assumption is made that there is complete information for one or two past years of origin and partial information for some development years of other years of origin. It also assumes payments are made annually and that the development of partial payments follows a stable payoff pattern from one year of origin to another. Two different models are presented: one for the number of claims (intensity) and one for claim amounts (severity). The advantage of using this procedure is that actuaries can derive the complete predictive distribution of the reserve requirements, from which, in turn, it is possible to obtain point estimates as well as probability intervals and other summary measures, such as mean, variance, and quantiles. Journal: North American Actuarial Journal Pages: 1-20 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596060 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596060 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Heekyung Youn Author-X-Name-First: Heekyung Author-X-Name-Last: Youn Author-Name: Arkady Shemyakin Author-X-Name-First: Arkady Author-X-Name-Last: Shemyakin Author-Name: Edwin Herman Author-X-Name-First: Edwin Author-X-Name-Last: Herman Title: “Authors’ Reply: A Re-examination of the Joint Mortality Function,” Heekyung Youn, Arkady Shemyakin, and Edwin Herman,” January 2002 - Discussion by S. David Promislow Journal: North American Actuarial Journal Pages: 116-116 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596071 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596071 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:116-116 Template-Type: ReDIF-Article 1.0 Author-Name: S. David Promislow Author-X-Name-First: S. Author-X-Name-Last: David Promislow Title: “A Re-examination of the Joint Mortality Function,” Heekyung Youn, Arkady Shemyakin, and Edwin Herman, January 2002 Journal: North American Actuarial Journal Pages: 114-116 Issue: 4 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596070 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596070 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:114-116 Template-Type: ReDIF-Article 1.0 Author-Name: Chuancun Yin Author-X-Name-First: Chuancun Author-X-Name-Last: Yin Author-Name: Sung Nok Chiu Author-X-Name-First: Sung Nok Author-X-Name-Last: Chiu Title: “The Time Value of Ruin in a Sparre Andersen Model,’ Hans U. Gerber and Elias S. W. Shiu, April 2005 Journal: North American Actuarial Journal Pages: 134-136 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596233 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596233 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:134-136 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Title: “The Time Value of Ruin in a Sparre Andersen Model,’ Hans U. Gerber and Elias S. W. Shiu, April 2005 Journal: North American Actuarial Journal Pages: 131-134 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596232 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596232 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:131-134 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: Pension Plan Termination and Retirement Abstract: Employee termination and retirement probabilities affect the valuation of employee benefit plans and thus are of concern to actuaries. To provide timely experience for the profession, the Society of Actuaries’ Non-Mortality Decrement Task Force organized a data collection effort. Thirty-two contributors provided over 1.7 million life years of pension plan turnover data for years 1994–2000. This article summarizes the results of this data collection effort.Traditionally, the most important determinants of termination and retirement are age, a proxy for attachment to the workforce, and service, a measure of attachment to a firm. This article documents the importance of these traditional quantities using current data and provides tables so that actuaries may quantitatively assess their importance when valuing pension plans.For the middle working years, ages 25–55, we find female termination probabilities are higher than males, although the differences are smaller than has been true historically. The differences are insignificant for the younger working years or early service years. Moreover, for ages 55 and older, males have higher retirement probabilities than females.We also document the effect of several plan characteristics: eligibility for postretirement health benefits, benefit formula, hourly/salary and union status, as well as plan size. To assess the effects of plan characteristics while controlling for age, service, and gender, we use multinomial logit analysis, a regression methodology suitable for categorical outcomes. We find that small plans have slightly higher termination probabilities compared to medium and large plans (plan size is our proxy for employer size). Union hourly plans have lower termination probabilities than salaried plans; in turn, salaried plans have lower termination probabilities than nonunion hourly plans. Firms that offer richer benefits enjoy lower turnover.The data for this study were gathered using a traditional industry experience studies approach. To highlight the strengths and weaknesses of this approach, we compare this data set to several government sponsored probability samples on job turnover. In general, these samples are smaller and thus provide less credible estimates yet they allow the analyst to explore the complex interactions of the effects of several variables on turnover. Journal: North American Actuarial Journal Pages: 1-27 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596222 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:1-27 Template-Type: ReDIF-Article 1.0 Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: M. Zaki Khorasanee Author-X-Name-First: M. Author-X-Name-Last: Zaki Khorasanee Title: “Pensions and Capital Structure: Why Hold Equities in the Pension Fund?”, John Ralfe, Cliff Speed, and Jon Palin, July 2004 Journal: North American Actuarial Journal Pages: 125-130 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596231 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596231 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:125-130 Template-Type: ReDIF-Article 1.0 Author-Name: Frank Bensics Author-X-Name-First: Frank Author-X-Name-Last: Bensics Title: “Pensions and Capital Structure: Why Hold Equities in the Pension Fund?”, John Ralfe, Cliff Speed, and Jon Palin, July 2004 Journal: North American Actuarial Journal Pages: 123-125 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596230 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596230 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:123-125 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Joss Author-X-Name-First: Paul Author-X-Name-Last: Joss Title: The Earnings Implications of Pension Expense Abstract: Recent challenges to the actuarial pension model and a movement to harmonize international accounting standards both suggest that the current Canadian standards for pension accounting, CICA 3461, may see substantial revision during upcoming years. To understand better the implications of these possible accounting changes, this paper presents the results of a stochastic analysis that quantifies how the volatility of pension expense for a sample of ten Canadian companies sponsoring defined benefit plans will be increased by the adoption of immediate recognition accounting. For certain companies this increase is significant and is shown to have a material earnings impact. The implications of this earnings volatility for the future of defined benefit pension plans are also explored. Journal: North American Actuarial Journal Pages: 43-55 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596224 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596224 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:43-55 Template-Type: ReDIF-Article 1.0 Author-Name: Na Jia Author-X-Name-First: Na Author-X-Name-Last: Jia Author-Name: Lawrence Tsui Author-X-Name-First: Lawrence Author-X-Name-Last: Tsui Title: Epidemic Modelling using Sars as a Case Study Abstract: The recent Severe Acute Respiratory Syndrome (SARS) epidemic has highlighted a new dimension to the risks confronting insurance companies. Conventional approaches to insurance pricing take an almost exclusively retrospective view of future mortality experience, extrapolating past mortality trends into the future. Such an approach fails to take account of mortality shocks such as epidemics, which may arise spontaneously and that are not reflected in past experience. If actuaries are to maintain their position as risk experts in an ever-changing world, it is important for the actuarial profession to adopt a more comprehensive approach to assessing risks that goes beyond past experience.This paper will take a look at the modelling of epidemics, using SARS as a case study, and will examine the potential impact of SARS and similar epidemics on insurance companies. Journal: North American Actuarial Journal Pages: 28-42 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596223 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596223 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:28-42 Template-Type: ReDIF-Article 1.0 Author-Name: Howard Bolnick Author-X-Name-First: Howard Author-X-Name-Last: Bolnick Title: A Health Research Agenda Journal: North American Actuarial Journal Pages: iii-v Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596235 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596235 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:iii-v Template-Type: ReDIF-Article 1.0 Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Author-Name: Tom Hoedemakers Author-X-Name-First: Tom Author-X-Name-Last: Hoedemakers Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Title: Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables Abstract: In this paper we consider different approximations for computing the distribution function or risk measures related to a discrete sum of nonindependent lognormal random variables. Comonotonic upper and lower bound approximations for such sums have been proposed in Dhaene et al. (2002a,b). We introduce the comonotonic “maximal variance” lower bound approximation. We also compare the comonotonic approximations with two well-known moment-matching approximations: the lognormal and the reciprocal Gamma approximations. We find that for a wide range of parameter values the comonotonic “maximal variance” lower bound approximation outperforms the other approximations. Journal: North American Actuarial Journal Pages: 71-82 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596226 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596226 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:71-82 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors' Reply: The Time Value of Ruin in a Sparre Andersen Model, Hans U. Gerber and Elias S. W. Shiu, April 2005 - Discussion by Andrew C. Y. Ng, Chuancun Yin, and Sung Nok Chiu Journal: North American Actuarial Journal Pages: 136-136 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596234 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596234 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:136-136 Template-Type: ReDIF-Article 1.0 Author-Name: Changki Kim Author-X-Name-First: Changki Author-X-Name-Last: Kim Title: Modeling Surrender and Lapse Rates With Economic Variables Abstract: This paper presents surrender rate models with explanatory variables such as the difference between reference and crediting rates, policy age since issue, financial crises, unemployment and economy growth rates, and seasonal effects. The logit function and the complementary log-log function are used in modeling surrender rates.This paper shows that the logit model and the complementary log-log model generally perform better than the existing surrender rate models such as the arctangent model. It also shows that the surrender rate models are different according to insurance policy types, and it finds proper surrender rate models for four insurance groups: protection plans, education plans, endowment, and annuities. Journal: North American Actuarial Journal Pages: 56-70 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596225 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596225 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:56-70 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: On a Classical Risk Model with a Constant Dividend Barrier Abstract: This paper considers a risk model with a constant dividend barrier. It first points out interesting connections between some previous results for this model and those for spectrally negative Lévy processes. An expression is then obtained for the joint distribution of the surplus immediately prior to ruin and the deficit at ruin, discounted from the time of ruin. Such an expression involves known results on the joint distribution at ruin for a classical risk model without barrier. Also discussed are the joint distributions related to the time periods when dividends are paid. In particular, this paper obtains the Laplace transform for the total dividend payments until ruin, and another expression for the expected present value of the total amount of dividend payments until ruin. The results do not require the positive loading condition. Journal: North American Actuarial Journal Pages: 95-108 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596228 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596228 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:95-108 Template-Type: ReDIF-Article 1.0 Author-Name: Albert Wong Author-X-Name-First: Albert Author-X-Name-Last: Wong Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Title: Mixture Gaussian Time Series Modeling of Long-Term Market Returns Abstract: Stochastic modeling of investment returns is an important topic for actuaries who deal with variable annuity and segregated fund investment guarantees. The traditional lognormal stock return model is simple, but it is generally less appealing for longer-term problems. In recent years, the use of regime-switching lognormal (RSLN) processes for modeling maturity guarantees has been gaining popularity. In this paper we introduce the class of mixture Gaussian time series processes for modeling long-term stock market returns. It offers an alternative class of models to actuaries who may be experimenting with the RSLN process. We use monthly data from the Toronto Stock Exchange 300 and the Standard and Poor-s 500 indices to illustrate the mixture time series modeling procedures, and we compare the fits of the mixture models to the lognormal and RSLN models. Finally, we give a numerical example comparing risk measures for a simple segregated fund contract under different stochastic return models. Journal: North American Actuarial Journal Pages: 83-94 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596227 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596227 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:83-94 Template-Type: ReDIF-Article 1.0 Author-Name: Moshe Milevsky Author-X-Name-First: Moshe Author-X-Name-Last: Milevsky Title: Real Longevity Insurance with a Deductible: Introduction to Advanced-Life Delayed Annuities (ALDA) Abstract: This paper explores the financial properties of a concept product called an advanced-life delayed annuity (ALDA). The ALDA is a variant of a pure deferred annuity contract that is acquired by installments, adjusted for consumer price inflation, and pays off toward the end of the human life cycle. The ALDA concept is aimed at the growing population of North Americans without access to a traditional defined benefit (DB) pension plan and the implicit longevity insurance that a DB plan contains. I show that under quite reasonable pricing assumptions, a consumer can invest or allocate $1 per month, while saving for retirement, and receive between $20 and $40 per month in benefits, assuming the deductible in this insurance policy is set high enough. The ALDA concept might go a long way in mitigating the psychological barrier to voluntary lump-sum annuitization. Journal: North American Actuarial Journal Pages: 109-122 Issue: 4 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596229 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596229 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:109-122 Template-Type: ReDIF-Article 1.0 Author-Name: Uditha Balasooriya Author-X-Name-First: Uditha Author-X-Name-Last: Balasooriya Author-Name: Chan-Kee Low Author-X-Name-First: Chan-Kee Author-X-Name-Last: Low Title: Modeling Insurance Claims with Extreme Observations: Transformed Kernel Density and Generalized Lambda Distribution Abstract: In modeling insurance claims, when there are extreme observations in the data, the commonly used loss distributions often are able to fit the bulk of the data well but fail to do so at the tail. One approach to overcome this problem is to focus on the extreme observations only and model them with the generalized Pareto distribution, as supported by extreme value theory. However, this approach discards useful information about the small and medium-sized claims, which is important for many actuarial purposes. In this article we consider modeling large skewed data using a highly flexible distribution, the generalized lambda distribution, and the recently proposed semiparametric transformed kernel density estimation. Our results suggest that both these approaches are credible options for the investigator when modeling insurance claims data that typically contain large extreme observations. In addition, even at the extreme tails they perform well when compared with the generalized Pareto distribution. Journal: North American Actuarial Journal Pages: 129-142 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597507 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:129-142 Template-Type: ReDIF-Article 1.0 Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals Abstract: We present an explicit formula for the Laplace transform of the distribution of the aggregate discounted claims when interclaim times follow a Markovian arrival process. In addition, we derive explicit formulas for the first two moments and then show that the higher moments may be obtained by numerically solving a system of ordinary differential equations. Journal: North American Actuarial Journal Pages: 198-206 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597510 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597510 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:198-206 Template-Type: ReDIF-Article 1.0 Author-Name: Shangzhen Luo Author-X-Name-First: Shangzhen Author-X-Name-Last: Luo Title: Ruin Minimization for Insurers with Borrowing Constraints Abstract: We consider an optimal dynamic control problem for an insurance company with opportunities of proportional reinsurance and investment. The company can purchase proportional reinsurance to reduce its risk level and invest its surplus in a financial market that has a Black-Scholes risky asset and a risk-free asset. When investing in the risk-free asset, three practical borrowing constraints are studied individually: (B1) the borrowing rate is higher than lending (saving) rate, (B2) the dollar amount borrowed is no more than K > 0, and (B3) the proportion of the borrowed amount to the surplus level is no more than k > 0. Under each of the constraints, the objective is to minimize the probability of ruin. Classical stochastic control theory is applied to solve the problem. Specifically, the minimal ruin probability functions are obtained in closed form by solving Hamilton-Jacobi-Bellman (HJB) equations, and their associated optimal reinsurance-investment policies are found by verification techniques. Journal: North American Actuarial Journal Pages: 143-174 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597508 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597508 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:143-174 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals,” Jiandong Ren April 2008 Journal: North American Actuarial Journal Pages: 206-207 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597511 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597511 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:206-207 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Merz Author-X-Name-First: Michael Author-X-Name-Last: Merz Author-Name: Mario Wüthrich Author-X-Name-First: Mario Author-X-Name-Last: Wüthrich Title: Prediction Error of the Multivariate Chain Ladder Reserving Method Abstract: In this paper we consider the claims reserving problem in a multivariate context: that is, we study the multivariate chain-ladder (CL) method for a portfolio of N correlated runoff triangles based on multivariate age-to-age factors. This method allows for a simultaneous study of individual runoff subportfolios and facilitates the derivation of an estimator for the mean square error of prediction (MSEP) for the CL predictor of the ultimate claim of the total portfolio. However, unlike the already existing approaches we replace the univariate CL predictors with multivariate ones. These multivariate CL predictors reflect the correlation structure between the subportfolios and are optimal in terms of a classical optimality criterion, which leads to an improvement of the estimator for the MSEP. Moreover, all formulas are easy to implement on a spreadsheet because they are in matrix notation. We illustrate the results by means of an example. Journal: North American Actuarial Journal Pages: 175-197 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597509 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597509 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:175-197 Template-Type: ReDIF-Article 1.0 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: “The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model,” Jiandong Ren, July 2007 Journal: North American Actuarial Journal Pages: 208-210 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597512 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597512 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:208-210 Template-Type: ReDIF-Article 1.0 Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Title: “The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model,” Jiandong Ren, July 2007 Journal: North American Actuarial Journal Pages: 210-212 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597513 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597513 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:210-212 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Title: “Asset Allocation with Hedge Funds on the Menu,” Phelim Boyle and Sun Siang Liew, October 2007 Journal: North American Actuarial Journal Pages: 213-215 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597514 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597514 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:213-215 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Authors’ Reply: On Optimal Dividend Strategies in the Compound Poisson Model - Discussion by Bangwon Ko, July 2006 Journal: North American Actuarial Journal Pages: 216-219 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597515 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597515 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:216-219 Template-Type: ReDIF-Article 1.0 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Title: Gerard Cornuejols and Reha Tütüncü Journal: North American Actuarial Journal Pages: 220-220 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597516 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597516 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:220-220 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Schobel Author-X-Name-First: Bruce Author-X-Name-Last: Schobel Title: Editorial Journal: North American Actuarial Journal Pages: iii-iii Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597517 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597517 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Liang Peng Author-X-Name-First: Liang Author-X-Name-Last: Peng Title: Estimating the Probability of a Rare Event via Elliptical Copulas Abstract: A rare event happens with an extremely small probability but may cost billions of dollars. How to model and estimate the small probability of such an event is of importance to the insurance industry. Based on multivariate extreme value theory, methods have been proposed to extrapolate data into a far tail region. However, questions still remain open, such as the direction of extrapolation for a multivariate distribution and threshold selection for both marginals and the tail dependence function. In this paper we provide a way to estimate the probability of a rare event via modeling marginals and dependence by heavy tailed distributions and elliptical copulas, respectively. Hence, the direction of extrapolation becomes irrelevant. Moreover we employ recent threshold selection procedures to choose tuning parameters automatically. Journal: North American Actuarial Journal Pages: 116-128 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597506 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597506 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:116-128 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: Threshold Life Tables and Their Applications Abstract: The rapid emergence of centenarians has highlighted the importance of survival probabilities at extreme ages and has motivated actuaries to look for alternative ways to close of life tables in place of assigning a death probability of 1 at an arbitrarily chosen age. Using the asymptotic results of modern extreme value theory, we propose a model, which we call the threshold life table, to extrapolate survival distributions to extreme ages and to determine the appropriate end point of a life table. By combining the threshold life table with the Lee-Carter model for stochastic mortality forecasting, we consider applications to the valuation of a life annuity portfolio and to the prediction of the highest attained age. We illustrate the theoretical results using U.S., Canadian, and Japanese mortality data. Journal: North American Actuarial Journal Pages: 99-115 Issue: 2 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597505 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597505 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:99-115 Template-Type: ReDIF-Article 1.0 Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Author-Name: Lihong Zhang Author-X-Name-First: Lihong Author-X-Name-Last: Zhang Title: The Joint Distribution of Surplus Immediately before Ruin and the Deficit at Ruin under Interest Force Abstract: In this paper we consider a compound Poisson risk model with a constant interest force. We investigate the joint distribution of the surplus immediately before and after ruin. By adapting the techniques in Sundt and Teugels (1995), we obtain integral equations satisfied by the joint distribution function and a Lundberg-type inequality. In the case of zero initial reserve and the case of exponential claim sizes, we obtain explicit expressions for the joint distribution function. Journal: North American Actuarial Journal Pages: 92-103 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596001 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:92-103 Template-Type: ReDIF-Article 1.0 Author-Name: Yong Yao Author-X-Name-First: Yong Author-X-Name-Last: Yao Title: State Price Density, Esscher Transforms, and Pricing Options on Stocks, Bonds, and Foreign Exchange Rates Abstract: The state price density is modeled as an exponential function of the underlying state variables, and the Esscher transform is used to specify the forward-risk-adjusted measure. With the aid of state price densities, Esscher transforms, and characteristic functions, this paper provides a consistent framework for pricing options on stocks, interest rates, and foreign exchange rates. The framework discussed is quite general and is related to many popular models. Journal: North American Actuarial Journal Pages: 104-117 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596002 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:104-117 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Howell Tong Author-X-Name-First: Howell Author-X-Name-Last: Tong Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Bayesian Risk Measures for Derivatives via Random Esscher Transform Abstract: This paper proposes a model for measuring risks for derivatives that is easy to implement and satisfies a set of four coherent properties introduced in Artzner et al. (1999). We construct our model within the context of Gerber-Shiu’s option-pricing framework. A new concept, namely Bayesian Esscher scenarios, which extends the concept of generalized scenarios, is introduced via a random Esscher transform. Our risk measure involves the use of the risk-neutral Bayesian Esscher scenario for pricing and a family of real-world Bayesian Esscher scenarios for risk measurement. Closed-form expressions for our risk measure can be obtained in some special cases. Journal: North American Actuarial Journal Pages: 78-91 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596000 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596000 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:78-91 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Jianxun Liu Author-X-Name-First: Jianxun Author-X-Name-Last: Liu Title: The Shift to Defined Contribution Pension Plans Abstract: There has been a strong shift away from defined benefit (DB) pension plans toward defined contribution (DC) pension plans in the United States over the last 20 years. A variety of reasons for this shift have been proposed. In another paper in this issue, Krzysztof Ostaszewski presents a new hypothesis to explain the shift to DC plans in the United States. He argues that the decline in importance of DB plans is due to a shift in the way relative returns to macroeconomic factors of production, that is, capital and labor, are being rewarded in the national economy.This paper attempts to test the Ostaszewski hypothesis using Canadian data. In Canada there has been only a slight decrease in DB plan coverage. It is shown that the Ostaszewski theory does not fit the Canadian experience well. Instead, it is argued that pension regulation and tax legislation play a crucial role in pension design and reform. It is also argued that the difference in pension regulation and taxation in Canada versus the United States has directly influenced plan sponsors in considering their pension objectives, costs, and risks. Differences in the proportion of the workforce that is unionized may also be important. The paper concludes that pension regulation and taxation are more important variables than are macroeconomic reward systems in the use of DB versus DC pension plans. Journal: North American Actuarial Journal Pages: 65-77 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595999 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595999 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:65-77 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution - Discussion by Vytaras Brazauskas; Robert Serfling Journal: North American Actuarial Journal Pages: 126-128 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596005 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596005 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:126-128 Template-Type: ReDIF-Article 1.0 Author-Name: Krzysztof Ostaszewski Author-X-Name-First: Krzysztof Author-X-Name-Last: Ostaszewski Title: Macroeconomic Aspects of Private Retirement Programs Abstract: The decline in importance of private defined benefit plans in relation to defined contribution plans in the United States is a major issue of interest to pension actuaries. This decline has been attributed to numerous factors: costs of government regulation, societal and cultural changes, changed employer attitudes, and employees’ lack of understanding of defined benefit plans. It has also caused some observers to proclaim the end of private defined benefit plans. This paper analyzes possible macroeconomic factors contributing to the crisis of defined benefit plans and proposes an alternative hypothesis for the cause of the crisis: the decline of the relative attractiveness of defined benefit plans in relation to defined contribution plans when these are viewed as investments, that is, as securities in capital markets. Journal: North American Actuarial Journal Pages: 52-64 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595998 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595998 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:52-64 Template-Type: ReDIF-Article 1.0 Author-Name: Ya-Chun Huang Author-X-Name-First: Ya-Chun Author-X-Name-Last: Huang Title: “Valuing Equity-Indexed Annuities,” Serena Tiong, October 2000 Journal: North American Actuarial Journal Pages: 128-133 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596006 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596006 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:128-133 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Dynamic Fund Protection”, Junichi Imai; Phelim P. Boyle, July 2001 Journal: North American Actuarial Journal Pages: 49-51 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595997 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595997 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:49-51 Template-Type: ReDIF-Article 1.0 Author-Name: David Lange Author-X-Name-First: David Author-X-Name-Last: Lange Author-Name: Betty Simkins Author-X-Name-First: Betty Author-X-Name-Last: Simkins Title: “Calculating Funding Premiums for Universal Life Insurance,” Calvin Cherry, April 2000 Journal: North American Actuarial Journal Pages: 118-122 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596003 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596003 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:118-122 Template-Type: ReDIF-Article 1.0 Author-Name: Junichi Imai Author-X-Name-First: Junichi Author-X-Name-Last: Imai Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Title: Dynamic Fund Protection Abstract: Dynamic fund protection provides an investor with a floor level of protection during the investment period. This feature generalizes the concept of a put option, which provides only a floor value at a particular time. The dynamic protection feature ensures that the fund value is upgraded if it ever falls below a certain threshold level. Gerber and Pafumi (2000) have recently derived a closed-form expression for the price of this protection when the basic portfolio follows geometric Brownian motion. In this paper we examine the pricing of this feature under the constant elasticity of variance process. Two approaches are used to obtain numerical results. First, we show how to extend the basic Monte Carlo approach to handle the particular features of dynamic protection. When a discrete-time simulation approach is used to value a derivative that is subject to continuous monitoring, there is a bias. We show how to remove this bias. Second, a partial differential equation approach is used to price dynamic protection. We demonstrate that the price of the dynamic protection is sensitive to the investment assumptions. We also discuss a discrete time modification of the dynamic protection feature that is suitable for practical implementation. The paper deals just with pricing and does not consider the important question of reserving for these contracts. Journal: North American Actuarial Journal Pages: 31-47 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595996 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595996 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:31-47 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Bilodeau Author-X-Name-First: Martin Author-X-Name-Last: Bilodeau Title: “Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution,” Vytaras Brazauskas and Robert Serfling, October 2000. Journal: North American Actuarial Journal Pages: 123-126 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596004 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596004 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:123-126 Template-Type: ReDIF-Article 1.0 Author-Name: J. F. Carrière Author-X-Name-First: J. F. Author-X-Name-Last: Carrière Title: A Gaussian Process of Yield Rates Calibrated with Strips Abstract: This paper presents a Gaussian multivariate factor model of the term structure of interest rates. It shows that there exists a martingale valuation law of the factors so that the price function of a zero-coupon bond is an exponential spline. The model’s linear and Gaussian structure yields a simple model where estimation and calibration are relatively easy to do. Using yield data on stripped bonds, the spline model gives a very good approximation of the yield curve at all times. Moreover, the crucial Gaussian assumption is reasonable when modeling the dynamics for short periods like one year. Journal: North American Actuarial Journal Pages: 19-30 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595995 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595995 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:19-30 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Adam Kolkiewicz Author-X-Name-First: Adam Author-X-Name-Last: Kolkiewicz Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: Valuation of the Reset Options Embedded in Some Equity-Linked Insurance Products Abstract: This paper proposes a method for valuing American options using a Monte Carlo simulation approach. Our approach can be used to price the reset feature found in some equity-linked insurance contracts. We model this feature as a multiple shout option and give examples based on certain equity-linked insurance products that are very popular in Canada. These contracts are known as segregated fund contracts and the valuation of the embedded options in these contracts has posed serious challenges for actuaries. One of the advantages of the Monte Carlo approach in this connection is that it can be extended to handle different investment assumptions as well as multiple assets. We show how to modify the stochastic mesh model of Broadie and Glasserman (1997b) to incorporate quasi-Monte Carlo in the simulation and thus improve the efficiency. We benchmark the efficiency gains in our method using standard American options and multiple shout options. Journal: North American Actuarial Journal Pages: 1-18 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595994 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595994 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:1-18 Template-Type: ReDIF-Article 1.0 Author-Name: Hangsuck Lee Author-X-Name-First: Hangsuck Author-X-Name-Last: Lee Title: “Valuing Equity-Indexed Annuities,” Serena Tiong, October 2000 Journal: North American Actuarial Journal Pages: 133-136 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596007 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596007 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:133-136 Template-Type: ReDIF-Article 1.0 Author-Name: S. David Promislow Author-X-Name-First: S. Author-X-Name-Last: David Promislow Title: Stampfli, Joseph, and Goodman, Victor, 2001, Journal: North American Actuarial Journal Pages: 137-138 Issue: 3 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596008 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596008 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:137-138 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Robert Miller Author-X-Name-First: Robert Author-X-Name-Last: Miller Title: Authors’ Reply: Designing Effective Graphs - Discussion by William C. Cutlip; Douglas A. Eckley; Gary S. Lange; Edward M. Mailander; Alexander J. McNeil; Arnold F. Shapiro; Edward B. Kleinman Journal: North American Actuarial Journal Pages: 76-76 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595706 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595706 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:76-76 Template-Type: ReDIF-Article 1.0 Author-Name: Arnold Shapiro Author-X-Name-First: Arnold Author-X-Name-Last: Shapiro Author-Name: Edward Kleinman Author-X-Name-First: Edward Author-X-Name-Last: Kleinman Title: “Designing Effective Graphs”, Edward W. Frees and Robert B. Miller, April 1998 Journal: North American Actuarial Journal Pages: 74-76 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595705 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595705 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:74-76 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander McNeil Author-X-Name-First: Alexander Author-X-Name-Last: McNeil Title: “Designing Effective Graphs”, Edward W. Frees and Robert B. Miller, April 1998 Journal: North American Actuarial Journal Pages: 73-74 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595704 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595704 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:73-74 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Mailander Author-X-Name-First: Edward Author-X-Name-Last: Mailander Title: “Designing Effective Graphs”, Edward W. Frees and Robert B. Miller, April 1998 Journal: North American Actuarial Journal Pages: 72-72 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595703 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595703 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:72-72 Template-Type: ReDIF-Article 1.0 Author-Name: Alfred Raws Author-X-Name-First: Alfred Author-X-Name-Last: Raws Title: Overview of Reserving Practices for Substandard Life Policies Abstract: This paper reviews the various industry practices, both past and current, for determining statutory reserves for substandard life insurance policies This review begins with single-life policies but also considers the application of single-life practice to joint-life policies The increased popularity of joint-life policies has taken place without much discussion in the technical journals of how to handle such issues as reserves on substandard business. This paper is intended to provoke such a discussion and to provide a framework for it. Journal: North American Actuarial Journal Pages: 102-108 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595709 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595709 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:102-108 Template-Type: ReDIF-Article 1.0 Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Title: An Actuarial Index of the Right-Tail Risk Abstract: A common characteristic for many insurance risks is the right-tail risk, representing low-frequency, large-loss events. In this paper I propose a measure of the right-tail risk by defining the right-tail deviation and the right-tail index. I explain how the right-tail deviation measures the right-tail risk and compare it to traditional measures such as standard deviation, the Gini mean, and the expected policyholder deficit. The right-tail index is applied to some common parametric families of loss distributions. Journal: North American Actuarial Journal Pages: 88-101 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595708 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:88-101 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Title: A Statistical Control Model for Utilization Management Programs Abstract: A new approach is proposed for monitoring health-care costs to help in cost containment efforts. This informative essay is intended to provide information on and stimulate discussion of ways of improving the health-care management process.Data that are being collected by insurers and providers could be used to analyze and improve the health-care process. New statistical techniques, and better, more consistent input of data, will be critical to successful utilization management programs. Necessary conditions for the success of the new methods are (1) diagnosis protocols that are “true gold standards,” (2) a satisfactory disease classification system, (3) meaningful and consistently coded data, and (4) statistical methodology that takes advantage of as much of the available data as possible. The hospital admissions process is illustrated to show the incorporation of an inexpensive statistical control process for reducing the incidence of unnecessary hospitalizations. Journal: North American Actuarial Journal Pages: 77-87 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595707 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:77-87 Template-Type: ReDIF-Article 1.0 Author-Name: Douglas Eckley Author-X-Name-First: Douglas Author-X-Name-Last: Eckley Title: “Designing Effective Graphs”, Edward W. Frees and Robert B. Miller, April 1998 Abstract: Journal: North American Actuarial Journal Pages: 71-71 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595701 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595701 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:71-71 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Lange Author-X-Name-First: Gary Author-X-Name-Last: Lange Title: “Designing Effective Graphs”, Edward W. Frees and Robert B. Miller, April 1998 Journal: North American Actuarial Journal Pages: 71-72 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595702 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595702 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:71-72 Template-Type: ReDIF-Article 1.0 Author-Name: William Cutlip Author-X-Name-First: William Author-X-Name-Last: Cutlip Title: “Designing Effective Graphs”, Edward W. Frees and Robert B. Miller, April 1998 Journal: North American Actuarial Journal Pages: 70-71 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595700 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595700 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:70-71 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Robert Miller Author-X-Name-First: Robert Author-X-Name-Last: Miller Title: Designing Effective Graphs Abstract: Actuaries, like other business professionals, communicate quantitative ideas graphically. Because the process of reading, or decoding, graphs is more complex than reading text, graphs are vulnerable to abuse. To underscore this vulnerability, we give several examples of commonly encountered graphs that mislead and hide information. To help creators design more effective graphs and to help viewers recognize misleading graphs, this article summarizes guidelines for designing graphs that show important numerical information. When designing graphs, creators should:(1) Avoid chartjunk(2) Use small multiples to promote comparisons and assess change(3) Use complex graphs to portray complex patterns(4) Relate graph size to information content(5) Use graphical forms that promote comparisons(6) Integrate graphs and text(7) Demonstrate an important message(8) Know the audience.Some of these guidelines for designing effective graphs, such as (6), (7) and (8), are drawn directly from principles for effective writing. Others, such as guidelines (3), (4) and (5), come from cognitive psychology, the science of perception. Guidelines (1) and (2) have roots both in effective writing and in graphical perception. For example, the writing principle of brevity demonstrates how eliminating pseudo three-dimensional perspectives and other forms of chartjunk improve graphs. As another example, the writing principle of parallel structure suggests using small multiple variations of a basic graphical form to visualize complex relationships across different groups and over time.To underscore the scientific aspect of graphical perception, we examine the process of communicating with a graph, beginning with a sender’s interpretation of data and ending with a receiver’s interpretation of the graph. In keeping with scientific tradition, this article discusses several studies in the literature on the effectiveness of graphs.We conclude that the actuarial profession has many opportunities to improve its practice, making communication more efficient and precise. Journal: North American Actuarial Journal Pages: 53-70 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595699 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595699 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:53-70 Template-Type: ReDIF-Article 1.0 Author-Name: Leda Minkova Author-X-Name-First: Leda Author-X-Name-Last: Minkova Author-Name: Nikolai Kolev Author-X-Name-First: Nikolai Author-X-Name-Last: Kolev Title: “Relative Importance of Risk Sources in Insurance Systems”, Edward W. Frees, April 1998 Journal: North American Actuarial Journal Pages: 50-51 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595697 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595697 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:50-51 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: Author’s Reply: Relative Importance of Risk Sources in Insurance Systems - Discussion by Emilia Di Lorenzo; Griselda Deelstra; Leda Minkova; Nikolai Kolev Journal: North American Actuarial Journal Pages: 51-52 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595698 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595698 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:51-52 Template-Type: ReDIF-Article 1.0 Author-Name: Emilia Di Lorenzo Author-X-Name-First: Emilia Author-X-Name-Last: Di Lorenzo Title: “Relative Importance of Risk Sources in Insurance Systems”, Edward W. Frees, April 1998 Journal: North American Actuarial Journal Pages: 49-49 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595695 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595695 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:49-49 Template-Type: ReDIF-Article 1.0 Author-Name: Griselda Deelstra Author-X-Name-First: Griselda Author-X-Name-Last: Deelstra Title: “Relative Importance of Risk Sources in Insurance Systems”, Edward W. Frees, April 1998 Journal: North American Actuarial Journal Pages: 49-50 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595696 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595696 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:49-50 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Social Security: Regressive or Progressive? - Discussion by John Beekman; Bernard Dussault; Kenneth Manton; Kenneth Land; Robert Myers; Krzysztof Ostaszewski Journal: North American Actuarial Journal Pages: 31-33 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595693 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595693 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:31-33 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: Relative Importance of Risk Sources in Insurance Systems Abstract: Actuaries, and other managers of uncertainty, identify factors in modeling insurance risks because they believe (1) that these factors affect the outcome of a risk or (2) that the factors can be managed, thus allowing analysts a degree of control over the insurance system. This paper shows how to use a statistical measure, the coefficient of determination, for quantifying the relative importance of a source of uncertainty. With a quantitative measure of relative importance, risk managers can sharpen their intuition about the relative importance of risk factors and become better custodians of financial security systems.This paper shows that the coefficient of determination is intuitively appealing in assessing the effectiveness of basic risk management techniques including risk exchange, pooling, and financial risk management. A single source common to all risks reduces the effectiveness of a pool; the risk measure quantifies the relative importance of this common source. The coefficient of determination is shown to have roots in the economics as well as the statistics literature. This connection provides further motivation for using the coefficient of determination and also suggests alternative measures for quantifying relative importance. The risk measure is useful in multivariate situations in which several factors affect a risk simultaneously. The paper illustrates this usefulness by considering a pool of policies that is subject to mortality, a common disaster, and a common investment environment. Journal: North American Actuarial Journal Pages: 34-49 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595694 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595694 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:34-49 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: “Social Security: Regressive or Progressive?”, Robert L. Brown, April 1998 Journal: North American Actuarial Journal Pages: 28-30 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595691 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595691 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:28-30 Template-Type: ReDIF-Article 1.0 Author-Name: Krzysztof Ostaszewski Author-X-Name-First: Krzysztof Author-X-Name-Last: Ostaszewski Title: “Social Security: Regressive or Progressive?”, Robert L. Brown, April 1998 Journal: North American Actuarial Journal Pages: 30-31 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595692 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595692 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:30-31 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Wang Author-X-Name-First: Joseph Author-X-Name-Last: Wang Title: “Complex Dynamics, Market Mediation and Stock Price Behavior”, Richard H. Day, July 1997 Journal: North American Actuarial Journal Pages: 117-118 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595715 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595715 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:117-118 Template-Type: ReDIF-Article 1.0 Author-Name: John Pemberton Author-X-Name-First: John Author-X-Name-Last: Pemberton Title: “Current Actuarial Modeling Practice and Related Issues and Questions”, Angus Macdonald, July 1997 Journal: North American Actuarial Journal Pages: 116-117 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595714 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595714 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:116-117 Template-Type: ReDIF-Article 1.0 Author-Name: Kenneth Manton Author-X-Name-First: Kenneth Author-X-Name-Last: Manton Author-Name: Kenneth Land Author-X-Name-First: Kenneth Author-X-Name-Last: Land Title: “Social Security: Regressive or Progressive?”, Robert L. Brown, April 1998 Journal: North American Actuarial Journal Pages: 27-28 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595690 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595690 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:27-28 Template-Type: ReDIF-Article 1.0 Author-Name: David Creswell Author-X-Name-First: David Author-X-Name-Last: Creswell Title: “Risk-Adjusted Economic Value Analysis,” Alastair Longley-Cook, January 1998 Abstract: Journal: North American Actuarial Journal Pages: 111-113 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595710 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595710 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:111-113 Template-Type: ReDIF-Article 1.0 Author-Name: Alastair Longley-Cook Author-X-Name-First: Alastair Author-X-Name-Last: Longley-Cook Title: Author’s Reply: Risk-Adjusted Economic Value Analysis - Discussion by David L. Creswell Journal: North American Actuarial Journal Pages: 113-114 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595711 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595711 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:113-114 Template-Type: ReDIF-Article 1.0 Author-Name: Kenneth Kortanek Author-X-Name-First: Kenneth Author-X-Name-Last: Kortanek Author-Name: V. G. Medvedev Author-X-Name-First: V. G. Author-X-Name-Last: Medvedev Title: “Skewness and Stock Option Prices”, Hans Gerber and Bruno Landry, July 1997 Journal: North American Actuarial Journal Pages: 114-116 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595712 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595712 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:114-116 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Bruno Landry Author-X-Name-First: Bruno Author-X-Name-Last: Landry Title: Authors’ Reply: Skewness and Stock Option Prices - Discussion by Kenneth O. Kortanek and V. G. Medvedev Journal: North American Actuarial Journal Pages: 116-116 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595713 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595713 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:116-116 Template-Type: ReDIF-Article 1.0 Author-Name: Bernard Dussault Author-X-Name-First: Bernard Author-X-Name-Last: Dussault Title: “Social Security: Regressive or Progressive?”, Robert L. Brown, April 1998 Journal: North American Actuarial Journal Pages: 23-27 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595689 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595689 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:23-27 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Title: “Social Security: Regressive or Progressive?”, Robert L. Brown, April 1998 Journal: North American Actuarial Journal Pages: 23-23 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595688 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595688 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:23-23 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: Social Security Abstract: The evidence is growing that a positive correlation exists between income levels and longevity. In short, high-income earners live longer. That also means that high-income earners get larger retirement-income security benefits from social security. This correlation raises the following questions: If social security contributions are a level percentage of earnings and high-income earners live longer and receive larger social security benefits, then is social security regressive?If higher income actually causes enhanced longevity, then would providing more social security benefits enhance population life expectancy?This paper analyzes both the Old-Age, Survivors, and Disability Insurance (OASDI) system of the U.S. and the Canada/Quebec Pension Plans (C/QPP) in Canada to determine whether these systems are “a good deal” and whether they are regressive or progressive as defined above. Journal: North American Actuarial Journal Pages: 1-23 Issue: 2 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595687 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595687 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:1-23 Template-Type: ReDIF-Article 1.0 Author-Name: Ryen Robinson Author-X-Name-First: Ryen Author-X-Name-Last: Robinson Author-Name: Christian DesRochers Author-X-Name-First: Christian Author-X-Name-Last: DesRochers Title: “Voluntary Termination of Life Insurance Policies: Evidence from the U.S. Market,” Shi-jie Jiang, Vol. 14, No. 3, 2010 Journal: North American Actuarial Journal Pages: 468-471 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597631 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597631 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:468-471 Template-Type: ReDIF-Article 1.0 Author-Name: Xiang Lin Author-X-Name-First: Xiang Author-X-Name-Last: Lin Author-Name: Yanfang Li Author-X-Name-First: Yanfang Author-X-Name-Last: Li Title: Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model Abstract: We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary. Journal: North American Actuarial Journal Pages: 417-431 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597628 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597628 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:417-431 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Voluntary Termination of Life Insurance Policies: Evidence from the U.S. Market by Shi-jie Jiang - Discussion by Ryen Robinson; Christian Desrochers Journal: North American Actuarial Journal Pages: 471-472 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597632 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:471-472 Template-Type: ReDIF-Article 1.0 Author-Name: Leonid Gavrilov Author-X-Name-First: Leonid Author-X-Name-Last: Gavrilov Author-Name: Natalia Gavrilova Author-X-Name-First: Natalia Author-X-Name-Last: Gavrilova Title: Mortality Measurement at Advanced Ages Abstract: Accurate estimates of mortality at advanced ages are essential to improving forecasts of mortality and the population size of the oldest old age group. However, estimation of hazard rates at extremely old ages poses serious challenges to researchers: (1) The observed mortality deceleration may be at least partially an artifact of mixing different birth cohorts with different mortality (heterogeneity effect); (2) standard assumptions of hazard rate estimates may be invalid when risk of death is extremely high at old ages and (3) ages of very old people may be exaggerated. One way of obtaining estimates of mortality at extreme ages is to pool together international records of persons surviving to extreme ages with subsequent efforts of strict age validation. This approach helps researchers to resolve the third of the above-mentioned problems but does not resolve the first two problems because of inevitable data heterogeneity when data for people belonging to different birth cohorts and countries are pooled together. In this paper we propose an alternative approach, which gives an opportunity to resolve the first two problems by compiling data for more homogeneous single-year birth cohorts with hazard rates measured at narrow (monthly) age intervals. Possible ways of resolving the third problem of hazard rate estimation are elaborated. This approach is based on data from the Social Security Administration Death Master File (DMF). Some birth cohorts covered by DMF could be studied by the method of extinct generations. Availability of month of birth and month of death information provides a unique opportunity to obtain hazard rate estimates for every month of age. Study of several single-year extinct birth cohorts shows that mortality trajectory at advanced ages follows the Gompertz law up to the ages 102–105 years without a noticeable deceleration. Earlier reports of mortality deceleration (deviation of mortality from the Gompertz law) at ages below 100 appear to be artifacts of mixing together several birth cohorts with different mortality levels and using cross-sectional instead of cohort data. Age exaggeration and crude assumptions applied to mortality estimates at advanced ages may also contribute to mortality underestimation at very advanced ages. Journal: North American Actuarial Journal Pages: 432-447 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597629 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597629 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:432-447 Template-Type: ReDIF-Article 1.0 Author-Name: Min Ji Author-X-Name-First: Min Author-X-Name-Last: Ji Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Title: Markovian Approaches to Joint-Life Mortality Abstract: Many insurance products provide benefits that are contingent on the combined survival status of two lives. To value such benefits accurately, we require a statistical model for the impact of the survivorship of one life on another. In this paper we first set up two models, one Markov and one semi-Markov, to model the dependence between the lifetimes of a husband and wife. From the models we can measure the extent of three types of dependence: (1) the instantaneous dependence due to a catastrophic event that affect both lives, (2) the short-term impact of spousal death, and (3) the long-term association between lifetimes. Then we apply the models to a set of jointlife and last-survivor annuity data from a large Canadian insurance company. Given the fitted models, we study the impact of dependence on annuity values and examine the potential inaccuracy in pricing if we assume lifetimes are independent. Finally, we compare our Markovian models with two copula models considered in previous research on modeling joint-life mortality. Journal: North American Actuarial Journal Pages: 357-376 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597625 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597625 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:357-376 Template-Type: ReDIF-Article 1.0 Author-Name: Jae Youn Ahn Author-X-Name-First: Jae Youn Author-X-Name-Last: Ahn Author-Name: Nariankadu Shyamalkumar Author-X-Name-First: Nariankadu Author-X-Name-Last: Shyamalkumar Title: Large Sample Behavior of the CTE and VaR Estimators under Importance Sampling Abstract: The α-level value at risk (Var) and the α-level conditional tail expectation (CTE) of a continuous random variable X are defined as its α-level quantile (denoted by qα) and its conditional expectation given the event {X > qα}, respectively. Var is a popular risk measure in the banking sector, for both external and internal reporting purposes, while the CTE has recently become the risk measure of choice for insurance regulation in North America. Estimation of the CTE for company assets and liabilities is becoming an important actuarial exercise, and the size and complexity of these liabilities make inference procedures with good small sample performance very desirable. A common situation is one in which the CTE of the portfolio loss is estimated using simulated values, and in such situations use of variance reduction techniques such as importance sampling have proved to be fruitful. Construction of confidence intervals for the CTE relies on the availability of the asymptotic distribution of the normalized CTE estimator, and although such a result has been available to actuaries, it has so far been supported only by heuristics. The main goal of this paper is to provide an honest theorem establishing the convergence of the normalized CTE estimator under importance sampling to a normal distribution. In the process, we also provide a similar result for the Var estimator under importance sampling, which improves upon an earlier result. Also, through examples we motivate the practical need for such theoretical results and include simulation studies to lend insight into the sample sizes at which these asymptotic results become meaningful. Journal: North American Actuarial Journal Pages: 393-416 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597627 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597627 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:393-416 Template-Type: ReDIF-Article 1.0 Author-Name: Colin Ramsay Author-X-Name-First: Colin Author-X-Name-Last: Ramsay Author-Name: Victor Oguledo Author-X-Name-First: Victor Author-X-Name-Last: Oguledo Title: Optimum Allocations to Health Care Flexible Spending Accounts Abstract: Models used to derive optimal contributions to health care flexible spending accounts (FSAs) typically assume an employee’s household annual out-of-pocket health care expenses are an absolutely continuously random variable. This assumption, however, ignores the fact that some employees may be able to accurately predict a portion of their household annual out-of-pocket health care expenses and often actually incur only those expenses during the plan year, implying that a mixed random variable may be more appropriate. In addition, data have shown that employees are setting contributions at lower levels than existing absolutely continuous models would suggest is optimal. Using a mixed model of household annual out-of-pocket health care expenses we prove that it is often optimal for employees to contribute an amount equal to their household annual predictable out-of-pocket expenses, thus avoiding the risk of forfeiture. We also propose a practical rule of thumb that employees may use for setting their FSA contributions. Overall, we recommend that employees use their FSAs to cover only their highly predictable out-of-pocket health care expenses rather than use their FSAs as a contingency fund to pay for unlikely or unexpected outof-pocket health care expenses. Journal: North American Actuarial Journal Pages: 448-467 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597630 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597630 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:448-467 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Jie Gao Author-X-Name-First: Jie Author-X-Name-Last: Gao Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Title: Predicting the Frequency and Amount of Health Care Expenditures Abstract: This article extends the standard two-part model for predicting health care expenditures to the case where multiple events may occur within a one-year period. The first part of the extended model represents the frequency of events, such as the number of inpatient hospital stays or outpatient visits, and the second part models expenditure per event. Both component models also use independent variables that consist of an individual’s demographic and access characteristics, socioeconomic status, health status, health insurance coverage, employment status, and industry classification. The second part of the model also includes a variable representing the number of events to predict the expenditure per event, thus capturing dependencies between the first and second parts. This article introduces closed-form predictors of annual total expenditures and demonstrates how to create simulated predictive distributions for individuals and groups. The data for this study are from the Medical Expenditure Panel Survey (MEPS). MEPS panels 7 and 8 from 2003 were used for estimation; panels 8 and 9 from 2004 were used to validate predictions. This annual expenditures model provided a better fit to the data than standard two-part models. The count variable was significant in predicting outpatient expenditures. The aggregate expenditures model provided better point predictions of held-out total expenditures than competing models, including the standard two-part model. The predictive distribution for aggregate expenditures for small groups is long tailed, with both the variability and skewness decreasing as the group size increases, an important point for programs designed to manage expenditures. Journal: North American Actuarial Journal Pages: 377-392 Issue: 3 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597626 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597626 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:3:p:377-392 Template-Type: ReDIF-Article 1.0 Author-Name: M. Govorun Author-X-Name-First: M. Author-X-Name-Last: Govorun Author-Name: B. L. Jones Author-X-Name-First: B. L. Author-X-Name-Last: Jones Author-Name: X. Liu Author-X-Name-First: X. Author-X-Name-Last: Liu Author-Name: D. A. Stanford Author-X-Name-First: D. A. Author-X-Name-Last: Stanford Title: Physiological Age, Health Costs, and Their Interrelation Abstract: We demonstrate the impact of an observable health-related quantity on the evaluation of individual physiological ages by extending the phase-type aging model proposed by Lin and Liu in 2007. In their model, an individual of a given calendar age has a determinable distribution of his or her physiological age. In our article, we use observable information to refine this distribution, thereby better connecting physiological age with the health of the individual. We illustrate our model using health cost data, and we investigate the impact of an observed health cost on the distribution of an individual’s physiological age. We also explore the impact on the expected present value of future health costs. Journal: North American Actuarial Journal Pages: 323-340 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2017.1404476 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1404476 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:323-340 Template-Type: ReDIF-Article 1.0 Author-Name: Alexandru V. Asimit Author-X-Name-First: Alexandru V. Author-X-Name-Last: Asimit Author-Name: Tao Gao Author-X-Name-First: Tao Author-X-Name-Last: Gao Author-Name: Junlei Hu Author-X-Name-First: Junlei Author-X-Name-Last: Hu Author-Name: Eun-Seok Kim Author-X-Name-First: Eun-Seok Author-X-Name-Last: Kim Title: Optimal Risk Transfer: A Numerical Optimization Approach Abstract: Capital efficiency and asset/liability management are part of the Enterprise Risk Management Process of any insurance/reinsurance conglomerate and serve as quantitative methods to fulfill the strategic planning within an insurance organization. A considerable amount of work has been done in this ample research field, but invariably one of the last questions is whether or not, numerically, the method is practically implementable, which is our main interest. The numerical issues are dependent on the traits of the optimization problem, and therefore we plan to focus on the optimal reinsurance design, which has been a very dynamic topic in the last decade. The existing literature is focused on finding closed-form solutions that are usually possible when economic, solvency, and other constraints are not included in the model. Including these constraints, the optimal contract can be found only numerically. The efficiency of these methods is extremely good for some well-behaved convex problems, such as Second-Order Conic Problems. Specific numerical solutions are provided to better explain the advantages of appropriate numerical optimization methods chosen to solve various risk transfer problems. The stability issues are also investigated together with a case study performed for an insurance group that aims capital efficiency across the entire organization. Journal: North American Actuarial Journal Pages: 341-364 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2017.1421472 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1421472 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:341-364 Template-Type: ReDIF-Article 1.0 Author-Name: Sylvestre Frezal Author-X-Name-First: Sylvestre Author-X-Name-Last: Frezal Title: Solvency II Is Not Risk-Based—Could It Be? Evidence from Non-Life Calibrations Abstract: Risk-based prudential regulations are spreading. For example, the capital requirements of Solvency II are considered to be founded on a risk measure. We focus on premium and reserving risks, which represent 40% of capital requirements for non-life insurance companies in Europe, and draw on internal robustness tests to demonstrate that these measures are unreliable. There are three possible explanations for this lack of reliability: a political economy factor, an idiosyncratic factor, and an epistemological barrier. We examine each of these and evaluate their significance, thus casting doubts on the feasibility of such ambition and providing insights to adapt the design of any prudential regulation intended to be risk-based to such pitfalls. Journal: North American Actuarial Journal Pages: 365-379 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2017.1421473 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1421473 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:365-379 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas R. Berry-Stölzle Author-X-Name-First: Thomas R. Author-X-Name-Last: Berry-Stölzle Author-Name: Evan M. Eastman Author-X-Name-First: Evan M. Author-X-Name-Last: Eastman Author-Name: Jianren Xu Author-X-Name-First: Jianren Author-X-Name-Last: Xu Title: CEO Overconfidence and Earnings Management: Evidence from Property-Liability Insurers' Loss Reserves Abstract: This study investigates the relation between managerial overconfidence and loss-reserving practices in the U.S. property-liability insurance industry. We find robust evidence that CEO overconfidence is significantly associated with relatively low loss reserves, resulting in relatively high reported earnings. This finding is consistent with the theoretical predication that overconfident managers overestimate the returns on their investment projects and underestimate losses. Our result contributes to the literature linking CEOs' personality traits and firms' accounting policy as well as to the literature on insurer loss-reserving practices. Journal: North American Actuarial Journal Pages: 380-404 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2017.1421977 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1421977 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:380-404 Template-Type: ReDIF-Article 1.0 Author-Name: Simon C. K. Lee Author-X-Name-First: Simon C. K. Author-X-Name-Last: Lee Author-Name: Sheldon Lin Author-X-Name-First: Sheldon Author-X-Name-Last: Lin Title: Delta Boosting Machine with Application to General Insurance Abstract: In this article, we introduce Delta Boosting (DB) as a new member of the boosting family. Similar to the popular Gradient Boosting (GB), this new member is presented as a forward stagewise additive model that attempts to reduce the loss at each iteration by sequentially fitting a simple base learner to complement the running predictions. Instead of relying on the negative gradient, as is the case for GB, DB adopts a new measure called delta as the basis. Delta is defined as the loss minimizer at an observation level. We also show that DB is the optimal boosting member for a wide range of loss functions. The optimality is a consequence of DB solving for the split and adjustment simultaneously to maximize loss reduction at each iteration. In addition, we introduce an asymptotic version of DB that works well for all twice-differentiable strictly convex loss functions. This asymptotic behavior does not depend on the number of observations, but rather on a high number of iterations that can be augmented through common regularization techniques. We show that the basis in the asymptotic extension differs from the basis in GB only by a multiple of the second derivative of the log-likelihood. The multiple is considered to be a correction factor, one that corrects the bias toward the observations with high second derivatives in GB. When negative log-likelihood is used as the loss function, this correction can be interpreted as a credibility adjustment for the process variance. Simulation studies and real data application we conducted suggest that DB is a significant improvement over GB. The performance of the asymptotic version is less dramatic, but the improvement is still compelling. Like GB, DB provides a high transparency to users, and we can review the marginal influence of variables through relative importance charts and the partial dependence plots. We can also assess the overall model performance through evaluating the losses, lifts, and double lifts on the holdout sample. Journal: North American Actuarial Journal Pages: 405-425 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2018.1431131 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1431131 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:405-425 Template-Type: ReDIF-Article 1.0 Author-Name: Colin M. Ramsay Author-X-Name-First: Colin M. Author-X-Name-Last: Ramsay Author-Name: Victor I. Oguledo Author-X-Name-First: Victor I. Author-X-Name-Last: Oguledo Author-Name: Annika Krutto Author-X-Name-First: Annika Author-X-Name-Last: Krutto Title: Exploring the Optimal Design of an Employer-Sponsored Sickness-Disability Compensation Insurance Plan When Sickness Presenteeism Is Penalized Abstract: We explore the impact of presenteeism, absenteeism, and shirking on the optimal design of an employer-sponsored sickness-disability compensation insurance plan when the employer penalizes sickness presenteeism. We assume an employee's health follows a simple multistate model with a “severely ill” sickness state. To combat absenteeism, the employer randomly verifies an employee's claim of sickness. However, to combat presenteeism, we also introduce the new concept of a presenteeism penalty whereby employees who are found to be at work in the “severely ill” sickness state are sent home and receive a penalized sick pay that is lower than the normal sick pay. Thus sick employees must decide whether to stay at home and receive a sick pay or go to work sick and run the risk of being sent home and penalized. We further assume (1) employees are risk-averse utility maximizers, (2) each employee has a strategy for staying home or working while sick that maximizes his or her lifetime expected discounted utility, and (3) an employee's strategy is unknown to the employer. The primary plan design factors that affect an employee's lifetime expected discounted utility and the employer's discounted expected accounting profits over an employee's working lifetime are the sick pay, the presenteeism penalty, and two health check probabilities. Volterra integral equations are used to derive expressions for an employee's lifetime expected discounted utility and the employer's expected discounted accounting profits over an employee's lifetime under various employee strategies. Laplace transforms are used to derive asymptotic expressions for the solutions to these integral equations. These asymptotic solutions are used to explore the impact of these factors on the optimal sickness compensation insurance plan design. Journal: North American Actuarial Journal Pages: 426-457 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2018.1435287 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1435287 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:426-457 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick L. Brockett Author-X-Name-First: Patrick L. Author-X-Name-Last: Brockett Author-Name: Linda L. Golden Author-X-Name-First: Linda L. Author-X-Name-Last: Golden Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Title: Potential “Savings” of Medicare: The Analysis of Medicare Advantage and Accountable Care Organizations Abstract: Medicare faces significant financial challenges because of rising health care costs. In response, Medicare reform efforts have been testing various payment and service delivery models, including accountable care organizations (ACOs), aiming to reduce expenditures while preserving or enhancing the coordination of quality care. The idea behind ACOs is to form an organizational network to coordinate all care for Medicare beneficiaries and in so doing, at least theoretically, improve quality of care and hopefully reduce medical costs. The purpose of this research is to apply Data Envelopment Analysis (DEA) to assess the potential savings of Medicare obtainable through optimally efficient implementation of ACOs and Medicare Advantage plans. DEA comparisons across plans achieve this purpose by identifying which Medicare plans operate relatively more efficiently and which are inefficient, and additionally, for inefficient plans, the DEA analysis generates target levels of “inputs” and “outputs” required to bring the plan into efficient operation. Knowing sources of inefficiency can also provide insights into Medicare reform, such as Medicare privatization and innovation models. Our results show that Medicare Advantage plans are more efficient in reducing health expenditures but incur higher administrative costs. Health expenditure savings can also be achievable by promoting government-sponsored managed Medicare such as ACOs. Finally, compared to the profit efficiency of Medicaid managed care plans, Medicare Advantage should have the potential for more Medicare market penetration from the supply (insurer) side. Journal: North American Actuarial Journal Pages: 458-472 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2018.1436445 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1436445 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:458-472 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Erhardt Author-X-Name-First: Robert Author-X-Name-Last: Erhardt Author-Name: David Engler Author-X-Name-First: David Author-X-Name-Last: Engler Title: An Extension of Spatial Dependence Models for Estimating Short-Term Temperature Portfolio Risk Abstract: Temperature risk is any adverse financial outcome caused by temperature outcomes. The Chicago Mercantile Exchange lists a series of financial products that link payments to temperature outcomes, and these products can help buyers manage temperature risk. Financial institutions can also hold a portfolio of these products as counterparty to the buyers facing temperature risk. Here we take an actuarial perspective to measuring the risk by modeling the daily temperatures directly. These models are then used to simulate distributions of future temperature outcomes. The model for daily temperature is a spatial ARMA-EGARCH statistical model that incorporates dependence in both time and space, in addition to modeling the volatility. Simulations from this model are used to build up distributions of temperature outcomes, and we demonstrate how actuarial risk measures of the portfolio can then be estimated from these distributions. Journal: North American Actuarial Journal Pages: 473-490 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2018.1444496 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1444496 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:473-490 Template-Type: ReDIF-Article 1.0 Author-Name: Marcus C. Christiansen Author-X-Name-First: Marcus C. Author-X-Name-Last: Christiansen Author-Name: Mogens Steffensen Author-X-Name-First: Mogens Author-X-Name-Last: Steffensen Title: Around the Life Cycle: Deterministic Consumption-Investment Strategies Abstract: We study a classical continuous-time consumption-investment problem of a power utility investor with deterministic labor income with the important feature that the consumption-investment process is constrained to be deterministic. This is motivated by the design of modern pension schemes of defined contribution type where, typically, the savings rate is constant and the proportional investment in growth stocks is a function of age or time-to-retirement, a so-called life-cycle investment strategy. We derive and study the optimal behavior corresponding to the optimal product design within this realistic family of products with deterministic decision profiles. We also propose a couple of suboptimal deterministic strategies inspired from the optimal stochastic strategy and compare the optimal stochastic control, the optimal deterministic control, and these suboptimal deterministic controls. The conclusion is that only little is lost by constraining to deterministic strategies and only little is lost by implementing the suboptimal simple explicit strategies rather than the optimal one we derive. Journal: North American Actuarial Journal Pages: 491-507 Issue: 3 Volume: 22 Year: 2018 Month: 7 X-DOI: 10.1080/10920277.2018.1450156 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1450156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:491-507 Template-Type: ReDIF-Article 1.0 Author-Name: David Munroe Author-X-Name-First: David Author-X-Name-Last: Munroe Author-Name: David Odell Author-X-Name-First: David Author-X-Name-Last: Odell Author-Name: Serge Sandler Author-X-Name-First: Serge Author-X-Name-Last: Sandler Author-Name: Ben Zehnwirth Author-X-Name-First: Ben Author-X-Name-Last: Zehnwirth Title: A Solution for Solvency II Quantitative Requirements Modeling with Long-Tail Liabilities Abstract: The European Parliament’s Solvency II Directive introduced a new regulation for insurance and reinsurance business designed to establish a consistently improved level of policyholder protection by means of a three-pillar process. Pillar 1 of the directive contains quantitative requirements for the insurance industry in respect to technical provisions (TPs) and the solvency capital requirement (SCR). The cornerstone of Solvency II one-year risk horizon is the Fair Value of Liabilities (FVL). The SCR and Economic Balance Sheet at inception should be able to withstand a first future calendar year in distress (at the level of 1-in-200-year event). We provide a rigorous statistical treatment of the risk metrics required to fulfil Solvency II requirements for internal models applicable to reserve risk with long-tail liabilities. The proposed internal model is novel in not relying on the proportionality proxy. A tractable simulation based solution ensures adequate capital to restore the economic balance sheet to its FVL should the first future calendar year be in distress. Journal: North American Actuarial Journal Pages: 79-93 Issue: 2 Volume: 19 Year: 2015 Month: 4 X-DOI: 10.1080/10920277.2014.997934 File-URL: http://hdl.handle.net/10.1080/10920277.2014.997934 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:2:p:79-93 Template-Type: ReDIF-Article 1.0 Author-Name: Ya-Wen Hwang Author-X-Name-First: Ya-Wen Author-X-Name-Last: Hwang Author-Name: Shih-Chieh Chang Author-X-Name-First: Shih-Chieh Author-X-Name-Last: Chang Author-Name: Yang-Che Wu Author-X-Name-First: Yang-Che Author-X-Name-Last: Wu Title: Capital Forbearance, Ex Ante Life Insurance Guaranty Schemes, and Interest Rate Uncertainty Abstract: Insurance guaranty funds have been adopted in many countries to compensate policyholders for losses resulting from insurers’ insolvencies. In this article we focus on the risk-based premiums in ex ante insurance guaranty schemes since a preassessment mechanism could reduce the shareholders’ incentive to engage in risk-taking behavior. We derive the closed-form solutions of the risk-based premium charged by the insurance guaranty fund in a setting that incorporates financial leverage, asset allocation, early closure, and capital forbearance during the grace period. Most importantly, we assume that the interest rate is stochastic, and we find that the premium is underpriced if the uncertainty of the interest rate is neglected by the insurance guaranty fund. Moreover, the influence of stochastic interest rate for the premium is more significant when we consider the capital forbearance mechanism. The impacts of the key factors in our model that decide the fair premium of the guaranty fund are examined numerically. The results of our analysis could provide valuable insights for regulators in terms of revising regulatory policies and insurance guaranty schemes. Journal: North American Actuarial Journal Pages: 94-115 Issue: 2 Volume: 19 Year: 2015 Month: 4 X-DOI: 10.1080/10920277.2014.1001911 File-URL: http://hdl.handle.net/10.1080/10920277.2014.1001911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:2:p:94-115 Template-Type: ReDIF-Article 1.0 Author-Name: Séverine Arnold (-Gaille) Author-X-Name-First: Séverine Author-X-Name-Last: Arnold (-Gaille) Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Causes-of-Death Mortality: What Do We Know on Their Dependence? Abstract: Over the last century, the assumption usually made was that causes of death are independent, although it is well-known that dependancies exist. Recent developments in econometrics allow, through Vector Error Correction Models (VECMs), to model multivariate dynamic systems including time dependency between economic variables. Common trends that exist between the variables may then be highlighted, the relation between these variables being represented by a long-run equilibrium relationship. In this work, VECMs are developed for causes-of-death mortality. We analyze the five main causes of death across 10 major countries representing a diversity of developed economies. The World Health Organization website provides cause-of-death information for about the last 60 years. Our analysis reveals that long-run equilibrium relationships exist between the five main causes of death, improving our understanding of the nature of dependence between these competing risks over recent years. It also highlights that countries usually had different past experience in regard to cause-of-death mortality trends, and, thus, applying results from one country to another may be misleading. Journal: North American Actuarial Journal Pages: 116-128 Issue: 2 Volume: 19 Year: 2015 Month: 4 X-DOI: 10.1080/10920277.2015.1011279 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1011279 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:2:p:116-128 Template-Type: ReDIF-Article 1.0 Author-Name: Vincenzo Russo Author-X-Name-First: Vincenzo Author-X-Name-Last: Russo Author-Name: Rosella Giacometti Author-X-Name-First: Rosella Author-X-Name-Last: Giacometti Author-Name: Svetlozar Rachev Author-X-Name-First: Svetlozar Author-X-Name-Last: Rachev Author-Name: Frank J. Fabozzi Author-X-Name-First: Frank J. Author-X-Name-Last: Fabozzi Title: A Three-Factor Model for Mortality Modeling Abstract: In this article, we propose a three-factor model for mortality modeling in which the dynamic of the entire term structure of mortality rates can be expressed in closed form as a function of three variables x, t, and y. Due to this feature, we are able to project mortality rates across age (x), across time (t), and for y years (y ⩾ 1) after t. Our proposal differs from most existing models where only the one-year mortality rate is considered (y = 1). The model is characterized by three parameters that are calibrated yearly. We describe the stochastic dynamic of the three factors with correlated autoregressive processes. We generate stochastic scenarios accounting for the historical mortality trend in a consistent manner with the Gompertz law. Using population mortality data for Italy, the U.S., and the U.K., the model’s forecasting capability is assessed, and a comparative analysis with other models is provided. Journal: North American Actuarial Journal Pages: 129-141 Issue: 2 Volume: 19 Year: 2015 Month: 4 X-DOI: 10.1080/10920277.2015.1015262 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1015262 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:2:p:129-141 Template-Type: ReDIF-Article 1.0 Author-Name: X. Lin Author-X-Name-First: X. Author-X-Name-Last: Lin Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Pricing Annuity Guarantees Under a Regime-Switching Model Abstract: We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees. Journal: North American Actuarial Journal Pages: 316-332 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597557 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597557 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:316-332 Template-Type: ReDIF-Article 1.0 Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Title: “On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model,” David Landriault and Gordon Willmot, Volume 13, No. 2, 2009 Journal: North American Actuarial Journal Pages: 404-406 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597565 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597565 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:404-406 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Author-Name: Linda Goldens Author-X-Name-First: Linda Author-X-Name-Last: Goldens Author-Name: Min-Ming Wen Author-X-Name-First: Min-Ming Author-X-Name-Last: Wen Author-Name: Charles Yang Author-X-Name-First: Charles Author-X-Name-Last: Yang Title: Pricing Weather Derivatives Using the Indifference Pricing Approach Abstract: This paper adopts an incomplete market pricing model–the indifference pricing approach–to analyze valuation of weather derivatives and the viability of the weather derivatives market in a hedging context. It incorporates price risk, weather/quantity risk, and other risks in the financial market. In a mean-variance framework, the relationship between the actuarial price and the indifference price of weather derivatives is analyzed, and conditions are obtained concerning when the actuarial price does not provide an appropriate valuation for weather derivatives. Conditions for the viability of the weather derivatives market are examined. This paper also analyzes the effects of partial hedging, natural hedges, basis risk, quantity risk, and price risk on investors’ indifference prices by examining the distributional impacts of the stochastic variables involved. Journal: North American Actuarial Journal Pages: 303-315 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597556 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597556 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:303-315 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Pricing Annuity Guarantees Under a Regime-Switching Model - Discussion by Robert J. Elliott and Tak Kuen Siu Journal: North American Actuarial Journal Pages: 337-338 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597559 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597559 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:337-338 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Elliott Author-X-Name-First: Robert Author-X-Name-Last: Elliott Author-Name: Tak Siu Author-X-Name-First: Tak Author-X-Name-Last: Siu Title: “Pricing Annuity Guarantees Under a Regime-Switching Model”, X. Sheldon Lin, Ken Seng Tan and Hailiang Yang, July 2009 Journal: North American Actuarial Journal Pages: 333-337 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597558 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597558 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:333-337 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Esther Frostig Author-X-Name-First: Esther Author-X-Name-Last: Frostig Title: Life Insurance Mathematics with Random Life Tables Abstract: When the insurer sells life annuities, projected life tables incorporating a forecast of future longevity must be used for pricing and reserving. To fix the ideas, the framework of Lee and Carter is adopted in this paper. The Lee-Carter model for mortality forecasting assumes that the death rate at age x in calendar year t is of the form exp(αx + (βxKt), where the time-varying parameter Kt reflects the general level of mortality and follows an ARIMA model. The future lifetimes are all influenced by the same time index Kt in this framework. Because the future path of this index is unknown and modeled as a stochastic process, the policyholders' lifetimes become dependent on each other. Consequently the risk does not disappear as the size of the portfolio increases: there always remains some systematic risk that cannot be diversified, whatever the number of policies. This paper aims to investigate some aspects of actuarial mathematics in the context of random life tables. First, the type of dependence existing between the insured life lengths is carefully examined. The way positive dependence influences the need for economic capital is assessed compared to mutual independence, as well as the effect of the timing of deaths through Bayesian credibility mechanisms. Then the distribution of the present value of payments under a closed group of life annuity policies is studied. Failing to account for the positive dependence between insured lifetimes is a dangerous strategy, even if the randomness in the future survival probabilities is incorporated in the actuarial computations. Numerical illustrations are performed on the basis of Belgian mortality statistics. The impact on the distribution of the present value of the additional variability that results from the Lee-Carter model is compared with the traditional method of mortality projection. Also, the impact of ignoring the dependence hat arises from the model is quantified. Journal: North American Actuarial Journal Pages: 339-355 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597560 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597560 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:339-355 Template-Type: ReDIF-Article 1.0 Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Impact of Underwriting Cycles on the Solvency of an Insurance Company Abstract: This paper studies the solvency of an insurance firm in the presence of underwriting cycles. A small or medium-size insurance company with a price-taker position in the market is considered. Its premium income is assumed to obey an autoregressive process with cycles. Specifically, the premium income for a specific calendar year is influenced by the market experience for the last couple years. Under this classical AR(2) dynamics governing the premium income, an explicit expression for the ultimate ruin probability is derived, using a martingale approach, in the lighttailed claims case. Furthermore, the logarithmic asymptotic behavior of the ultimate ruin probability as well as the typical path to ruin are investigated. Then a comparison is made with the classical case where the same company operates on a market without such cycles. Asymptotically, the presence of market cycles is shown to increase the risk for the company. Numerical illustrations are performed on Canadian motor insurance market data and support the theoretical analysis. Journal: North American Actuarial Journal Pages: 385-403 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597564 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597564 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:385-403 Template-Type: ReDIF-Article 1.0 Author-Name: Ken Kortanek Author-X-Name-First: Ken Author-X-Name-Last: Kortanek Title: “Cash Flow Matching: A Risk Management Approach”, Garud Iyengar and Alfred Ka Chun Ma, July, 2009 Journal: North American Actuarial Journal Pages: 378-384 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597563 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597563 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:378-384 Template-Type: ReDIF-Article 1.0 Author-Name: Garud Iyengar Author-X-Name-First: Garud Author-X-Name-Last: Iyengar Author-Name: Alfred Ma Author-X-Name-First: Alfred Author-X-Name-Last: Ma Title: Cash Flow Matching Abstract: We propose a scenario-based optimization framework for solving the cash flow matching problem where the time horizon of the liabilities is longer than the maturities of available bonds and the interest rates are uncertain. Standard interest rate models can be used for scenario generation within this framework. The optimal portfolio is found by minimizing the cost at a specific level of shortfall risk measured by the conditional tail expectation (CTE), also known as conditional valueat-risk (CVaR) or Tail-VaR. The resulting optimization problem is still a linear program (LP) as in the classical cash flow matching approach. This framework can be employed in situations when the classical cash flow matching technique is not applicable. Journal: North American Actuarial Journal Pages: 370-378 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597562 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597562 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:370-378 Template-Type: ReDIF-Article 1.0 Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Title: Robust and Efficient Fitting of Loss Models Abstract: We consider robust and efficient fitting of claim severity models whose parameters are estimated using the method of trimmed moments, which was recently introduced by Brazauskas, Jones, and Zitikis. In this article we take the “next” step by going beyond the theory and simulations. We address important issues that arise in practical application of the method. Specifically, we introduce two graphical diagnostic tools that can be used to choose the trimming proportions and hence help one to decide on the appropriate trade-off between robustness and efficiency. What is equally important, such tools are useful in model selection, for assessing the overall goodness of model fit, and for identification of outliers. Some insights about the choice between a “good” fit and an “even better” fit and its impact on risk evaluations are provided. Data analysis and illustrations are performed using real data that represent the total damage done by 827 fires in Norway for the year 1988. Journal: North American Actuarial Journal Pages: 356-369 Issue: 3 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597561 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597561 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:356-369 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Title: “Investing for Retirement: Optimal Capital Growth and Dynamic Asset Allocation”, Hans U. Gerber and Elias S.W. Shiu, April 2000 Journal: North American Actuarial Journal Pages: 58-59 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595900 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595900 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:58-59 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Hedging and Reserving for Single-Premium Segregated Fund Contracts Abstract: Three methods for determining suitable provision for maturity guarantees for single-premium segregated fund contracts are compared. Actuarial reserving assumes funds are held in risk-free assets, to give a prescribed probability of meeting the guarantee liability. Dynamic hedging uses the Black-Scholes framework to determine the replicating portfolio. Static hedging assumes a counterparty is willing to sell the options required to meet the guarantee. Using a stochastic cash flow projection, we consider how to assess which approach is most profitable. The example given assumes a typical Canadian segregated fund contract. Journal: North American Actuarial Journal Pages: 63-74 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595903 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595903 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:63-74 Template-Type: ReDIF-Article 1.0 Author-Name: Jean Lemaire Author-X-Name-First: Jean Author-X-Name-Last: Lemaire Author-Name: Krupa Subramanian Author-X-Name-First: Krupa Author-X-Name-Last: Subramanian Author-Name: Katrina Armstrong Author-X-Name-First: Katrina Author-X-Name-Last: Armstrong Author-Name: David Asch Author-X-Name-First: David Author-X-Name-Last: Asch Title: Pricing Term Insurance in the Presence of a Family History of Breast or Ovarian Cancer Abstract: We estimate the increased mortality and term life insurance costs for women who have a family history of breast or ovarian cancer. Using data from the medical literature on age-specific and family history-specific incidence rates, we develop double-decrement models to evaluate the actuarial impact of breast cancer and ovarian cancer in the family. We also calculate the increased mortality and term insurance costs for women who test positive for the BRCA1 or BRCA2 gene mutation. We find that the type of affected relative and her age at onset of the disease are key underwriting factors. We find substantial mortality increases (up to 100%) for women with two relatives with cancer and women with a first-degree relative who developed cancer at an early age. Mortality increases for women with the BRCA gene mutation reach 150%. While some females with a family history of cancer can be accepted at standard rates, others may need to be quoted substandard rates, depending on the underwriting policy of the company. Females with the gene mutation can possibly be accepted at a rate that incorporates a severe mortality surcharge. Journal: North American Actuarial Journal Pages: 75-87 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595904 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595904 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:75-87 Template-Type: ReDIF-Article 1.0 Author-Name: Gérard Pafumi Author-X-Name-First: Gérard Author-X-Name-Last: Pafumi Title: “Investing for Retirement: Optimal Capital Growth and Dynamic Asset Allocation”, Hans U. Gerber and Elias S.W. Shiu, April 2000 Journal: North American Actuarial Journal Pages: 60-61 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595901 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595901 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:60-61 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Authors’ Reply: Investing for Retirement: Optimal Capital Growth and Dynamic Asset Allocation - Discussion by Phelim P. Boyle; Gérard Pafumi Abstract: Journal: North American Actuarial Journal Pages: 61-62 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595902 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595902 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:61-62 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Cowell Author-X-Name-First: Michael Author-X-Name-Last: Cowell Title: “Excess Mortality In Asia Associated With Cigarette Smoking”, Robert J. Pokorski, April 2000 Journal: North American Actuarial Journal Pages: 114-115 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595907 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595907 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:114-115 Template-Type: ReDIF-Article 1.0 Author-Name: Adam Reese Author-X-Name-First: Adam Author-X-Name-Last: Reese Title: Development of the Last-Year-of-Life Valuation Model for Retiree Medical Plans Abstract: The last-year-of-life valuation model is an alternative to the average-claims-cost life annuity model that is currently in general use for valuing retiree medical benefits. The last-year-of-life valuation model splits an average cost into a higher than average decedent cost and a lower than average survival cost. This paper explains how the model can be constructed from existing age-graded claims with very little additional effort. The model can be used in several different situations; it sheds some light on the high costs associated with the increased utilization of hospital and medical services at the end of life and may produce a better estimate of the value of retiree medical benefits when improvements in life expectancy are anticipated. Improvements in life expectancy over the past decade have eroded the margin of conservatism built into the mortality tables currently in use, and it is anticipated that, spurred on by regulatory assumption sets that will soon be mandated for certain pension plan funding calculations, employee-benefit actuaries will soon update their assumptions to reflect expectations of further improvements in mortality. As average per capita claims costs implicitly represent today’s mortality rates, use of the averageclaims-cost valuation model with a projected mortality table will likely overstate the long-term cost of the benefits while the last-year-of-life valuation model can be used to provide an unbiased measure of the long-term cost of the benefits. Journal: North American Actuarial Journal Pages: 116-123 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595908 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595908 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:116-123 Template-Type: ReDIF-Article 1.0 Author-Name: John Mange Author-X-Name-First: John Author-X-Name-Last: Mange Title: Measuring Foreign Exchange Risk in Insurance Transactions Abstract: A macroeconomic model of exchange rates is mixed with classical life insurance, annuity and compound Poisson aggregate claim models to create foreign exchange-adjusted insurance models. The resulting models may be used to measure the potential foreign exchange risk of mixed currency products, for example, products for which premiums are collected and benefits are paid in different currencies. Numerical examples illustrate the foreign exchange risks of such products. Journal: North American Actuarial Journal Pages: 88-100 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595905 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595905 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:88-100 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Pokorski Author-X-Name-First: Robert Author-X-Name-Last: Pokorski Title: Excess Mortality In Asia Associated With Cigarette Smoking Abstract: Cigarette smoking has reached epidemic proportions in many Asian countries, and epidemiologists predict massive increases in the number of smoking-related deaths in future decades. This information is of great interest to insurers who would like to sell coverage in these markets with smoker/nonsmoker-distinct pricing. This review examines excess mortality due to cigarette smoking in Asia as determined by a second-quarter 1998 Internet search of the world’s English-language medical literature for references published during the preceding five years. Studies to date which observed fairly low relative risks of mortality in smokers compared with nonsmokers in Asia despite a high prevalence of smoking can be explained by the fact that health outcome data represent early experience. Given similar associations between smoking and mortality in Asian and Western studies, it is likely that mortality patterns of smokers in Asia eventually will mirror those seen in the U.S. and the United Kingdom. Journal: North American Actuarial Journal Pages: 101-113 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595906 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595906 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:101-113 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Don Author-X-Name-First: Harry Author-X-Name-Last: Don Title: “Development of the Last-Year-of-Life Valuation Model for Retiree Medical Plans”, Adam J. Reese, April 2000 Journal: North American Actuarial Journal Pages: 123-123 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595909 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595909 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:123-123 Template-Type: ReDIF-Article 1.0 Author-Name: Philip Booth Author-X-Name-First: Philip Author-X-Name-Last: Booth Author-Name: Yakoub Yakoubov Author-X-Name-First: Yakoub Author-X-Name-Last: Yakoubov Title: Investment Policy for Defined-Contribution Pension Scheme Members Close to Retirement Abstract: This paper considers the investment decision facing a defined-contribution pension scheme investor close to retirement. Specifically, it investigates the lifestyle strategy whereby investors automatically switch investment policy in the years before retirement. The argument for switching is that investors may become more risk averse as they approach retirement and will wish to prevent unnecessary volatility of their fund. This argument is intuitively attractive. However there are counterarguments. During the switching period, investors will not be able to benefit from possible excess returns from equities; if investment markets are inefficient, investors may benefit from keeping investment discretion; and the nature of the risk in a defined-contribution plan may be more complex than many plan holders anticipate. It is important to define risk criteria before determining optimal investment policy. Movement into cash before retirement may stabilize the cash value of the fund but will put the investor at risk of falling interest rates and rising annuity prices; movement into conventional bonds before retirement may protect the investor from changes in interest rates but put the investor at risk from a change in inflation expectations if an index-linked annuity (priced from index-linked bond yields) is required at retirement; even movement into index-linked bonds puts the investor at risk from changes in real yields unless the duration of the index-linked bonds in the investment fund is equal to the duration of the required annuity.The methodology of the research involved finding the distribution of the accumulated cash fund, fixed nominal annuities and fixed real annuities from different investment strategies in a defined-contribution pension fund, using different investment strategies. All available postwar data is used. The paper finds that there is no evidence to suggest that a lifestyle investment strategy, which involves moving into cash, bonds, or index-linked bonds, is beneficial. These results are found when using either empirical data or stochastic modeling to find distributions of outcomes. A diversified portfolio of real assets (including international equities) seems to give the investor reasonable risk protection for two reasons. First, diversification protects the individual from falls in particular markets. Second, equities are themselves interest-rate (and, particularly in the U.K., real-interest) sensitive. This means that part of the explanation for falling equity prices lies in changes in real investment yields. If real interest rates change, equity values can change but there can be a partially offsetting change in index-linked annuity prices. Also, there can be hidden risks in investing in cash, conventional bonds, or index-linked bonds immediately before retirement. These investments can be subject to “real shocks” and can underperform salary growth significantly: specific examples of this phenomenon are given. Additionally, bond investment only eliminates risk if the duration of the bond fund is equal to the duration of the required annuity at retirement. Such matching by duration is likely to prove difficult in practice except for investors with very large funds. Specific examples of this problem are also given. Journal: North American Actuarial Journal Pages: 1-19 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595892 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595892 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:1-19 Template-Type: ReDIF-Article 1.0 Author-Name: Terence Chan Author-X-Name-First: Terence Author-X-Name-Last: Chan Title: “Pricing Dynamic Investment Fund Protection”, Gérard Pafumi, April 2000 Journal: North American Actuarial Journal Pages: 37-37 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595895 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595895 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:37-37 Template-Type: ReDIF-Article 1.0 Author-Name: François-Serge Lhabitant Author-X-Name-First: François-Serge Author-X-Name-Last: Lhabitant Title: “Pricing Dynamic Investment Fund Protection”, Hans U. Gerber and Gérard Pafumi, April 2000 Journal: North American Actuarial Journal Pages: 37-38 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595896 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595896 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:37-38 Template-Type: ReDIF-Article 1.0 Author-Name: Calvin Cherry Author-X-Name-First: Calvin Author-X-Name-Last: Cherry Title: Calculating Funding Premiums for Universal Life Insurance Abstract: This paper provides a brief overview of the most commonly used methods for calculating the level gross premium required to achieve a specific funding target under a typical universal life product design. The first method described utilizes summation techniques from numerical analysis to derive a general accumulation formula. Manipulating this formula leads to an expression for the modal gross funding premium. The second method uses a partial Taylor series expansion to derive a variant of the Newton-Raphson iteration formula, which can be shown to provide second-order convergence to the funding premium. Other iteration methods providing first-order convergence are also described. A more detailed discussion of these methods and their applicability can be found in the author’s paper “Calculating Funding Premiums for Universal Life Insurance, with Examples,” scheduled to be published in the 1999–2000 volume of the TSA Reports. Journal: North American Actuarial Journal Pages: 20-27 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595893 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595893 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:20-27 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rappaport Author-X-Name-First: Anna Author-X-Name-Last: Rappaport Title: “Development of the Last-Year-of-Life Valuation Model for Retiree Medical Plans”, Adam J. Reese, April 2000 Journal: North American Actuarial Journal Pages: 126-127 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595911 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:126-127 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Gérard Pafumi Author-X-Name-First: Gérard Author-X-Name-Last: Pafumi Title: Pricing Dynamic Investment Fund Protection Abstract: We consider an investment fund whose unit value is modeled by a geometric Brownian motion. Different forms of dynamic investment fund protection are examined. The basic form is a guarantee that instantaneously provides the necessary payments so that the upgraded fund unit value does not fall below a protected level. A closed form expression for the price of such a guarantee is derived. This result can also be applied to price a guarantee where the protected level is an exponential function of time. Moreover, it is explicitly shown how the protection can be generated by construction of the replicating portfolio. The dynamic investment fund protection is compared with the corresponding put option, and it is shown that for short time intervals the ratio of the prices approaches 2. Finally, a more exotic guarantee is considered, where the protected level is a given percentage of the maximal observed fund unit value. Assuming that the protected level remains constant once the payments have started, we obtain a surprisingly simple formula for the price of a perpetual guarantee. Several numerical and graphical illustrations show how the theoretical results can be implemented in practice. Journal: North American Actuarial Journal Pages: 28-37 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595894 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595894 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:28-37 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Petertil Author-X-Name-First: Jeffrey Author-X-Name-Last: Petertil Title: “Development of the Last-Year-of-Life Valuation Model for Retiree Medical Plans”, Adam J. Reese, April 2000 Journal: North American Actuarial Journal Pages: 124-126 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595910 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595910 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:124-126 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Investing for Retirement Abstract: A frequently quoted rule of thumb for allocating assets in a pension plan is that at any time 60% should be in stocks and 40% in bonds. How can these percentages be justified? What are the criteria under which this type of dynamic investment strategy is optimal, and what are the optimal strategies, if the criteria are modified?Suppose that an investor has a certain decision horizon and has chosen an appropriate utility function for measuring his utility of wealth at that time. Then, maximizing the expected utility of wealth at the decision horizon leads to a rational compromise between risk and return. First, we consider the one-period model, in which arbitrary random payments, due at the end of the time period, are traded at the beginning of the interval and valued by a price density. To facilitate understanding of the optimal decision, we introduce the risk tolerance function that is associated with the utility function, and also the implied utility function, that is, the maximal expected utility considered a function of the initial wealth. Second, we consider continuous-time complete securities market models, in which rebalancing of the asset portfolios can take place dynamically over time. This seemingly more complex problem can be reduced to the first problem. The key is that the optimal investment strategy corresponds to the self-financing portfolio that replicates the optimal payoff in the first problem. If there are only two investment vehicles, a risky and a risk-free asset, then the optimal investment strategy is as follows: at any time, the amount invested in the risky asset must be the product of the current risk tolerance and the risk premium on the risky asset, divided by the square of the diffusion coefficient of the risky asset. This result can be restated as follows: the Merton ratio, which is the fraction of current wealth invested in the risky asset, must be the risk-neutral Esscher parameter divided by the elasticity, with respect to current wealth, of the expected marginal utility of optimal terminal wealth. In the more realistic case with more than one risky asset, equally explicit rules are given for the optimal investment strategy. For example, the ratios of the amounts invested in the different risky assets are constant in time; the ratios depend only on the risk-neutral Esscher parameters. Hence, the risky assets can be replaced by a single mutual fund with the right asset mix. In this sense, the case of multiple risky assets can be reduced to the case of a single risky asset. Throughout the paper, explicit formulas are given for the cases of linear risk tolerance utility functions. Journal: North American Actuarial Journal Pages: 42-58 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595899 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595899 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:42-58 Template-Type: ReDIF-Article 1.0 Author-Name: Svein-Arne Persson Author-X-Name-First: Svein-Arne Author-X-Name-Last: Persson Title: “Pricing Dynamic Investment Fund Protection”, Hans U. Gerber and Gérard Pafumi, April 2000 Journal: North American Actuarial Journal Pages: 39-40 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595897 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595897 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:39-40 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Gérard Pafumi Author-X-Name-First: Gérard Author-X-Name-Last: Pafumi Title: Author’s Reply: Pricing Dynamic Investment Fund Protection - Discussion by Terence Chan; François-Serge Lhabitant; Svein-Arne Persson Journal: North American Actuarial Journal Pages: 40-41 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595898 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595898 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:40-41 Template-Type: ReDIF-Article 1.0 Author-Name: Dan Clark Author-X-Name-First: Dan Author-X-Name-Last: Clark Title: “Social Security-Adequacy, Equity, and Progressiveness: A Review of Criteria Based on Experience in Canada and the United States,” Robert L. Brown and Jeffrey Ip, January 2000 Journal: North American Actuarial Journal Pages: 143-144 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595916 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595916 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:143-144 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Jeffrey Ip Author-X-Name-First: Jeffrey Author-X-Name-Last: Ip Title: Authors’ Reply: Social Security-Adequacy, Equity, and Progressiveness: A Review of Criteria Based on Experience in Canada and the United States - Discussion by Dan Clark Journal: North American Actuarial Journal Pages: 144-144 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595917 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595917 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:144-144 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Title: Björk, Tomas, 1998, Journal: North American Actuarial Journal Pages: 146-148 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595918 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595918 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:146-148 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Preaching What We Practice Journal: North American Actuarial Journal Pages: iii-iii Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595919 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595919 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Dennis Scanlon Author-X-Name-First: Dennis Author-X-Name-Last: Scanlon Author-Name: Michael Chernew Author-X-Name-First: Michael Author-X-Name-Last: Chernew Title: Managed Care and Performance Measurement Abstract: Performance measurement systems and report cards which attempt to measure and report the quality of care provided by managed health-care organizations, have become mainstream in health insurance markets as managed care penetration continues to increase. However, little is known about the impact formal plan evaluations have on the contracting and enrollment decisions made by health insurance purchasers and consumers. Information regarding the link between performance evaluations and enrollment is crucial for those charged with projecting future enrollments in and risk profiles of managed care organizations. This paper describes the performance measurement systems currently being used to evaluate managed care plans and reviews the empirical literature for evidence regarding the impact of measures on plan enrollments. Journal: North American Actuarial Journal Pages: 128-138 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595912 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595912 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:128-138 Template-Type: ReDIF-Article 1.0 Author-Name: Frank Reynolds Author-X-Name-First: Frank Author-X-Name-Last: Reynolds Title: “Actuaries at the Dawn of the Computer Age,” James C. Hickman and Linda Heacox, July 1999 Journal: North American Actuarial Journal Pages: 139-140 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595913 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595913 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:139-140 Template-Type: ReDIF-Article 1.0 Author-Name: Clyde Beers Author-X-Name-First: Clyde Author-X-Name-Last: Beers Title: “The Public Responsibility of Actuaries in American Pensions,” Donald S. Grubbs, October 1999 Journal: North American Actuarial Journal Pages: 140-142 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595914 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595914 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:140-142 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Evans Author-X-Name-First: Mark Author-X-Name-Last: Evans Title: “The Society of Actuaries Education and Examination System, 1949–1999,” Harold G. Ingraham, Jr., October 1999 Journal: North American Actuarial Journal Pages: 142-143 Issue: 2 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595915 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595915 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:2:p:142-143 Template-Type: ReDIF-Article 1.0 Author-Name: Werner Hürlimann Author-X-Name-First: Werner Author-X-Name-Last: Hürlimann Title: Bounds for Actuarial Present Values Under the Fractional Independence Assumption Abstract: We consider the fractional independence (FI) survival model, studied by Willmot (1997), for which the curtate future lifetime and the fractional part of it satisfy the statistical independence assumption, called the fractional independence assumption.The ordering of risks of the FI survival model is analyzed, and its consequences for the evaluation of actuarial present values in life insurance is discussed. Our main fractional reduction (FR) theorem states that two FI future lifetime random variables with identical distributed curtate future lifetime are stochastically ordered (stop-loss ordered) if, and only if, their fractional parts are stochastically ordered (stop-loss ordered).The well-known properties of these stochastic orders allow to find lower and upper bounds for different types of actuarial present values, for example when the random payoff functions of the considered continuous life insurances are convex (concave), or decreasing (increasing), or convex not decreasing (concave not increasing) in the future lifetime as argument. These bounds are obtained under the assumption that some information concerning the moments of the fractional part is given. A distinction is made according to whether the fractional remaining lifetime has a fixed mean or a fixed mean and variance. In the former case, simple unique optimal bounds are obtained in case of a convex (concave) present value function.The obtained results are illustrated at the most important life insurance quantities in a continuous random environment, which include bounds for net single premiums, net level annual premiums and prospective net reserves. Journal: North American Actuarial Journal Pages: 70-76 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595827 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595827 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:70-76 Template-Type: ReDIF-Article 1.0 Author-Name: Douglas Hodes Author-X-Name-First: Douglas Author-X-Name-Last: Hodes Author-Name: Sholom Feldblum Author-X-Name-First: Sholom Author-X-Name-Last: Feldblum Author-Name: Antoine Neghaiwi Author-X-Name-First: Antoine Author-X-Name-Last: Neghaiwi Title: The Financial Modeling of Property-Casualty Insurance Companies Abstract: This paper describes a financial model currently being used by a major U.S. multiline property-casualty insurer. The model, which was first developed for solvency monitoring purposes, is now being employed for a variety of internal management purposes as well, including (1) the allocation of equity to corporate units, thereby allowing measurements of profitability by business segment and policy year, as well as analysis of the progression of “free surplus,” (2) the analysis of major risks–such as inflation risks, interest rate risks, and reserving risks–that have heretofore been difficult to quantify, and (3) consideration of varying scenarios on the company’s financial performance, both of macroeconomic conditions as well as of the insurance environment.Many aspects of financial modeling do not differ significantly between life and property-casualty insurers, and these are not discussed in the paper. Rather, the paper focuses on the following topics:1. Surplus allocation and profitability: how economic surplus and the returns on this surplus are determined by line of business, separately for new business and for the runoff of existing business, and how the progression of free surplus is viewed.2. Multifaceted risks: how to model risks that affect multiple components of the insurer’s operations, such as economic risks and financial risks. The multiple effects of macroeconomic conditions and changing inflation rates on workers’ compensation claim frequencies and severities complicate the basic interest rate path modeling of life insurance products and annuity contracts.3. Scenario building: how to construct scenarios of macroeconomic conditions or industry cyclical movements to test the resilience of the company to changing external conditions. Journal: North American Actuarial Journal Pages: 41-69 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595826 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595826 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:41-69 Template-Type: ReDIF-Article 1.0 Author-Name: Aaron Tenenbein Author-X-Name-First: Aaron Author-X-Name-Last: Tenenbein Title: “Combining Life Table Data”, Gilbert W. Fellingham and H. Dennis Tolley, July, 1999 Journal: North American Actuarial Journal Pages: 39-40 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595825 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595825 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:39-40 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Stallard Author-X-Name-First: Eric Author-X-Name-Last: Stallard Title: “Combining Life Table Data”, Gilbert W. Fellingham and H. Dennis Tolley, July, 1999 Journal: North American Actuarial Journal Pages: 38-39 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595824 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595824 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:38-39 Template-Type: ReDIF-Article 1.0 Author-Name: Barnet Berin Author-X-Name-First: Barnet Author-X-Name-Last: Berin Title: Kindig, David A., 1997, Journal: North American Actuarial Journal Pages: 158-159 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595849 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595849 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:158-159 Template-Type: ReDIF-Article 1.0 Author-Name: Barnet Berin Author-X-Name-First: Barnet Author-X-Name-Last: Berin Title: Renn, Derek, editor, 1998, Journal: North American Actuarial Journal Pages: 158-158 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595848 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595848 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:158-158 Template-Type: ReDIF-Article 1.0 Author-Name: Bradley Carlin Author-X-Name-First: Bradley Author-X-Name-Last: Carlin Title: “Summary of Results of Survey of Seminar Attendees,” Marjorie Rosenberg and Warren Luckner, October 1998 Journal: North American Actuarial Journal Pages: 156-158 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595847 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595847 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:156-158 Template-Type: ReDIF-Article 1.0 Author-Name: Ole Hesselager Author-X-Name-First: Ole Author-X-Name-Last: Hesselager Title: “Bounds for Actuarial Present Values Under the Fractional Independence Assumption”, Werner Hürlimann, July, 1999 Journal: North American Actuarial Journal Pages: 79-81 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595829 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595829 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:79-81 Template-Type: ReDIF-Article 1.0 Author-Name: John Pemberton Author-X-Name-First: John Author-X-Name-Last: Pemberton Title: “Forecasting Changes In Mortality: A Search for a Law of Causes and Effects,“ Sam Gutterman and Irwin Vanderhoof, October 1998 Journal: North American Actuarial Journal Pages: 156-156 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595846 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595846 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:156-156 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: “Bounds for Actuarial Present Values Under the Fractional Independence Assumption”, Werner Hürlimann, July, 1999 Journal: North American Actuarial Journal Pages: 76-79 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595828 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595828 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:76-79 Template-Type: ReDIF-Article 1.0 Author-Name: Kim Balls Author-X-Name-First: Kim Author-X-Name-Last: Balls Author-Name: David Sandberg Author-X-Name-First: David Author-X-Name-Last: Sandberg Title: “Economic Valuation Models for Insurers,” David F. Babbel and Craig Merrill, July 1998 Journal: North American Actuarial Journal Pages: 145-152 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595844 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595844 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:145-152 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Lunnon Author-X-Name-First: Martin Author-X-Name-Last: Lunnon Title: “A Logical, Simple Method for Solving the Problem of Properly Indexing Social Security Benefits,” Robert J. Myers, July 1998 Journal: North American Actuarial Journal Pages: 153-155 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595845 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595845 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:153-155 Template-Type: ReDIF-Article 1.0 Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Title: “Author’s Reply: An Actuarial Index of the Right-Tail Risk,” Shaun Wang, April 1998 - Discussion by James G. Berberian and Benjamin W. Wurzburger Journal: North American Actuarial Journal Pages: 141-144 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595842 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595842 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:141-144 Template-Type: ReDIF-Article 1.0 Author-Name: Irwin Vanderhoof Author-X-Name-First: Irwin Author-X-Name-Last: Vanderhoof Title: “Economic Valuation Models for Insurers,” David F. Babbel and Craig Merrill, July 1998 Journal: North American Actuarial Journal Pages: 144-145 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595843 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595843 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:144-145 Template-Type: ReDIF-Article 1.0 Author-Name: Jacques Carriere Author-X-Name-First: Jacques Author-X-Name-Last: Carriere Title: “Author’s Reply: Long-Term Yield Rates for Actuarial Valuations”, Jacques F. Carriere, July, 1999 - Discussions by Michael Sherris and Elias S. W. Shiu Journal: North American Actuarial Journal Pages: 24-24 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595822 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595822 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:24-24 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: “Term Structure Models: A Perspective from the Long Rate”, Yong Yao, July, 1999 Journal: North American Actuarial Journal Pages: 138-138 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595840 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595840 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:138-138 Template-Type: ReDIF-Article 1.0 Author-Name: Gilbert Fellingham Author-X-Name-First: Gilbert Author-X-Name-Last: Fellingham Author-Name: H. Dennis Tolley Author-X-Name-First: H. Author-X-Name-Last: Dennis Tolley Title: Combining Life Table Data Abstract: Actuaries are often required to form opinions or make value assessments entailing data from several tables, possibly generated from different sources. Often, no formal methods of combining tables are used. This paper illustrates a method for combining tables of count data using maximum likelihood methods. Combining data tables can be problematic for several reasons. Often, not all cells will contain data when multiple tables are combined. Also, since the same level of aggregation over covariates is often not available in each of the constituent tables, some data will exist only on the margins. The method we present is appropriate when data for some cells are missing and even when data are available only on the margins. To illustrate the method, we combine mortality tables from three different sources with different classification information. The analysis indicates the possible presence of a health risk factor beyond the use of alcohol and tobacco in a population of active members of a church. Journal: North American Actuarial Journal Pages: 25-38 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595823 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595823 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:25-38 Template-Type: ReDIF-Article 1.0 Author-Name: Benjamin Wurzburger Author-X-Name-First: Benjamin Author-X-Name-Last: Wurzburger Title: “An Actuarial Index of the Right-Tail Risk,” Shaun Wang, April 1998 Journal: North American Actuarial Journal Pages: 139-141 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595841 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595841 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:139-141 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: “Long-Term Yield Rates for Actuarial Valuations”, Jacques F. Carriere, July, 1999 Journal: North American Actuarial Journal Pages: 22-23 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595820 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595820 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:22-23 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Long-Term Yield Rates for Actuarial Valuations”, Jacques F. Carriere, July, 1999 Journal: North American Actuarial Journal Pages: 23-24 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595821 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595821 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:23-24 Template-Type: ReDIF-Article 1.0 Author-Name: George Lundberg Author-X-Name-First: George Author-X-Name-Last: Lundberg Title: The State of Medicine in the Next 50 Years Journal: North American Actuarial Journal Pages: iv-x Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595852 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595852 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:iv-x Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Brave New Era–With Caution Journal: North American Actuarial Journal Pages: ebiii-ebiii Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595851 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595851 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:ebiii-ebiii Template-Type: ReDIF-Article 1.0 Author-Name: Yong Yao Author-X-Name-First: Yong Author-X-Name-Last: Yao Title: Term Structure Models: A Perspective from the Long Rate Abstract: Term structure models based on dynamic asset-pricing theory are discussed by taking a perspective from the long rate. This paper partially answers two questions about the asymptotic behavior of yields on default-free zero-coupon bonds: in frictionless markets having no arbitrage, what should the behavior be; and, in known term structure models, what can the behavior be.In frictionless markets having no arbitrage, yields of all maturities should be positive and uniformly bounded from above. The yield curve should level out as term to maturity increases. Slopes with large absolute values occur only in the early maturities. In a continuous-time framework, the longer the maturity of the yield is, the less volatile it will be. The long rate should be a nondecreasing process. Furthermore, the long rate in continuous-time factor models with nonsingular volatility matrices should be a nondecreasing deterministic function.In the Black, Derman, and Toy model and factor models with the short rate having the mean reversion property, yields of all maturities are uniformly bounded from above. The long rate in the Duffie and Kan model with the mean reversion property is a constant. The long rate in the Heath, Jarrow, and Morton model can be infinite or a nondecreasing process. Examples with the long rate increasing are given in this paper. A model with the long rate and short rate as two state variables is then obtained. Journal: North American Actuarial Journal Pages: 122-138 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595839 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595839 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:122-138 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Walter Klem 1904-1999 Journal: North American Actuarial Journal Pages: 160-160 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595850 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595850 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:160-160 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Linda Heacox Author-X-Name-First: Linda Author-X-Name-Last: Heacox Title: Actuaries at the Dawn of the Computer Age Abstract: The NAAJ is honoring the Society of Actuaries in 1999, its golden anniversary year, by publishing a series of articles on the contributions of actuaries to the development of ideas. In this issue, we look at the advent of the use of computers in insurance operations. We begin with a short essay by James C. Hickman and conclude with comments by the actuaries who were there when computers entered the world of business, changing it forever. Journal: North American Actuarial Journal Pages: 1-3 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595818 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595818 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:1-3 Template-Type: ReDIF-Article 1.0 Author-Name: Octavio Maupomé-Carvantes Author-X-Name-First: Octavio Author-X-Name-Last: Maupomé-Carvantes Title: “Author’s Reply: Critique of Mexico’s New Social Security Act”, Octavio Maupomé-Carvantes, July, 1999 Journal: North American Actuarial Journal Pages: 103-104 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595836 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:103-104 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: “Critique of Mexico’s New Social Security Act”, Octavio Maupomé-Carvantes, July, 1999 Journal: North American Actuarial Journal Pages: 102-103 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595835 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:102-103 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Pokorski Author-X-Name-First: Robert Author-X-Name-Last: Pokorski Title: 12-Year Experience Following Bone Marrow Transplantation with Emphasis on Acute and Chronic Leukemia Abstract: New therapies for a serious impairment can be problematic from a risk classification perspective because insured lives data would not be available to provide guidance when these individuals later apply for insurance coverage. This uncertainty can be decreased by studying reports in the medical literature that observed large cohorts with the desired characteristics. This paper analyzes one of the world’s largest series, which asked the question “What is the long-term mortality and morbidity risk among patients who have already survived for five or more years after bone marrow transplantation?” Data indicate that medical advances have substantially improved prognosis. However, mortality and morbidity risks remain high compared to what would be expected in the general population, and data on a small number of long-term survivors suggest such risk might remain elevated indefinitely. Journal: North American Actuarial Journal Pages: 118-121 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595838 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595838 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:118-121 Template-Type: ReDIF-Article 1.0 Author-Name: Jacques Carriere Author-X-Name-First: Jacques Author-X-Name-Last: Carriere Title: Long-Term Yield Rates for Actuarial Valuations Abstract: Consider the problem of valuing a life insurance or annuity on a person aged 20. The valuation formula requires that we know the prices of pure-discount bonds with maturities of up to 100 years. This article investigates the problem of estimating the yield rate for a pure-discount bond that matures in 100 years. It is shown how to estimate this yield rate with parametric and nonparametric models on the price of U.S. Treasury strips. Moreover, confidence intervals on these rates are constructed with bootstrap methods. Journal: North American Actuarial Journal Pages: 13-22 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595819 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595819 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:13-22 Template-Type: ReDIF-Article 1.0 Author-Name: M. Iqbal Owadally Author-X-Name-First: M. Author-X-Name-Last: Iqbal Owadally Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: Pension Fund Dynamics and Gains/Losses Due to Random Rates of Investment Return Abstract: A simple model for defined benefit pension plans with independent and identically distributed rates of investment return and a stationary membership is considered. Three methods of adjusting the normal cost as gains or losses arise are compared, and a suitable choice of amortization or spread period is made. We also investigate the evolution in time of the first and second moments of the pension fund and contribution levels. Journal: North American Actuarial Journal Pages: 105-117 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595837 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595837 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:105-117 Template-Type: ReDIF-Article 1.0 Author-Name: Werner Hürlimann Author-X-Name-First: Werner Author-X-Name-Last: Hürlimann Title: “Author’s Reply: Bounds for Actuarial Present Values Under the Fractional Independence Assumption”, Werner Hürlimann, July, 1999 Journal: North American Actuarial Journal Pages: 82-84 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595831 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595831 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:82-84 Template-Type: ReDIF-Article 1.0 Author-Name: Octavio Maupomé-Carvantes Author-X-Name-First: Octavio Author-X-Name-Last: Maupomé-Carvantes Title: Critique of Mexico’s New Social Security Act Abstract: The new Social Security Act in Mexico implies not only an important reform in terms of the funding mechanism, but will also have consequences of great importance for the economy, the financial sector, labor markets, and politics. The analysis presented here describes the recent history of Social Security in Mexico and the problems it faced before the reform. This paper refers to research done by actuaries and other professionals to outline the main weaknesses (rather than the presupposed superiority) of fully funded schemes vs. a pay-as-you-go (paygo) method, as well as the main pitfalls of the so-called Chilean model. It also presents the ideas of experts showing that an individual capitalization system is not necessarily more secure than a paygo system and that it transfers risks to workers. I am not of the opinion that the former paygo system was optimal, but I do strongly believe that the reform was done inappropriately, among other reasons because the new system abandons insurance techniques and focuses on investment techniques, despite both concepts being complementary. I suggest that a hybrid, two-tiered system, consisting of a paygo system for low-income workers and an individual accounts system for higher-income workers, could have been a better option for Mexico. Journal: North American Actuarial Journal Pages: 85-98 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595832 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595832 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:85-98 Template-Type: ReDIF-Article 1.0 Author-Name: Enrique de Alba Author-X-Name-First: Enrique Author-X-Name-Last: de Alba Author-Name: Tapen Sinha Author-X-Name-First: Tapen Author-X-Name-Last: Sinha Title: “Critique of Mexico’s New Social Security Act”, Octavio Maupomé-Carvantes, July, 1999 Journal: North American Actuarial Journal Pages: 98-101 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595833 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595833 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:98-101 Template-Type: ReDIF-Article 1.0 Author-Name: Kenneth Manton Author-X-Name-First: Kenneth Author-X-Name-Last: Manton Author-Name: Kenneth Land Author-X-Name-First: Kenneth Author-X-Name-Last: Land Title: “Critique of Mexico’s New Social Security Act”, Octavio Maupomé-Carvantes, July, 1999 Journal: North American Actuarial Journal Pages: 101-102 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595834 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595834 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:101-102 Template-Type: ReDIF-Article 1.0 Author-Name: Alfred Müller Author-X-Name-First: Alfred Author-X-Name-Last: Müller Title: “Bounds for Actuarial Present Values Under the Fractional Independence Assumption”, Werner Hürlimann, July, 1999 Journal: North American Actuarial Journal Pages: 81-82 Issue: 3 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595830 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595830 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:81-82 Template-Type: ReDIF-Article 1.0 Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Title: “Weighted Pricing Functionals with Applications to Insurance: An Overview,” Edward Furman and Ricardas Zitikis, Vol. 13, No. 4, 2009 Journal: North American Actuarial Journal Pages: 278-279 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597590 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597590 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:278-279 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Weighted Pricing Functionals with Applications to Insurance: An Overview,” Edward Furman and Ricardas Zitikis, Vol. 13, No. 4, 2009 Journal: North American Actuarial Journal Pages: 280-280 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597591 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597591 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:280-280 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Elliott Author-X-Name-First: Robert Author-X-Name-Last: Elliott Author-Name: Chuin Liew Author-X-Name-First: Chuin Author-X-Name-Last: Liew Author-Name: Tak Siu Author-X-Name-First: Tak Author-X-Name-Last: Siu Title: “Pricing Asian Options and Equity-Indexed Annuities with Regime Switching by the Trinomial Tree Method”, Fei Lung Yuen and Hailiang Yang, April, 2010 Journal: North American Actuarial Journal Pages: 272-277 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597589 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597589 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:272-277 Template-Type: ReDIF-Article 1.0 Author-Name: Fei Yuen Author-X-Name-First: Fei Author-X-Name-Last: Yuen Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Pricing Asian Options and Equity-Indexed Annuities with Regime Switching by the Trinomial Tree Method Abstract: Equity-indexed annuities (EIAs) provide investors with a minimum rate of return and at the same time the opportunity of gaining a profit that is linked to the performance of an equity index. These properties make EIAs a popular product in the market. For modeling the equity index process and calculating the price of EIAs, as the maturity of EIAs usually is long, it is more reasonable to assume that the interest rate and the volatility of the equity index are stochastic processes. One simple way is to apply the regime-switching model, which allows these parameters depending on the market situation. However, the valuation of derivatives in such models is challenging, especially for the strong path-dependent options such as Asian options. A trinomial tree model is introduced to provide an efficient way to solve this problem. The valuation of Asian options is studied and extended to Asian-option-related EIAs. Journal: North American Actuarial Journal Pages: 256-272 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597588 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597588 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:256-272 Template-Type: ReDIF-Article 1.0 Author-Name: Mario Wüthrich Author-X-Name-First: Mario Author-X-Name-Last: Wüthrich Title: Accounting Year Effects Modeling in the Stochastic Chain Ladder Reserving Method Abstract: In almost all stochastic claims reserving models one assumes that accident years are independent. In practice this assumption is violated most of the time. Typical examples are claims inflation and accounting year effects that influence all accident years simultaneously. We study a Bayesian chain ladder model that allows for accounting (calendar) year effects modeling. A case study of a general liability dataset shows that such accounting year effects contribute substantially to the prediction uncertainty and therefore need a careful treatment within a risk management and solvency framework. Journal: North American Actuarial Journal Pages: 235-255 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597587 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597587 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:235-255 Template-Type: ReDIF-Article 1.0 Author-Name: Jae Ahn Author-X-Name-First: Jae Author-X-Name-Last: Ahn Author-Name: Nariankadu Shyamalkumar Author-X-Name-First: Nariankadu Author-X-Name-Last: Shyamalkumar Title: An Asymptotic Analysis of the Bootstrap Bias Correction for the Empirical CTE Abstract: The a-level Conditional Tail Expectation (CTE) of a continuous random variable X is defined as its conditional expectation given the event {X > qα} where qα represents its α-level quantile. It is well known that the empirical CTE (the average of the n(1 – a) largest order statistics in a sample of size n) is a negatively biased estimator of the CTE. This bias vanishes as the sample size increases but in small samples can be significant. Hence the need for bias correction. Although the bootstrap method has been suggested for correcting the bias of the empirical CTE, recent research shows that alternate kernel-based methods of bias correction perform better in some practical examples. To further understand this phenomenon, we conduct an asymptotic analysis of the exact bootstrap bias correction for the empirical CTE, focusing on its performance as a point estimator of the bias of the empirical CTE.We provide heuristics suggesting that the exact bootstrap bias correction is approximately a kernel-based estimator, albeit using a bandwidth that converges to zero faster than mean square optimal bandwidths. This approximation provides some insight into why the bootstrap method has markedly less residual bias, but at the cost of having higher variance. We prove a central limit theorem (CLT) for the exact bootstrap bias correction using an alternate representation as an /1 distance of the sample observations from the α-level empirical quantile. The CLT, in particular, shows that the bootstrap bias correction has a relative error of n-¼. In contrast, for any given ε > 0, and under the assumption that the sampling density is sufficiently smooth, relative error of order O(n-½+ε) is attainable using kernel-based estimators. Thus, in an asymptotic sense, the bootstrap bias correction as a point estimator of the bias is not optimal in the case of smooth sampling densities. Bootstrapped risk measures have recently found interest as estimators in their own right; as an application we derive the CLT for the bootstrap expectation of the empirical CTE. We also report on a simulation study of the effect of small sample sizes on the quality of the approximation provided by the CLT.In support of the bootstrap method we show that the bootstrap bias correction is optimal if the sampling density is constrained only to be Lipschitz of order 1/2 (or, loosely speaking, to have only half a derivative). Because in practice densities are at least twice differentiable, this optimality result largely fails to make the bootstrap method attractive to practitioners. Journal: North American Actuarial Journal Pages: 217-234 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597586 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597586 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:217-234 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Kim Author-X-Name-First: Joseph Author-X-Name-Last: Kim Title: Conditional Tail Moments of the Exponential Family and Its Related Distributions Abstract: The risk measure is a central theme in the risk management literature. For good reasons, the conditional tail expectation (CTE) has received much interest in both insurance and finance applications. It provides for a measure of the expected riskiness in the tail of the loss distribution. In this article we derive explicit formulas of the CTE and higher moments for the univariate exponential family class, which extends the natural exponential family, using the canonical representation. In addition we show how to compute the conditional tail expectations of other related distributions using transformation and conditioning. Selected examples are presented for illustration, including the generalized Pareto and generalized hyperbolic distributions. We conclude that the conditional tail expectations of a wide range of loss distributions can be analytically obtained using the methods shown in this article. Journal: North American Actuarial Journal Pages: 198-216 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597585 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597585 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:198-216 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Emms Author-X-Name-First: Paul Author-X-Name-Last: Emms Title: Relative Choice Models for Income Drawdown in a Defined Contribution Pension Scheme Abstract: This paper extends a target-based model of income drawdown developed in Gerrard et al. (Insurance: Mathematics and Economics 35: 321–342 [2006]) (GHV) for the distribution phase of a defined contribution pension scheme. The optimal investment strategy of the pension fund and the optimal drawdown are found using linear-quadratic optimization, which minimizes the deviation of the fund and the drawdown from prescribed targets. The GHV model is modified by nondimensionalizing the loss function, so that there is a relative choice between outcomes.Using this model, three classes of target are studied. Endogenous deterministic targets are suggested from the form of the optimal controls, while exogenous deterministic targets can be stated without knowledge of the optimization problem. The third class of stochastic targets is similar to recent annuity products, which incorporate investment risk. Each scheme represents a trade-off between investment risk and return, and this is illustrated by numerical simulation with reference to a canonical example. A particularly attractive form of income drawdown is given by an implied rate of return target. This yields a reasonable investment strategy and a robust consumption profile with age. In addition, it can be easily explained to pension scheme members. Journal: North American Actuarial Journal Pages: 176-197 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597584 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597584 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:176-197 Template-Type: ReDIF-Article 1.0 Author-Name: Linda Golden Author-X-Name-First: Linda Author-X-Name-Last: Golden Author-Name: Charles Yang Author-X-Name-First: Charles Author-X-Name-Last: Yang Author-Name: Hong Zou Author-X-Name-First: Hong Author-X-Name-Last: Zou Title: The Effectiveness of Using a Basis Hedging Strategy to Mitigate the Financial Consequences of Weather-Related Risks Abstract: This paper examines the effectiveness of using a hedging strategy involving a basis derivative instrument to reduce the negative financial consequences of weather-related risks. We examine the effectiveness of using this basis derivative strategy for both summer and winter seasons, using both linear and nonlinear hedging instruments and the impacts of default risk and perception errors on weather hedging efficiency. We also compare the hedging effectiveness obtained using weather indices produced by both the Chicago Mercantile Exchange (CME) and Risk Management Solutions, Inc. (RMS). The results indicate that basis hedging is significantly more effective for the winter season than for the summer season, whether using the CME or RMS weather indices, and whether using linear or nonlinear derivative instruments. It is also found that the RMS regional weather indices are more effective than the CME weather indices, and the effectiveness of using either linear or nonlinear hedging instruments for weather risk management can vary significantly depending on the region of the country. In addition, the results indicate that default risk has some impact on nonlinear basis hedging efficiency but no impact on linear basis hedging efficiency, and reasonable perception errors on default risk have no impact on either linear or nonlinear basis hedging efficiency. Journal: North American Actuarial Journal Pages: 157-175 Issue: 2 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597583 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597583 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:2:p:157-175 Template-Type: ReDIF-Article 1.0 Author-Name: Yaniv Zaks Author-X-Name-First: Yaniv Author-X-Name-Last: Zaks Author-Name: Esther Frostig Author-X-Name-First: Esther Author-X-Name-Last: Frostig Author-Name: Benny Levikson Author-X-Name-First: Benny Author-X-Name-Last: Levikson Title: Pricing a Heterogeneous Portfolio Based on a Demand Function Abstract: Consider a portfolio containing number of risk classes. Each class has its own demand function, which determines the number of insureds in this class as a function of the premium. The insurer determines the premiums based on the number of insureds in each class. The “market” reacts by updating the number of the policyholders, then the insurer updates the premium, and so on. We show that this process has an equilibrium point, and then we characterize this point. Journal: North American Actuarial Journal Pages: 65-73 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597500 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597500 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:65-73 Template-Type: ReDIF-Article 1.0 Author-Name: Zhongfei Li Author-X-Name-First: Zhongfei Author-X-Name-Last: Li Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty Abstract: In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time. Journal: North American Actuarial Journal Pages: 47-64 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597499 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597499 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:47-64 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Asset Allocation with Hedge Funds on the Menu” Phelim Boyle and Sun Siang Liew, October 2007 Journal: North American Actuarial Journal Pages: 89-90 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597502 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597502 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:89-90 Template-Type: ReDIF-Article 1.0 Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Title: Recursive Calculation of the Dividend Moments in a Multi-threshold Risk Model Abstract: In this article, we consider the class of risk models with Markovian claim arrivals studied by Badescu et al. (2005) and Ramaswami (2006), among others. Under a multi-threshold dividend structure, we develop a recursive algorithm for the calculation of the moments of the discounted dividend payments before ruin. Capitalizing on the connection between an insurer’s surplus process and its corresponding fluid flow process, our approach generalizes results obtained by Albrecher and Hartinger (2007) and Zhou (2006) in the framework of the classical compound Poisson risk model (with phase-type claim sizes). Contrary to the traditional analysis of the discounted dividend payments in risk theory, we develop a sample-path-analysis procedure that allows the determination of these moments with or without ruin occurrence (separately). Numerical examples are then considered to illustrate our main results and show the contribution of each component to the moments of the discounted dividend payments. Journal: North American Actuarial Journal Pages: 74-88 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597501 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597501 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:74-88 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Cowell Author-X-Name-First: Michael Author-X-Name-Last: Cowell Title: “Trajectories of Morbidity, Disability, and Mortality among the U.S. Elderly Population: Evidence from the 1984-1999 NLTCS,” Eric Stallard, July 2007 Journal: North American Actuarial Journal Pages: 94-98 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597504 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597504 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:94-98 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Title: “Markov Aging Process and Phase-Type Law of Mortality,” X. Sheldon Lin and Xiaoming Liu, October 2007 Journal: North American Actuarial Journal Pages: 90-94 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597503 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597503 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:90-94 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Christina Erlwein Author-X-Name-First: Christina Author-X-Name-Last: Erlwein Author-Name: Rogemar Mamon Author-X-Name-First: Rogemar Author-X-Name-Last: Mamon Title: The Pricing of Credit Default Swaps under a Markov-Modulated Merton’s Structural Model Abstract: We consider the valuation of credit default swaps (CDSs) under an extended version of Merton’s structural model for a firm’s corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm’s value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm’s value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation. Journal: North American Actuarial Journal Pages: 18-46 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597498 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597498 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:18-46 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Phillip Farrell Author-X-Name-First: Phillip Author-X-Name-Last: Farrell Title: Predictive Modeling of Costs for a Chronic Disease with Acute High-Cost Episodes Abstract: Chronic diseases account for 75% of U.S. national health care expenditures as estimated by the Centers for Disease Control. Many chronic diseases are punctuated by acute episodes of illnesses that occur randomly and create cost spikes in utilization from one year to the next. Modeling to account for these random events provides better estimates of (1) future costs and (2) their variability.A Bayesian statistical model is used to predict the incidence and cost of hospitalizations for one chronic disease. A two-part statistical model is described that separately models the utilization and cost of hospitalization. Individual demographic characteristics are included as well as a simple biological classification system to adjust for the severity of disease among individuals.Results by child, as well as by calendar year, are presented. Using a simple approach to incorporate severity, the model produces reasonable estimates of the number of hospitalizations and cost of hospitalization for the group in total, as well as for a separate group of High Utilizers.The study reflects real-world experiences of persons entering and leaving a group. Modeling at an individual level provides a way to adjust for individual-level severity. The ability to model uneven and unpredictable occurrence of utilization, and potential cost, would be beneficial in the design of insurance programs or for disease management programs. Journal: North American Actuarial Journal Pages: 1-19 Issue: 1 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597497 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597497 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:1:p:1-19 Template-Type: ReDIF-Article 1.0 Author-Name: Donald Jones Author-X-Name-First: Donald Author-X-Name-Last: Jones Title: “Credibility Using a Loss Function from Spline Theory”, Virginia R. Young, January 1998 Journal: North American Actuarial Journal Pages: 114-114 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595683 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595683 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:114-114 Template-Type: ReDIF-Article 1.0 Author-Name: Pierre Lemaire Author-X-Name-First: Pierre Author-X-Name-Last: Lemaire Title: “Bonus-Malus Systems: The European and Asian Approach to Merit-Rating”, Jean Lemaire, January 1998 Journal: North American Actuarial Journal Pages: 45-47 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595670 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595670 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:45-47 Template-Type: ReDIF-Article 1.0 Author-Name: F. De Vylder Author-X-Name-First: F. Author-X-Name-Last: De Vylder Title: “Credibility Using a Loss Function from Spline Theory”, Virginia R. Young, January 1998 Journal: North American Actuarial Journal Pages: 111-114 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595682 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595682 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:111-114 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Credibility Using a Loss Function from Spline Theory Abstract: Current formulas in credibility theory often estimate expected claims as a function of the sample mean of the experience claims of a policyholder. An actuary may wish to estimate future claims as a function of some statistic other than the sample arithmetic mean of claims, such as the sample geometric mean. This can be suggested to the actuary through the exercise of regressing claims on the geometric mean of prior claims. It can also be suggested through a particular probabilistic model of claims, such as a model that assumes a lognormal conditional distribution. In the first case, the actuary may lean towards using a linear function of the geometric mean, depending on the results of the data analysis. On the other hand, through a probabilistic model, the actuary may want to use the most accurate estimator of future claims, as measured by squared-error loss. However, this estimator might not be linear.In this paper, I provide a method for balancing the conflicting goals of linearity and accuracy. The credibility estimator proposed minimizes the expectation of a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear. I consider only those families of distributions with a one-dimensional sufficient statistic and estimators that are functions of that sufficient statistic or of the sample mean. Claim estimators are evaluated by comparing their conditional mean squared errors. In general, functions of the sufficient statistics prove to be better credibility estimators than functions of the sample mean. Journal: North American Actuarial Journal Pages: 101-111 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595681 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595681 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:101-111 Template-Type: ReDIF-Article 1.0 Author-Name: F. De Vylder Author-X-Name-First: F. Author-X-Name-Last: De Vylder Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Title: “On the Time Value of Ruin”, Hans U. Gerber and Elias S.W. Shiu, January 1998 Journal: North American Actuarial Journal Pages: 72-74 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595672 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:72-74 Template-Type: ReDIF-Article 1.0 Author-Name: Alastair Longley-Cook Author-X-Name-First: Alastair Author-X-Name-Last: Longley-Cook Title: Author’s Reply: Risk-Adjusted Economic Value Analysis - Discussion by Kenneth S. Roberts Journal: North American Actuarial Journal Pages: 99-100 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595680 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595680 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:99-100 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: On the Time Value of Ruin Abstract: This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The time of ruin is analyzed in terms of its Laplace transforms, which can naturally be interpreted as discounting. Hence the classical risk theory model is generalized by discounting with respect to the time of ruin. We show how to calculate an expected discounted penalty, which is due at ruin and may depend on the deficit at ruin and on the surplus immediately before ruin. The expected discounted penalty, considered as a function of the initial surplus, satisfies a certain renewal equation, which has a probabilistic interpretation. Explicit answers are obtained for zero initial surplus, very large initial surplus, and arbitrary initial surplus if the claim amount distribution is exponential or a mixture of exponentials. We generalize Dickson’s formula, which expresses the joint distribution of the surplus immediately prior to and at ruin in terms of the probability of ultimate ruin. Explicit results are obtained when dividends are paid out to the stockholders according to a constant barrier strategy. Journal: North American Actuarial Journal Pages: 48-72 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595671 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595671 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:48-72 Template-Type: ReDIF-Article 1.0 Author-Name: Alastair Longley-Cook Author-X-Name-First: Alastair Author-X-Name-Last: Longley-Cook Title: Risk-Adjusted Economic Value Analysis Abstract: The ability of commonly used profitability measures to reflect risk exposure appropriately is evaluated and found lacking. As an alternative, a modern portfolio theory approach, based on utility theory, is recommended. Generalized formulas for calculating risk-adjusted economic values by deriving risk adjustments from certainty equivalents are developed by using the Markowitz expected utility maxim. Practical applications are described. Where appropriate, simplifying assumptions are shown to result in closed-form solutions, thereby reducing the need for extensive, stochastic cashflow simulations. The resulting formulas can be used to measure financial performance on a risk-adjusted basis consistently across different lines of business or to evaluate risk exposures in strategic alternatives. Journal: North American Actuarial Journal Pages: 87-98 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595678 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595678 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:87-98 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: A Model for Analyzing the Impact of Selective Lapsation on Mortality Abstract: This paper presents a model for examining the effect of various relationships between mortality rates and lapse rates on the mortality experience of a cohort of insured lives. The approach is individual rather than the aggregate traditionally used in analyzing selective lapsation. The model assumes that insured lives are healthy at policy issue, but later may move to an impaired state from which the lapse rate is zero. Associated with each insured is an unobservable “risk level” random variable, which reflects the heterogeneity of the insured group. Individual mortality and lapse rates are functions of the risk level. A numerical illustration provides some interesting results obtained by using this model. Journal: North American Actuarial Journal Pages: 79-86 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595677 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595677 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:79-86 Template-Type: ReDIF-Article 1.0 Author-Name: Kenneth Roberts Author-X-Name-First: Kenneth Author-X-Name-Last: Roberts Title: “Risk-Adjusted Economic Value Analysis”, Alastair G. Longley-Cook, January 1998 Journal: North American Actuarial Journal Pages: 99-99 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595679 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595679 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:99-99 Template-Type: ReDIF-Article 1.0 Author-Name: Krupa Subramanian Author-X-Name-First: Krupa Author-X-Name-Last: Subramanian Title: “Bonus-Malus Systems: The European and Asian Approach to Merit-Rating”, Jean Lemaire, January 1998 Journal: North American Actuarial Journal Pages: 38-44 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595669 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595669 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:38-44 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Kalashnikov Author-X-Name-First: Vladimir Author-X-Name-Last: Kalashnikov Title: “On the Time Value of Ruin”, Hans U. Gerber and Elias S.W. Shiu, January 1998 Journal: North American Actuarial Journal Pages: 74-75 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595674 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595674 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:74-75 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Author’s Reply: Credibility Using a Loss Function from Spline Theory: Parametric Models with a One-Dimensional Sufficient Statistic - Discussion by F. Etienne De Vylder; Donald A. Jones; Bjørn Sundt; Gregory C. Taylor Journal: North American Actuarial Journal Pages: 117-117 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595686 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595686 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:117-117 Template-Type: ReDIF-Article 1.0 Author-Name: Jean Lemaire Author-X-Name-First: Jean Author-X-Name-Last: Lemaire Title: Bonus-Malus Systems Abstract: Bonus-malus is a merit-rating technique used in most of Europe and Asia, and some Latin American and African countries. Policyholders from a given risk cell are subdivided into bonus-malus classes. Their claims histories then modify the class upon each renewal. Markov chain theory provides the tools for the design, evaluation, and comparison of these systems. In this article, definitions and examples of bonus-malus systems are provided (Section 2). The main actuarial tools for the study and design of bonus-malus systems are reviewed (Section 3). In the discussions that follow, Krupa Subramanian outlines a model for analyzing market shares in a competitive environment, a crucial research topic given current deregulation trends, and Pierre Lemaire compares actuarial with regulatory approaches to bonus-malus. Journal: North American Actuarial Journal Pages: 26-38 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595668 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595668 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:26-38 Template-Type: ReDIF-Article 1.0 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Title: “On the Time Value of Ruin”, Hans U. Gerber and Elias S.W. Shiu, January 1998 Journal: North American Actuarial Journal Pages: 74-74 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595673 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595673 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:74-74 Template-Type: ReDIF-Article 1.0 Author-Name: Gregory Taylor Author-X-Name-First: Gregory Author-X-Name-Last: Taylor Title: “Credibility Using a Loss Function from Spline Theory”, Virginia R. Young, January 1998 Journal: North American Actuarial Journal Pages: 116-117 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595685 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595685 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:116-117 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Emiliano Valdez Author-X-Name-First: Emiliano Author-X-Name-Last: Valdez Title: Understanding Relationships Using Copulas Abstract: This article introduces actuaries to the concept of “copulas,” a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of probabilistic metric spaces. The literature on the statistical properties and applications of copulas has been developing rapidly in recent years. This article explores some of these practical applications, including estimation of joint life mortality and multidecrement models. In addition, we describe basic properties of copulas, their relationships to measures of dependence, and several families of copulas that have appeared in the literature. An annotated bibliography provides a resource for researchers and practitioners who wish to continue their study of copulas. For those who wish to use copulas for statistical inference, we illustrate statistical inference procedures by using insurance company data on losses and expenses. For these data, we (1) show how to fit copulas and (2) describe their usefulness by pricing a reinsurance contract and estimating expenses for pre-specified losses. Journal: North American Actuarial Journal Pages: 1-25 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595667 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595667 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:1-25 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Authors’ Reply: On the Time Value of Ruin - Discussion by F. Etienne De Vylder; Marc J. Goovaerts; David C.M. Dickson; Vladimir Kalashnikov; Gérard Pafumi Journal: North American Actuarial Journal Pages: 77-78 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595676 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595676 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:77-78 Template-Type: ReDIF-Article 1.0 Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: “Credibility Using a Loss Function from Spline Theory”, Virginia R. Young, January 1998 Journal: North American Actuarial Journal Pages: 114-116 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595684 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595684 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:114-116 Template-Type: ReDIF-Article 1.0 Author-Name: Gérard Pafumi Author-X-Name-First: Gérard Author-X-Name-Last: Pafumi Title: “On the Time Value of Ruin”, Hans U. Gerber and Elias S.W. Shiu, January 1998 Abstract: Journal: North American Actuarial Journal Pages: 75-76 Issue: 1 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595675 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595675 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:1:p:75-76 Template-Type: ReDIF-Article 1.0 Author-Name: Kathryn Watts Author-X-Name-First: Kathryn Author-X-Name-Last: Watts Author-Name: Debbie Dupuis Author-X-Name-First: Debbie Author-X-Name-Last: Dupuis Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: An Extreme Value Analysis Of Advanced Age Mortality Data Abstract: Extreme value theory describes the behavior of random variables at extremely high or low levels. The application of extreme value theory to statistics allows us to fit models to data from the upper tail of a distribution. This paper presents a statistical analysis of advanced age mortality data, using extreme value models to quantify the upper tail of the distribution of human life spans.Our analysis focuses on mortality data from two sources. Statistics Canada publishes the annual number of deaths in Canada, broken down by angender and age. We use the deaths data from 1949 to 1997 in our analysis. The Japanese Ministry of Health, Labor, and Welfare also publishes detailed annual mortality data, including the 10 oldest reported ages at death in each year. We analyze the Japanese data over the period from 1980 to 2000.Using the r-largest and peaks-over-threshold approaches to extreme value modeling, we fit generalized extreme value and generalized Pareto distributions to the life span data. Changes in distribution by birth cohort or over time are modeled through the use of covariates. We then evaluate the appropriateness of the fitted models and discuss reasons for their shortcomings. Finally, we use our findings to address the existence of a finite upper bound on the life span distribution and the behavior of the force of mortality at advanced ages. Journal: North American Actuarial Journal Pages: 162-178 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597419 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597419 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:162-178 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Pai Author-X-Name-First: Jeffrey Author-X-Name-Last: Pai Author-Name: Kevin Shand Author-X-Name-First: Kevin Author-X-Name-Last: Shand Author-Name: Xikui Wang Author-X-Name-First: Xikui Author-X-Name-Last: Wang Title: Compound Poisson Model with Covariates Abstract: Pet insurance in North America continues to be a growing industry. Unlike in Europe, where some countries have as much as 50% of the pet population insured, very few pets in North America are insured. Pricing practices in the past have relied on market share objectives more so than on actual experience. Pricing still continues to be performed on this basis with little consideration for actuarial principles and techniques. Developments of mortality and morbidity models to be used in the pricing model and new product development are essential for pet insurance. This paper examines insurance claims as experienced in the Canadian market. The time-to-event data are investigated using the Cox’s proportional hazards model. The claim number follows a nonhomogenous Poisson process with covariates. The claim size random variable is assumed to follow a lognormal distribution. These two models work well for aggregate claims with covariates. The first three central moments of the aggregate claims for one insured animal, as well as for a block of insured animals, are derived. We illustrate the models using data collected over an eight-year period. Journal: North American Actuarial Journal Pages: 219-234 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597423 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597423 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:219-234 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Bachler Author-X-Name-First: Robert Author-X-Name-Last: Bachler Author-Name: Ian Duncan Author-X-Name-First: Ian Author-X-Name-Last: Duncan Author-Name: Iver Juster Author-X-Name-First: Iver Author-X-Name-Last: Juster Title: A Comparative Analysis Of Chronic And Nonchronic Insured Commercial Member Cost Trends Abstract: Disease management (DM) is increasingly encountered in health plans and employer groups as a health care intervention targeted to individuals with chronic diseases (“Chronics”). To justify the investment by payers in DM, it is important to demonstrate beneficial clinical and financial outcomes. In the absence of randomized control studies, financial results are often estimated in a pre/post-study in which the cost of Chronics in the absence of DM can be predicted by their pre-DM year cost (on a per member per month basis) adjusted for the Nonchronic population’s cost trend. The assumption made, not previously tested, is that absent DM, the Chronic and Nonchronic trends are identical.We calculated Chronic and Nonchronic trends between 1999 and 2002 and compared them under different assumptions regarding identification of chronic disease and medical services. Qualification for the Chronic group was defined as having coronary artery disease, heart failure, diabetes, asthma, or chronic obstructive lung disease. Our base case used an algorithm that identified a member as Chronic prospectively (that is, from the point of identification forward), with one or more of the chronic conditions. We used a data set of 1.5 million commercially insured members.When Chronic and Nonchronic members are identified and included in the population prospectively, the average three-year trend over the study period for chronic and nonchronic members adjusted for high cost outliers were 4.9% and 13.9%, respectively. Adjusting the population experience for differences in service mix had little effect on the divergence in trends. However, altering the Chronic selection algorithm to eliminate migration between groups (thus classifying a member as always Chronic if identified as Chronic at any point in the four years) caused the trends to converge (Chronics, 16.3%; Nonchronics 17.2%; total 16.0%). Using the original selection algorithm but risk-adjusting the populations annually also caused their trends to converge (Chronics, 12.5%; Nonchronics 11.9%). Finally, applying an annual “requalification” process (in which members who qualify as Chronic in one year but not the next are excluded in the year in which they fail to qualify), we see some, although not complete, convergence of trends.Estimating DM program financial outcomes based on the assumption that absent the program, the Chronic population would have had the same trend as the Nonchronic population can lead to erroneous conclusions. Identification of a Chronic member and the point at which that member is reclassified from one subpopulation to another can significantly affect the observed trends in both subpopulations, implying that great care must be taken over classification and interpretation of the resulting trends, and their use in DM savings calculations. Trends calculated using a prospective identification methodology introduce a bias into estimates of outcomes. We refer to this effect, which has not previously been described or discussed in the literature, as “migration bias.” It is critical to understand how trends in a reference population can vary according to selection criteria for disease in the chronic population, service mix, and changes in risk over time. Journal: North American Actuarial Journal Pages: 76-89 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597414 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597414 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:76-89 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “On The Expected Discounted Penalty function for Lévy Risk Processes”, José Garrido and Manuel Morales, October 2006 Journal: North American Actuarial Journal Pages: 216-218 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597422 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597422 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:216-218 Template-Type: ReDIF-Article 1.0 Author-Name: D. J. Pritchard Author-X-Name-First: D. J. Author-X-Name-Last: Pritchard Title: Modeling Disability in Long-Term Care Insurance Abstract: Long-term care (LTC) costs and, in particular, those arising under an LTC insurance contract, are difficult to estimate. This is because of the complex effects of the processes of aging—disability and cognitive impairment. As disability is a gradual, as opposed to a discrete, process, and as the effects are sometimes reversible, a fairly complex model is necessary to capture its nature. This paper concentrates on modeling the disability process of aging only and, in particular, fully incorporates the recovery process as dictated by the data. With the recovery process modeled, the effect on the estimated model costs of disability of the common simplifying assumption that recoveries can be ignored is easily assessed.This paper has twin objectives: (1) to present novel methodology, the penalized likelihood, for using interval-censored longitudinal data, such as the National Long-Term Care Study, to parameterize Markov models; and (2) to estimate the costs arising under an LTC insurance contract in respect of disability. The model is also used to show that ignoring recovery from disability can lead to significant overestimation of LTC insurance costs—suggesting that claims underwriting in LTC insurance may be an important factor in managing claims costs. Journal: North American Actuarial Journal Pages: 48-75 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597413 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597413 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:48-75 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Kaiser Author-X-Name-First: Thomas Author-X-Name-Last: Kaiser Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Title: Interval Estimation of Actuarial Risk Measures Abstract: This article investigates performance of interval estimators of various actuarial risk measures. We consider the following risk measures: proportional hazards transform (PHT), Wang transform (WT), value-at-risk (VaR), and conditional tail expectation (CTE). Confidence intervals for these measures are constructed by applying nonparametric approaches (empirical and bootstrap), the strict parametric approach (based on the maximum likelihood estimators), and robust parametric procedures (based on trimmed means).Using Monte Carlo simulations, we compare the average lengths and proportions of coverage (of the true measure) of the intervals under two data-generating scenarios: “clean” data and “contaminated” data. In the “clean” case, data sets are generated by the following (similar shape) parametric families: exponential, Pareto, and lognormal. Parameters of these distributions are selected so that all three families are equally risky with respect to a fixed risk measure. In the “contaminated” case, the “clean” data sets from these distributions are mixed with a small fraction of unusual observations (outliers). It is found that approximate knowledge of the underlying distribution combined with a sufficiently robust estimator (designed for that distribution) yields intervals with satisfactory performance under both scenarios. Journal: North American Actuarial Journal Pages: 249-268 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597425 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597425 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:249-268 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: R. Freeland Author-X-Name-First: R. Author-X-Name-Last: Freeland Author-Name: Matthew Till Author-X-Name-First: Matthew Author-X-Name-Last: Till Title: Validation Of Long-Term Equity return Models For Equity-Linked Guarantees Abstract: A number of models have been proposed for the equity return process for equity-linked guarantees, following the introduction of stochastic modeling requirements by the Canadian Institute of Actuaries and the American Academy of Actuaries. In this paper we present some of the models that have become well known and discuss the use of residuals to test the fit. After showing that the use of the static, “actuarial approach” to risk management can result in two models with very similar likelihood and residuals giving very different capital requirements, we propose an extension of the bootstrap to compare all the models and to determine whether the optimistic or pessimistic view of the long-term left tail risk is more consistent with the data. Our context is the determination of capital requirements, so we are concerned in this work with real-world rather than riskneutral processes. Journal: North American Actuarial Journal Pages: 28-47 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597412 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597412 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:28-47 Template-Type: ReDIF-Article 1.0 Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Author-Name: José Garrido Author-X-Name-First: José Author-X-Name-Last: Garrido Title: Regime-Switching Periodic Models For Claim Counts Abstract: We study a Cox risk model that accounts for both seasonal variations and random fluctuations in the claims intensity. This occurs with natural phenomena that evolve in a seasonal environment and affect insurance claims, such as hurricanes.More precisely, we define an intensity process governed by a periodic function with a random peak level. The periodic intensity function follows a deterministic pattern in each short-term period and is illustrated by a beta-type function. A Markov chain with m states, corresponding to different risk levels, is chosen for the level process, yielding a so-called regime-switching process.The properties of the corresponding claim-counting process are discussed in detail. By properly defining a Lundberg-type coefficient, we derive upper bounds for finite time ruin probabilities in a two-state case. Journal: North American Actuarial Journal Pages: 235-248 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597424 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597424 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:235-248 Template-Type: ReDIF-Article 1.0 Author-Name: Debbie Dupuis Author-X-Name-First: Debbie Author-X-Name-Last: Dupuis Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: Multivariate Extreme Value Theory And Its Usefulness In Understanding Risk Abstract: This paper gathers recent results in the analysis of multivariate extreme values and illustrates their actuarial application. We review basic and essential background on univariate extreme value theory and stochastic dependence and then provide an introduction to multivariate extreme value theory. We present important concepts for the analysis of multivariate extreme values and collect research results in this area. We draw particular attention to issues related to extremal dependence and show the importance of model selection when fitting an upper tail copula to observed joint exceedances. These ideas are illustrated on four data sets: loss amount and allocated loss adjustment expense under insurance company indemnity claims, lifetimes of pairs of joint and lastsurvivor annuitants, hurricane losses in two states, and returns on two stocks. In each case the extremal dependence structure has an important financial impact. Journal: North American Actuarial Journal Pages: 1-27 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597411 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597411 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:1-27 Template-Type: ReDIF-Article 1.0 Author-Name: Zhaoxia Ren Author-X-Name-First: Zhaoxia Author-X-Name-Last: Ren Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: “Optimal Dividends in an Ornstein-Uhlenbeck Type Model with Credit and Debit Interest,” by Jun Cai, Hans U. Gerber, Hailang Yang, April 2006 Journal: North American Actuarial Journal Pages: 280-283 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597427 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597427 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:280-283 Template-Type: ReDIF-Article 1.0 Author-Name: Kristen Moore Author-X-Name-First: Kristen Author-X-Name-Last: Moore Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Optimal and Simple, Nearly Optimal Rules for Minimizing the Probability Of Financial Ruin in Retirement Abstract: The increasing risk of poverty in retirement has been well documented; it is projected that current and future retirees’ living expenses will significantly exceed their savings and income. In this paper, we consider a retiree who does not have sufficient wealth and income to fund her future expenses, and we seek the asset allocation that minimizes the probability of financial ruin during her lifetime. Building on the work of Young (2004) and Milevsky, Moore, and Young (2006), under general mortality assumptions, we derive a variational inequality that governs the ruin probability and optimal asset allocation. We explore the qualitative properties of the ruin robability and optimal strategy, present a numerical method for their estimation, and examine their sensitivity to changes in model parameters for specific examples. We then present an easy-to-implement allocation rule and demonstrate via simulation that it yields nearly optimal ruin probability, even under discrete portfolio rebalancing. Journal: North American Actuarial Journal Pages: 145-161 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597418 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597418 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:145-161 Template-Type: ReDIF-Article 1.0 Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Author-Name: Lianzeng Zhang Author-X-Name-First: Lianzeng Author-X-Name-Last: Zhang Title: Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims Abstract: Growing research interest has been shown in finite-time ruin probabilities for discrete risk processes, even though the literature is not as extensive as for continuous-time models. The general approach is through the so-called Gerber-Shiu discounted penalty function, obtained for large families of claim severities and discrete risk models. This paper proposes another approach to deriving recursive and explicit formulas for finite-time ruin probabilities with exponential or geometric claim severities. The proposed method, as compared to the general Gerber-Shiu approach, is able to provide simpler derivation and straightforward expressions for these two special families of claims. Journal: North American Actuarial Journal Pages: 269-279 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597426 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597426 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:269-279 Template-Type: ReDIF-Article 1.0 Author-Name: Patrice Gaillardetz Author-X-Name-First: Patrice Author-X-Name-Last: Gaillardetz Author-Name: X. Lin Author-X-Name-First: X. Author-X-Name-Last: Lin Title: Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models Abstract: In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of Jarrow and Turnbull (1995), we derive three martingale probability measures associated with these basic insurance products. These measures are agedependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market. Journal: North American Actuarial Journal Pages: 117-144 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597417 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597417 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:117-144 Template-Type: ReDIF-Article 1.0 Author-Name: Kim Balls Author-X-Name-First: Kim Author-X-Name-Last: Balls Title: Immediate Annuity Pricing in the Presence of Unobserved Heterogeneity Abstract: One of the acknowledged difficulties with pricing immediate annuities is that underwriting the annuitantis life is the exception rather than the rule. In the absence of underwriting, the price paid for a life-contingent annuity is the same for all sales at a given age. This exposes the market (insurance company and potential policyholder alike) to antiselection. The insurance company worries that only the healthiest people choose a life-contingent annuity and therefore adjust mortality accordingly. The potential policyholders worry that they are not being compensated for their relatively poor health and choose not to purchase what would otherwise be a very beneficial product.This paper develops a model of underlying, unobserved health. Health is a state variable that follows a first-order Markov process. An individual reaches the state “death” either by accident from any health state or by progressively declining health state. Health state is one-dimensional, in the sense that health can either “improve” or “deteriorate” by moving farther from or close to the “death” state, respectively. The probability of death in a given year is a function of health state, not of age. Therefore, in this model a person is exactly as old as he or she feels.I first demonstrate that a multistate, ageless Markov model can match the mortality patterns in the common annuity mortality tables. The model is extended to consider several types of mortality improvements: permanent through decreasing probability of deteriorating health, temporary through improved distribution of initial health state, and plateau through the effects of past health improvements.I then construct an economic model of optimal policyholder behavior, assuming that the policyholder either knows his or her health state or has some limited information. the value of mortality risk transfer through purchasing a life-contingent annuity is estimated for each health state under various risk-aversion parameters. Given the economic model for optimal purchasing of annuities, the value of underwriting (limited information about policyholder health state) is demonstrated. Journal: North American Actuarial Journal Pages: 103-116 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597416 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597416 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:103-116 Template-Type: ReDIF-Article 1.0 Author-Name: Barbara Stucki Author-X-Name-First: Barbara Author-X-Name-Last: Stucki Title: Using Reverse Mortgages to Manage the Financial Risk of Long-Term Care Abstract: A penny saved is a penny earned. Poor Richards Almanack (1737)This sage advice of Benjamin Franklin highlights the fact that the basic strategy for ensuring retirement security has changed little over the past 200 years. The traditional formula is simple—accumulate assets during one’s working years and systematically draw down these assets after retirement. In recent years, however, more and more Americans are finding it difficult to save enough for retirement from earnings. The dramatic fall of the stock market between March 2000 and March 2001 exacerbated the problem, reducing personal wealth by an estimated $3.5 trillion in just one year (Weller 2003).These trends are troubling at a time when rising longevity places seniors at greater financial risk due to a chronic illness or disability. There is one bright spot, however—housing wealth has continued to rise. Average home equity in the United States increased more than 10 percent between 2003 and 2004 (Joint Center for Housing Studies 2005). Many older families have substantial amounts of untapped housing wealth, including households whose other retirement resources may be very modest. With more than $2 trillion tied up in home equity, this financial asset has the potential to dramatically increase the ability of seniors to pay for the services and supports that can help them to stay at home.Unlocking illiquid assets such as housing wealth requires us to look more closely at asset decumulation in retirement. Typically, elders sell their home to access the equity they have built up over time. When they move to a more appropriate living situation, the sale of a house can be very beneficial. Those elders with a chronic health condition, who are forced to sell their home to pay for long-term care, however, could face serious problems. Relocating often entails the loss of familiar activities along with support from family and friends. This can reduce quality of life and accelerate cognitive decline (Bassuk 1999). For physically or mentally impaired elders, a better approach would be to use the equity in the home to purchase services and devices that could enable them to stay at home. A new type of financial tool—the reverse mortgage—can help older Americans achieve this goal.Little work has been done to examine the role of reverse mortgages in managing the financial risk of long-term care among older households. Here we address this issue by examining the use of reverse mortgages to help impaired elders continue to live at home (termed “aging in place”). The article also identifies the potential links between reverse mortgages and long-term care insurance. The research presented here is part of a study conducted by the National Council on the Aging, which was funded by grants from the Robert Wood Johnson Foundation and the Centers for Medicare and Medicaid Services (Stucki 2005). The analysis is based on the 2000 Health and Retirement Study and data from the housing and mortgage industries. This study focuses specifically on households where the youngest homeowner is at least age 62, since this is the minimum age to qualify for a reverse mortgage. Because home values have increased substantially since 2000, the numbers presented here will likely underrepresent the potential of this financing option for long-term care.The results of this research suggest that liquidating housing wealth through reverse mortgages can play an important role in improving the way we pay for long-term care in this country. Elders who need assistance with activities of daily living or instrumental activities of daily living have, on average, substantial amounts of home equity that could be used to support informal caregivers and purchase a meaningful amount of services to promote aging in place. Journal: North American Actuarial Journal Pages: 90-102 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597415 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597415 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:90-102 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Cox Author-X-Name-First: Sam Author-X-Name-Last: Cox Title: Ten Years And Counting! Journal: North American Actuarial Journal Pages: iii-iv Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597410 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597410 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: José Garrido Author-X-Name-First: José Author-X-Name-Last: Garrido Author-Name: Manuel Morales Author-X-Name-First: Manuel Author-X-Name-Last: Morales Title: On The Expected Discounted Penalty function for Lévy Risk Processes Abstract: Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such a model is either a compound Poisson process itself or a process with an infinite number of small jumps. Later, in a series of now classical papers, the joint distribution of the time of ruin, the surplus before ruin, and the deficit at ruin was studied (Gerber and Shiu 1997, 1998a, 1998b; Gerber and Landry 1998). These works use the classical and the perturbed risk models and hint that the results can be extended to gamma and inverse Gaussian risk processes.In this paper we work out this extension to a generalized risk model driven by a nondecreasing Lévy process. Unlike the classical case that models the individual claim size distribution and obtains from it the aggregate claims distribution, here the aggregate claims distribution is known in closed form. It is simply the one-dimensional distribution of a subordinator. Embedded in this wide family of risk models we find the gamma, inverse Gaussian, and generalized inverse Gaussian processes. Expressions for the Gerber-Shiu function are given in some of these special cases, and numerical illustrations are provided. Journal: North American Actuarial Journal Pages: 196-216 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597421 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597421 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:196-216 Template-Type: ReDIF-Article 1.0 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Olivier Le Courtois Author-X-Name-First: Olivier Author-X-Name-Last: Le Courtois Author-Name: François Quittard-Pinon Author-X-Name-First: François Author-X-Name-Last: Quittard-Pinon Title: Development and Pricing of a New Participating Contract Abstract: This article designs and prices a new type of participating life insurance contract. Participating contracts are popular in the United States and European countries. They present many different covenants and depend on national regulations. In the present article we design a new type of participating contract very similar to the one considered in other studies, but with the guaranteed rate matching the return of a government bond. We prove that this new type of contract can be valued in closed form when interest rates are stochastic and when the company can default. Journal: North American Actuarial Journal Pages: 179-195 Issue: 4 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597420 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597420 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:179-195 Template-Type: ReDIF-Article 1.0 Author-Name: Colin M. Ramsay Author-X-Name-First: Colin M. Author-X-Name-Last: Ramsay Author-Name: Victor I. Oguledo Author-X-Name-First: Victor I. Author-X-Name-Last: Oguledo Title: Optimal Disability Insurance with Moral Hazards: Absenteeism, Presenteeism, and Shirking Abstract: Presenteeism occurs when employees are present at the workplace but cannot perform at their best because of ill-health or other reasons, while absenteeism occurs when employees are absent from the workplace. Although absenteeism is important, researchers now say presenteeism can be more costly to businesses and may be responsible for as much as three times the health-related lost productivity as compared to absenteeism and may cost the U.S. economy as much as $150 billion per year. Given the cost of absenteeism and presenteeism, one of the objectives of this article is to provide actuaries with the techniques and insights needed to design disability insurance policies that take into account the dynamics of absenteeism and presenteeism. To this end we develop a simple multistate sickness-disability model of the evolution of an employee’s health over time. We assume employees receive sick pay, the size of which depends on their health state, and there is a government-sponsored unemployment insurance program. In our model it is possible for employees in good health to avoid work by staying home, which is called shirking. To reduce shirking, the employer decides to check the health status of a certain percentage of employees who “call in sick.” Given the sick-pay structure, the probability of a health check, and the existence of unemployment insurance, employees develop rational strategies about whether to engage in shirking, absenteeism, or presenteeism. These strategies are captured in a set of Volterra integral equations. We use these Volterra integral equations to show how the employer can design a disability insurance plan that can incentivise employees to eliminate shirking and to act in a manner that will maximize the employer’s expected profits. Journal: North American Actuarial Journal Pages: 143-173 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1017110 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1017110 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:143-173 Template-Type: ReDIF-Article 1.0 Author-Name: Leonid A. Gavrilov Author-X-Name-First: Leonid A. Author-X-Name-Last: Gavrilov Author-Name: Natalia S. Gavrilova Author-X-Name-First: Natalia S. Author-X-Name-Last: Gavrilova Title: Predictors of Exceptional Longevity: Effects of Early-Life and Midlife Conditions, and Familial Longevity Abstract: Knowledge of strong predictors of mortality and longevity is very important for actuarial science and practice. Earlier studies found that parental characteristics as well as early-life conditions and midlife environment play a significant role in survival to advanced ages. However, little is known about the simultaneous effects of these three factors on longevity. This ongoing study attempts to fill this gap by comparing centenarians born in the United States in 1890–1891 with peers born in the same years who died at age 65. The records for centenarians and controls were taken from computerized family histories, which were then linked to 1900 and 1930 U.S. censuses. As a result of this linkage procedure, 765 records of confirmed centenarians and 783 records of controls were obtained. Analysis with multivariate logistic regression found the existence of both general and gender-specific predictors of human longevity. General predictors common for men and women are paternal and maternal longevity. Gender-specific predictors of male longevity are occupation as a farmer at age 40, Northeastern region of birth in the United States, and birth in the second half of year. A gender-specific predictor of female longevity is the availability of radio in the household according to the 1930 U.S. census. Given the importance of familial longevity as an independent predictor of survival to advanced ages, we conducted a comparative study of biological and nonbiological relatives of centenarians using a larger sample of 1,945 validated U.S. centenarians born in 1880–1895. We found that male gender of centenarian has a significant positive effect on survival of adult male relatives (brothers and fathers) but not female blood relatives. Life span of centenarian siblings-in-law is lower compared to life span of centenarian siblings and does not depend on centenarian gender. Wives of male centenarians (who share lifestyle and living conditions) have a significantly better survival compared to wives of centenarians' brothers. This finding demonstrates an important role of shared familial environment and lifestyle in human longevity. The results of this study suggest that familial background, some early-life conditions and midlife characteristics play an important role in longevity. Journal: North American Actuarial Journal Pages: 174-186 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1018390 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1018390 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:174-186 Template-Type: ReDIF-Article 1.0 Author-Name: Hsin Chung Wang Author-X-Name-First: Hsin Chung Author-X-Name-Last: Wang Author-Name: Jack C. Yue Author-X-Name-First: Jack C. Author-X-Name-Last: Yue Title: Mortality, Health, and Marriage: A Study Based on Taiwan's Population Data Abstract: Life expectancy has been increasing significantly since the start of the 20th century, and mortality improvement trends are likely to continue in the 21st century. Stochastic mortality models are used frequently to predict the expansion in life expectancy. In addition to gender, age, period, and cohort are the three main risk factors considered in constructing mortality models. Other than these factors, it is also believed that marital status is related to health and longevity, and many studies have found that married persons have a lower mortality rate than the unmarried. In this study, we have used Taiwan's marital data for the whole population (married, unmarried, divorced/widowed) to evaluate if the marital status can be a preferred criteria. Furthermore, we also want to know whether the preferred criteria will be valid in the future. We chose two popular mortality models, the Lee-Carter and age-period-cohort, to model the mortality improvements for various marital statuses. Because of a linear dependence in the parameters of the age-period-cohort model, we used a computer simulation to choose the appropriate estimation method. Based on Taiwan's marital data, we found that married persons have significantly lower mortality rates than the single, and if converting the difference into a life insurance policy, the discount amount is even larger than that for smokers/nonsmokers. Journal: North American Actuarial Journal Pages: 187-199 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1019518 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1019518 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:187-199 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: Mortality of Smoking by Gender Abstract: Exposure to cigarette smoke has had and will continue to have a huge effect on mortality. Significant differences in smoking prevalence rates by gender have contributed to varying levels and rates of improvement in mortality over the last several decades and are expected to continue to influence mortality improvement differently over the next several decades. The combined effect of greater historical smoking prevalence rates by males and their corresponding earlier and larger reduction has in part been responsible for the recent improvement in mortality rates for males compared to that for females in the United States. Similar patterns are evident in almost all economically developed countries, although their timing and levels differ. The patterns in less-developed countries will likely follow similar patterns as concerns emerge about the effect of smoking on the mortality of their citizens. The objective of this article is to compare smoking prevalence and cessation by gender and the effect on smoking-attributable and, in turn, all-cause mortality. A summary of mortality attribution approaches used to enhance the evaluation of the effect of smoking and projections of mortality rates by gender is also provided. Journal: North American Actuarial Journal Pages: 200-223 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1018389 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1018389 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:200-223 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: S. David Promislow Author-X-Name-First: S. David Author-X-Name-Last: Promislow Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Purchasing Term Life Insurance to Reach a Bequest Goal: Time-Dependent Case Abstract: We consider the problem of how an individual can use term life insurance to maximize the probability of reaching a given bequest goal, an important problem in financial planning. We assume that the individual buys instantaneous term life insurance with a premium payable continuously. We allow the force of mortality to vary with time, which, as we show, greatly complicates the problem. Journal: North American Actuarial Journal Pages: 224-236 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1033107 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1033107 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:224-236 Template-Type: ReDIF-Article 1.0 Author-Name: Hans U. Gerber Author-X-Name-First: Hans U. Author-X-Name-Last: Gerber Title: Discussion on “Empirical Approach for Optimal Reinsurance Design,” by Ken Seng Tan and Chengguo Weng, Volume 18(2) Journal: North American Actuarial Journal Pages: 237-237 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1065687 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1065687 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:237-237 Template-Type: ReDIF-Article 1.0 Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Title: Response to Hans U. Gerber on His Comments on Our Paper Entitled ”Empirical Approach for Optimal Reinsurance Design” Journal: North American Actuarial Journal Pages: 238-239 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1085752 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1085752 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:238-239 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Call for Papers: Risk Theory Society Annual Seminar Journal: North American Actuarial Journal Pages: 240-240 Issue: 3 Volume: 19 Year: 2015 Month: 7 X-DOI: 10.1080/10920277.2015.1087794 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1087794 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:3:p:240-240 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Thom Author-X-Name-First: Michael Author-X-Name-Last: Thom Title: The Prudential Supervision of Financial Conglomerates in the European Union Abstract: Around the world, the formation of financial conglomerates is gaining importance. In the United States, the provisional agreement between Congress and President Clinton’s administration to break down the barriers between banking, insurance, and securities firms by repealing the Glass-Steagall Act is no less than revolutionary. Meanwhile, in the European Union (EU), where the establishment of financial groups working in all three sectors has long been permitted, the Financial Services Action Plan (COM 1999),1 as endorsed by European Heads of State at the Köln Council, identifies the further development of prudential rules for financial conglomerates as a top priority for EU financial services legislation in the coming years.The focus of EU prudential legislation is on individual financial services undertakings, that is, on the bank, insurance company, or securities undertaking and not on the position and operation of the conglomerate as a whole. From this angle, the potential danger is one of a growing mismatch between the prudential approach, which looks at the individual legal undertakings separately, and the business approach, which manages and controls the conglomerate as a whole in different product and geographic areas. For this reason, the basic EU prudential framework has been supplemented to address the conglomerate dimension.This paper presents an overview of financial services prudential legislation in the EU. It explains the role of the European Commission and gives a summary of the basic prudential framework for financial services, focusing on the single passport concept and the principle of mutual recognition. It examines the recent history of financial concentration and conglomeration in Europe and discusses general prudential issues arising from financial conglomerates. The paper also examines existing EU prudential legislation on financial conglomerates and how this might be developed in the future. Finally, some conclusions are drawn. It is hoped that this brief overview of how the European Union has tackled and is tackling the difficult issue of financial conglomerate supervision might be of interest to North American readers at a time when the United States is changing its prudential legislation to permit the development of financial conglomerates. Journal: North American Actuarial Journal Pages: 121-130 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595930 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595930 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:121-130 Template-Type: ReDIF-Article 1.0 Author-Name: Larry Wall Author-X-Name-First: Larry Author-X-Name-Last: Wall Title: “The Prudential Supervision of Financial Conglomerates in the European Union”, Michael Thom, July 2000 Journal: North American Actuarial Journal Pages: 130-138 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595931 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595931 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:130-138 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Title: “The Society of Actuaries Education and Examination System, 1949–1999,” Harold G. Ingraham, Jr., October 1999 Journal: North American Actuarial Journal Pages: 139-144 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595932 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595932 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:139-144 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: Mitchell, Olivia S., Hammond, P. Brett, and Rappaport, Anna M., editors, 1999, Journal: North American Actuarial Journal Pages: 145-145 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595933 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595933 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:145-145 Template-Type: ReDIF-Article 1.0 Author-Name: Allen Berger Author-X-Name-First: Allen Author-X-Name-Last: Berger Title: The Integration of the Financial Services Industry Abstract: We examine the efficiency effects of the integration of the financial services industry and suggest directions for future research. We also propose a relatively broad working definition of integration and employ U.S. and European data on financial services industry mergers and acquisitions (M&As) to illustrate several types of integration. The analysis suggests that there is a large potential for efficiency gain from integration, but only a relatively small part of this potential may be realized. Integration appears to bring about larger revenue efficiency gains than cost efficiency gains, and most of the gains appear to be linked to benefits from risk diversification. Journal: North American Actuarial Journal Pages: 25-45 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595922 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595922 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:25-45 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Belth Author-X-Name-First: Joseph Author-X-Name-Last: Belth Title: Who Says Financial Services Integration Is In Consumers’ Best Interests? Journal: North American Actuarial Journal Pages: 20-24 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595921 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595921 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:20-24 Template-Type: ReDIF-Article 1.0 Author-Name: Elisa Bain Author-X-Name-First: Elisa Author-X-Name-Last: Bain Author-Name: Ian Harper Author-X-Name-First: Ian Author-X-Name-Last: Harper Title: Integration of Financial Services Abstract: This paper examines convergence in the Australian financial services industry. It traces the emergence of financial conglomeration in Australia from its origins in the 1950s. The institutions involved, their market shares, and their mix of financial activities are described. The causes of financial conglomeration in Australia are discussed, noting that conglomeration has occurred in two main phases in Australia. The regulatory treatment of financial conglomerates in Australia is described, including recent changes to the Australian regulatory framework following the 1997 Financial System Inquiry. The paper concludes with some speculation as to the likely future of financial conglomeration in Australia. Journal: North American Actuarial Journal Pages: 1-19 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595920 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595920 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:1-19 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Stein Author-X-Name-First: Robert Author-X-Name-Last: Stein Author-Name: Peter Porrino Author-X-Name-First: Peter Author-X-Name-Last: Porrino Title: The State of the Industry Abstract: The new millennium has arrived, bringing with it tougher competitive conditions than most insurance companies would have thought possible a few decades ago. While the state of the industry today is the direct result of the transformation of the overall financial services industry over the past 20 years, its metamorphosis is still in progress. Staggering changes have taken place in the financial services environment during this period. What do these changes mean for insurers, and what will the industry look like 20 years down the road?A brave new world lies before us—a world dominated by the advent of a more financially astute and demanding customer and the power of the Internet. The retail marketplace is being transformed as providers scramble to meet the needs of sophisticated, technology-smart consumers. To reach these consumers, insurance companies must rethink the way they do business, embracing multiple distribution channels and seeking out bold new alliances. The stakes are higher than ever, and companies that remain mired in the past will not be around for long. Journal: North American Actuarial Journal Pages: 113-120 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595929 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595929 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:113-120 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Smith Author-X-Name-First: Stephen Author-X-Name-Last: Smith Title: Remarks on “Financial Services Integration: Right for some, Wrong for Others?” Abstract: I have been asked to provide some introductory remarks on the structure of the financial services industry in the 21st century. Each of the panelists will give their own unique perspective on why consolidation is or is not a good idea for the firms where they work. I, on the other hand, would like to take a little time to provide an overview of what I see as competing “models” for the delivery of financial services. I will try to argue that these models are not necessarily mutually exclusive and that certain clientele may be attracted to one or the other. Thus, integration will indeed turn out to be right for some and wrong for others. Journal: North American Actuarial Journal Pages: 109-110 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595927 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595927 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:109-110 Template-Type: ReDIF-Article 1.0 Author-Name: Bob St. Jacques Author-X-Name-First: Bob St. Author-X-Name-Last: Jacques Title: Integration of Financial Services Abstract: Integration financial services is a term with many meanings. Definitions might include:ownership of different segments of financial services,the distribution of products of one segment by another, anda consumer-centric strategy driven to satisfy the needs of the customer regardless of organizational structures.For the purposes of my paper, I will define it as the erasing of boundaries leading to consumers receiving value propositions that are not restricted by traditional industry segment barriers. Journal: North American Actuarial Journal Pages: 111-112 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595928 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595928 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:111-112 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Pierre Daniel Author-X-Name-First: Jean-Pierre Author-X-Name-Last: Daniel Title: The Integration Of Financial Services in Europe Abstract: Changes over the last few decades in managing risk and investing money have been so radical that we can only describe them as being huge disruptions, maybe even revolutions. The boundaries that used to exist between the different financial activities have disappeared. Although things have accelerated rapidly over the last few decades, we should keep in mind that these developments are by no means new. The pawnbrokers and foreign exchange dealers of the Middle Ages, whose professions were separate and clearly identifiable, have seen their activities completely integrated into so-called universal banking services. More recently, merchant banks in France, who used to be the subject of specific regulation, have disappeared as separate legal entities. In the insurance field, it was barely 30 years ago, that some large businesses insured only against fire risks and others only casualty risks. The distinction between life and non-life, which is still maintained in the regulations, makes little sense in the everyday reality of insurance groups who transact these two activities together.However, when we talk of the integration of financial services, we have in mind an even more recent phenomenon. Financial integration incorporates two developments, known in French as bancassurance and assurfinance. Today, under extremely diverse legal guises but following the same economic logic, banks sell insurance products and insurance networks sell banking products.This movement can only be understood initially as the result of a need to diversify. Each one of these two large categories of financial intermediaries borrowed something from the other in order to increase its product range or bolster the know-how of its networks. It was simply about making sales organizations more cost effective by having them sell products outside of their traditional skills area, at more or less marginal cost. Today the expansion of offerings is done, approved, and even expounded on by theorists. And so now the next question is whether we should go further—turning our attention from distribution to manufacturing. This is where the current debate on the integration of financial services lies. Bluntly, if we allow banks to sell insurance policies and insurers to sell consumer credit, should we allow a joint organization to design such products and distribute them down both channels at the same time? More subtly, we might ask ourselves whether we should be exercising more specific control over these financial conglomerates that, while maintaining a formal legal separation between banking and insurance, constitute in fact a single decision-making center.This article sets out to portray what is perhaps not the state of the law, but at least the state of the art, on this topic in the European Union. In the first part, it will show that while sales integration is an undeniable fact, with the customer seeing fewer and fewer differences, it still remains that banks and insurance carriers are separate entities from a legal perspective and that the European Union remains totally committed to controlling financial conglomerates. In practice, integration of financial services takes different forms. In part two, we examine cases involving problems between entities doing the same job, and cooperation between design facilities without any apparent desire to go further. In the long run, this integration will succeed only if it receives the public�s approval. Part three addresses what consumers and investors want. We observe that after decades of exposure to specialized networks, consumers are not necessarily as enthusiastic as proponents of integration would have hoped. As adult consumers, they are not prepared to buy just any financial service anywhere they can, and they still largely place their trust in the brands they know. Journal: North American Actuarial Journal Pages: 53-63 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595925 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595925 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:53-63 Template-Type: ReDIF-Article 1.0 Author-Name: James Garven Author-X-Name-First: James Author-X-Name-Last: Garven Title: The Role of Electronic Commerce In Financial Services Integration Abstract: In recent years, the combined effects of deregulation in financial services, along with advances in telecommunications and information technology, are forcing far-reaching changes upon the insurance industry. The result is the industry is becoming more competitive. The emerging role of electronic commerce (e-commerce) is particularly important and interesting to study.I offer a brief survey of the role of e-commerce in the insurance industry. The paper is organized in the following manner: Section 1 summarizes Internet trends and discusses various related public policy issues; Section 2 addresses online insurance supply and demand; Section 3 discusses the economics of disintermediation and reintermediation and explains how this applies to e-commerce in the insurance industry. Finally, Section 4 offers a set of concluding remarks. Journal: North American Actuarial Journal Pages: 64-70 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595926 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595926 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:64-70 Template-Type: ReDIF-Article 1.0 Author-Name: J. David Cummins Author-X-Name-First: J. David Author-X-Name-Last: Cummins Title: “The Integration of the Financial Services Industry: Where Are the Efficiencies?”, Allen N. Berger, July 2000 Journal: North American Actuarial Journal Pages: 45-50 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595923 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595923 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:45-50 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Grace Author-X-Name-First: Martin Author-X-Name-Last: Grace Title: “The Integration of the Financial Services Industry: Where Are the Efficiencies?”, Allen N. Berger, July 2000 Journal: North American Actuarial Journal Pages: 50-52 Issue: 3 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595924 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595924 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:3:p:50-52 Template-Type: ReDIF-Article 1.0 Author-Name: Tim Verdonck Author-X-Name-First: Tim Author-X-Name-Last: Verdonck Author-Name: Martine Van Wouwe Author-X-Name-First: Martine Author-X-Name-Last: Van Wouwe Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Title: A Robustification of the Chain-Ladder Method Abstract: In a non-life insurance business an insurer often needs to build up a reserve to able to meet his or her future obligations arising from incurred but not reported completely claims. To forecast these claims reserves, a simple but generally accepted algorithm is the classical chain-ladder method. Recent research essentially focused on the underlying model for the claims reserves to come to appropriate bounds for the estimates of future claims reserves. Our research concentrates on scenarios with outlying data. On closer examination it is demonstrated that the forecasts for future claims reserves are very dependent on outlying observations. The paper focuses on two approaches to robustify the chain-ladder method: the first method detects and adjusts the outlying values, whereas the second method is based on a robust generalized linear model technique. In this way insurers will be able to find a reserve that is similar to the reserve they would have found if the data contained no outliers. Because the robust method flags the outliers, it is possible to examine these observations for further examination. For obtaining the corresponding standard errors the bootstrapping technique is applied. The robust chain-ladder method is applied to several run-off triangles with and without outliers, showing its excellent performance. Journal: North American Actuarial Journal Pages: 280-298 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597555 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597555 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:280-298 Template-Type: ReDIF-Article 1.0 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: Author’s Reply: On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model - Discussion by David C. M. Dickson; Jae-Kyung Woo; Hans U. Gerber; Elias S. W. Shiu Journal: North American Actuarial Journal Pages: 278-279 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597554 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597554 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:278-279 Template-Type: ReDIF-Article 1.0 Author-Name: Benjamin Avanzi Author-X-Name-First: Benjamin Author-X-Name-Last: Avanzi Title: Strategies for Dividend Distribution: A Review Abstract: In today’s world of financial uncertainty, one major public concern is to assess (and possibly improve) the stability of companies that take on risks. Actuaries have been aware of that issue for a very long time and have a great experience in modeling the activity of a risk business. During the first part of the twentieth century, they focused on the probability of ruin to assess the stability of their company. In his seminal paper of 1957 Bruno de Finetti criticized this approach and laid the foundations of what would become an increasingly popular topic: the study of dividend strategies. The contributions made by actuaries in that field constitute a substantial body of knowledge, whose interest is relevant not only to insurance but also to a much broader range of areas of practice. In this paper we aim at a taxonomical synthesis of the 50 years of actuarial research that followed de Finetti’s original paper. Journal: North American Actuarial Journal Pages: 217-251 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597549 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597549 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:217-251 Template-Type: ReDIF-Article 1.0 Author-Name: Doug Andrews Author-X-Name-First: Doug Author-X-Name-Last: Andrews Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: Is Defined Contribution a Panacea for Defined Benefit Social Security Funding Problems? Lessons from Two Countries Abstract: Many countries are changing their social security retirement program from a defined benefit (DB) to a defined contribution (DC) basis. Other countries, such as the United States, are discussing the introduction of a DC component. The replacement of a DB social security retirement system by a DC system raises many important social and economic issues. Thoughtful consideration must be given to the choice of criteria for prioritizing objectives and outcomes, as well as in weighing the advantages and disadvantages between different cohorts. For example, if any DB obligations are not fully funded at transition, a double burden will rest with transition generation(s). Moreover, economists tend to assess the value of the system based on measures of economic efficiency and the lack of impediments to a freely operating labor market. But such an assessment may not give adequate recognition to factors such as individual wealth/poverty an individual’s ability to make optimal investment decisions, and transaction costs associated with operating individual accounts. Indeed, some countries have suggested that notional defined contribution (NDC) accounts may be the best way to address such issues.Focusing on the adoption of a funded DC social security retirement program in Chile and the adoption of a pay-as-you-go NDC social security retirement program by Sweden, this research identifies factors of financial markets, economics, and demographics necessary to enable a move to DC accounts. In addition, it identifies the characteristics of the financial markets necessary to support payments (wealth transfers) to retirees from a DC social security retirement program.The paper considers the questions of social security funding and plan type (DB vs. DC) and attempts to assess the suitability of certain reform options for the United States. It approaches the issue by identifying the features of each type and the strengths and weaknesses associated with those features. A significant part of this analysis is the illustrative description of two real-world plans, Chilean and Swedish. It then uses the theoretical considerations and the experience of those plans to draw conclusions about reform proposals in the United States, particularly the President’s Commission to Strengthen Social Security Model 2. Journal: North American Actuarial Journal Pages: 186-201 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597547 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597547 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:186-201 Template-Type: ReDIF-Article 1.0 Author-Name: Hoi Wong Author-X-Name-First: Hoi Author-X-Name-Last: Wong Author-Name: Ka Lam Author-X-Name-First: Ka Author-X-Name-Last: Lam Title: Valuation of Discrete Dynamic Fund Protection Under Lévy Processes Abstract: This paper investigates the valuation of discrete dynamic fund protection (DFP) under Levy processes. Specifically, the analytical solution of discrete DFP under Lévy processes is obtained in terms of Fourier transforms. The derivation uses Spitzer’s formula and leads to a recursion on computing the characteristic function of the maximum protection-to-fund ratio using the Fourier inversion. DFP can then be valued efficiently and accurately via the fast Fourier transform. The pricing behavior of the discrete DFP is numerically examined using several Levy processes, such as geometric Brownian motion, jump-diffusion models, and variance gamma process. Numerical experiments confirm that the proposed approach produces highly accurate discrete DFP values within 1 second. Journal: North American Actuarial Journal Pages: 202-216 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597548 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597548 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:202-216 Template-Type: ReDIF-Article 1.0 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Title: “On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model”, David Landriault and Gordon E. Willmot, April, 2009 Journal: North American Actuarial Journal Pages: 271-272 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597551 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597551 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:271-272 Template-Type: ReDIF-Article 1.0 Author-Name: Norma Nielson Author-X-Name-First: Norma Author-X-Name-Last: Nielson Title: Examining the Effects of Guarantee Funds on Pension Plans Abstract: Bankruptcy risk falls to pension plan participants if a plan sponsor fails when a defined benefit (DB) pension plan is underfunded. This article examines the incidence of that risk and how it changes when public policy provides a guarantee fund. Although government-based guarantee funds are in a unique position to provide pension protection, primarily because of the extent to which the risk of sponsor default is systematic in nature, a looming question is the extent to which such guarantees are exposed to moral hazard. The article focuses on that question using data from four Canadian provinces, including one (Ontario) that operates a guarantee fund for pensions. The findings show that plan assets per DB-plan participant increase with the earnings of workers and decrease with higher unemployment, and that level of assets also is moderated by the influence of taxes, with higher plan assets observed when and where tax rates are higher. Plans in Ontario had on average $20,035 less in asset value per participant, and Ontario plans covered by the guarantee fund had an average of $16,497 less per participant than other Canadian DB plans not backed by a guarantee fund. A separate model finds the presence of a guarantee fund to be one of a very small number of variables significant in explaining variability in the plans’ funded ratios. These empirical results are consistent with the existence of moral hazard. Journal: North American Actuarial Journal Pages: 157-169 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597545 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597545 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:157-169 Template-Type: ReDIF-Article 1.0 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model Abstract: The seminal paper by Gerber and Shiu (1998) unified and extended the study of the event of ruin and related quantities, including the time at which the event of ruin occurs, the deficit at the time of ruin, and the surplus immediately prior to ruin. The first two of these quantities are fundamentally important for risk management techniques that utilize the ideas of Value-at-Risk and Tail Value-at-Risk. As is well known, calculation of these and related quantities requires knowledge of the associated probability distributions. In this paper we derive an explicit expression for the joint (defective) distribution of the time to ruin, the surplus immediately prior to ruin, and the deficit at ruin in the classical compound Poisson risk model. As a by-product, we obtain expressions for the three bivariate distributions generated by the time to ruin, the surplus prior to ruin, and the deficit at ruin. Finally, we consider mixed Erlang claim sizes and show how the joint (defective) distribution of the time to ruin, the surplus prior to ruin, and the deficit at ruin can be calculated. Journal: North American Actuarial Journal Pages: 252-270 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597550 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597550 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:252-270 Template-Type: ReDIF-Article 1.0 Author-Name: Eduardo de Melo Author-X-Name-First: Eduardo Author-X-Name-Last: de Melo Author-Name: Beatriz Mendes Author-X-Name-First: Beatriz Author-X-Name-Last: Mendes Title: Pricing Participating Inflation Retirement Funds Through Option Modeling and Copulas Abstract: Pension plans and life insurances offering minimum performance guarantees are very common worldwide. In the Brazilian market, the customers of a common type of defined contribution plan have the right to receive, over their savings, the positive difference between the return of a specified investment fund, usually a fixed income fund, and the minimum guaranteed rate, commonly defined as the composition of a fixed interest rate and a floating inflation rate. This instrument can be characterized as an option to exchange one asset, the minimum guaranteed rate, for another, the return of the specified investment fund. In this paper we provide a closed formula to evaluate this liability that depends on two stochastic rates assuming bivariate normality. We also explore the use of copulas for the modeling of the dependence structure and price the options using Monte Carlo simulation to compare the effects of the copula specification in their values. An application with real data is provided. The model makes use of a one-factor Vasicek framework for the term structures of interest rate and inflation rate. Journal: North American Actuarial Journal Pages: 170-185 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597546 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597546 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:170-185 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model”, David Landriault and Gordon E. Willmot, April, 2009 Journal: North American Actuarial Journal Pages: 277-278 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597553 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597553 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:277-278 Template-Type: ReDIF-Article 1.0 Author-Name: Jae-Kyung Woo Author-X-Name-First: Jae-Kyung Author-X-Name-Last: Woo Title: “On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model”, David Landriault and Gordon E. Willmot, April, 2009 Journal: North American Actuarial Journal Pages: 272-277 Issue: 2 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597552 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597552 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:2:p:272-277 Template-Type: ReDIF-Article 1.0 Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Guy Coughlan Author-X-Name-First: Guy Author-X-Name-Last: Coughlan Author-Name: David Epstein Author-X-Name-First: David Author-X-Name-Last: Epstein Author-Name: Marwa Khalaf-Allah Author-X-Name-First: Marwa Author-X-Name-Last: Khalaf-Allah Title: Backtesting Stochastic Mortality Models Abstract: This study sets out a backtesting framework applicable to the multiperiod-ahead forecasts from stochastic mortality models and uses it to evaluate the forecasting performance of six different stochastic mortality models applied to English & Welsh male mortality data. The models considered are the following: Lee-Carter’s 1992 one-factor model; a version of Renshaw-Haberman’s 2006 extension of the Lee-Carter model to allow for a cohort effect; the age-period-cohort model, which is a simplified version of Renshaw-Haberman; Cairns, Blake, and Dowd’s 2006 two-factor model; and two generalized versions of the last named with an added cohort effect. For the data set used herein, the results from applying this methodology suggest that the models perform adequately by most backtests and that prediction intervals that incorporate parameter uncertainty are wider than those that do not. We also find little difference between the performances of five of the models, but the remaining model shows considerable forecast instability. Journal: North American Actuarial Journal Pages: 281-298 Issue: 3 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597592 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597592 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:3:p:281-298 Template-Type: ReDIF-Article 1.0 Author-Name: Alice Wade Author-X-Name-First: Alice Author-X-Name-Last: Wade Title: Mortality Projections for Social Security Programs in the United States Abstract: Worldwide, the twentieth century brought tremendous reductions in mortality at all ages for both males and females. The reductions in mortality, combined with the aging of the baby boomers and lower fertility rates, are projected to increase the proportion of the U.S. population that is above age 65 in the coming decades. This paper examines past mortality trends, discusses how these trends may change over the next 75 years, and analyzes implications of these trends for the growth of the elderly population. In addition, this paper describes the methods and assumptions used to project future mortality rates and presents results, including assumed annual rates of mortality reduction and projected life expectancies. It also discusses stochastic time-series methods that are used to help quantify the variability in the mortality rate projections. Journal: North American Actuarial Journal Pages: 299-315 Issue: 3 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597593 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597593 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:3:p:299-315 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Montambeault Author-X-Name-First: Michel Author-X-Name-Last: Montambeault Author-Name: Jean-Claude Ménard Author-X-Name-First: Jean-Claude Author-X-Name-Last: Ménard Title: Mortality Projections for Social Security Programs in Canada Abstract: Worldwide, the 20th century brought tremendous reductions in mortality at all ages for both males and females. The reductions in mortality, combined with the aging of the baby boomers and lower fertility rates, are projected to increase the proportion of the Canadian population that is above age 65 in the coming decades. This paper examines past mortality trends in Canada and discusses how these trends may change over the next 75 years, thus influencing the growth of the elderly population. In addition, this paper describes the methods and assumptions used to project future mortality rates in Canada, and the results include assumed annual rates of mortality improvement and projected life expectancies. As well, this paper discusses stochastic time-series methods that are used to help quantify the variability in the mortality rate projections. Journal: North American Actuarial Journal Pages: 316-337 Issue: 3 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597594 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597594 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:3:p:316-337 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Yunjie (Winnie) Sun Author-X-Name-First: Yunjie Author-X-Name-Last: (Winnie) Sun Title: Household Life Insurance Demand Abstract: What types of households own life insurance? Who owns term life and who owns whole life insurance? These are questions of great interest to insurers that operate in a highly competitive market. To answer these questions, we jointly examine household demand of two types of insurance, term and whole life, using data from the Survey of Consumer Finances, a probability sample of the U.S. population. We model both the frequency and the severity of demand for insurance, building on the work of Lin and Grace by using explanatory variables that they developed. For the frequency portion, the household decisions about whether to own term and whole life insurance are modeled simultaneously with a bivariate probit regression model. Given ownership of life insurance by a household, the amounts of insurance are analyzed using generalized linear models with a normal copula. The copula permits the bivariate modeling of insurance amounts for households who own both term and whole life insurance, about 20% of our sample. These models allow analysts to predict who owns life insurance and how much they own, an important input to the marketing process.Moreover, our findings suggest that household demand for term and whole life insurance is jointly determined. After controlling for explanatory variables, there exists a negative relationship for a household’s decision to own both whole and term life insurance (the frequency part) and a positive relationship for the amount of insurance purchased (the severity part). This indicates that the greater the probability of holding one type, the smaller the probability of holding the other type of life insurance. However, higher demand for both types of insurance exists when a household decides to own both. This mixed effect extends prior work that established a negative relationship, suggesting that term life insurance and whole life insurance are substitutes for one another. In contrast, our findings reveal that the ownership decision involves substitution, but, for households owning both types of insurance, amounts are positively related. Therefore, term and whole life insurance are substitutes in the frequency yet complements in the severity. Journal: North American Actuarial Journal Pages: 338-354 Issue: 3 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597595 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597595 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:3:p:338-354 Template-Type: ReDIF-Article 1.0 Author-Name: Laura Ballotta Author-X-Name-First: Laura Author-X-Name-Last: Ballotta Title: Efficient Pricing of Ratchet Equity-Indexed Annuities in a Variance-Gamma Economy Abstract: In this paper we propose a new method for approximating the price of arithmetic Asian options in a Variance-Gamma (VG) economy, which is then applied to the problem of pricing equityindexed annuity contracts. The proposed procedure is an extension to the case of a VG-based model of the moment-matching method developed by Turnbull and Wakeman and Levy for the pricing of this class of path-dependent options in the traditional Black-Scholes setting. The accuracy of the approximation is analyzed against RQMC estimates for the case of ratchet equityindexed annuities with index averaging. Journal: North American Actuarial Journal Pages: 355-368 Issue: 3 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597639 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597639 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:3:p:355-368 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: A Bayesian Approach to Understanding Time Series Data Abstract: This paper explores the use of Bayesian models to analyze time series data. The Bayesian approach produces output that can be readily understood by actuaries and included in their own experience studies. We illustrate this Bayesian approach by analyzing U.S. unemployment rates, a macroeconomic time series. Understanding time series of macroeconomic variables can help actuaries in pricing and reserving their products. For example, a change in the level and/or variance of the unemployment series is of interest to actuaries, because its movement can explain a changing pattern of lapse rates of incidence rates. Our Bayesian analysis, based on models developed by McCulloch and Tsay (1993, 1994), allows for shifts in the level and in the error variance of a process. We develop a measure of model fit, based on the Akaike Information Criterion, that can be used in choosing between alternative models. Posterior prediction intervals for the fitted values are also created to pictorially show the range of paths that could result from the choice of a particular model. Journal: North American Actuarial Journal Pages: 130-143 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595808 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595808 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:130-143 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Social Security, Productivity, and Demographics Journal: North American Actuarial Journal Pages: 144-146 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595809 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595809 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:144-146 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Title: “Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison”, Vladimir Kalashnikov, April, 1999 Journal: North American Actuarial Journal Pages: 128-129 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595806 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595806 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:128-129 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Kalashnikov Author-X-Name-First: Vladimir Author-X-Name-Last: Kalashnikov Title: “Author’s Reply: Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison,” Vladimir Kalashnikov, April, 1999 - Discussion by John A. Beekman Journal: North American Actuarial Journal Pages: 129-129 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595807 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595807 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:129-129 Template-Type: ReDIF-Article 1.0 Author-Name: Julia Lynn Wirch Author-X-Name-First: Julia Lynn Author-X-Name-Last: Wirch Title: Raising Value at Risk Abstract: In this paper I consider the properties for a coherent risk measure, outlined by Artzner et al. (1996), and relate these requirements to a well-known measure, value at risk (VaR), which attempts to evaluate economic risk. I show how the usual method of calculating VaR does not adhere to the coherency requirements and discuss the implications of such a result. As well, I discuss the use of the mean excess loss function to help solve this problem. Journal: North American Actuarial Journal Pages: 106-115 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595804 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595804 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:106-115 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Kalashnikov Author-X-Name-First: Vladimir Author-X-Name-Last: Kalashnikov Title: Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison Abstract: Upper and lower bounds of ruin probabilities for the S. Andersen model with large claims are proposed. The bounds are stated in terms of the corresponding ladder height distribution and have a reasonable accuracy, which is illustrated by numerical examples. Comparison with other known bounds is given. Journal: North American Actuarial Journal Pages: 116-128 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595805 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:116-128 Template-Type: ReDIF-Article 1.0 Author-Name: Ronan O’Connor Author-X-Name-First: Ronan Author-X-Name-Last: O’Connor Author-Name: James Golden Author-X-Name-First: James Author-X-Name-Last: Golden Author-Name: Robert Reck Author-X-Name-First: Robert Author-X-Name-Last: Reck Title: A Value-At-Risk Calculation of Required Reserves for Credit Risk in Corporate Lending Portfolios Abstract: This paper demonstrates that the building blocks of the insurance process, under similar assumptions, produce identical results to the option-pricing approach in the case of pricing individual loans. We examine the performance of a collective of such building blocks, using portfolio historical performance to endogenously parameterize the default cost function unique to a particular portfolio. Having estimated the appropriate default cost function, we can then specify the reserve requirement for a bank operating such a portfolio. In this respect, the additivity of the Poisson parameter is a powerful feature, allowing one to decompose portfolio performance over time and homogeneous portfolio subsections. Portfolios with greater and lesser risk and profitability respectively are hypothesized, and a capital adequacy framework which equates risk across such portfolios is examined. Finally, we simulate the operation of the proposed capital adequacy model. Observed insolvencies are fewer than those observable under present regulation, and specific problems may be identified earlier than at present. Journal: North American Actuarial Journal Pages: 72-83 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595802 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595802 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:72-83 Template-Type: ReDIF-Article 1.0 Author-Name: William Panning Author-X-Name-First: William Author-X-Name-Last: Panning Title: The Strategic Uses of Value at Risk Abstract: In contrast to alternative measures of risk, value at risk (VaR) has important virtues–intelligibility, comparability, and practicality–that make it a potentially valuable tool for strategic decision making and capital management in a wide variety of industries. However, capital-management decisions in most industries–including financial services, such as property/casualty insurance–have time horizons far longer than the one-day horizon that prevails in commercial and investment banking, where the use of VaR is now concentrated. For VaR to be usefully applied to longhorizon decisions, it must address three fundamental problems unique to that context: estimation risk, adaptive risk modification, and franchise risk. This paper describes each of these problems, shows how they can be solved, and provides examples applicable to property/casualty insurance. Journal: North American Actuarial Journal Pages: 84-105 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595803 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595803 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:84-105 Template-Type: ReDIF-Article 1.0 Author-Name: Colin McKee Author-X-Name-First: Colin Author-X-Name-Last: McKee Title: A Bridge Too Var Abstract: Over recent years Value at Risk (VaR) has been accepted in the financial world, and particularly in the banking world, as the yardstick by which to measure portfolio risk. The use of VaR to assess the amount of risk capital an institution should set aside to cover its risks represents a significant increase in the importance of the role of VaR in the banking world. The science which surrounds VaR modeling can lead management to accept the results as being more accurate and reliable than they in fact are, and can also reduce awareness of the underlying factors which cause the risk in the first place. This paper demonstrates the importance of stress testing the model results themselves. Such analyses are useful in order to highlight the underlying model assumptions, the reliability of the assumptions which have been made, and (most importantly) the effect on the end results if these assumptions were to change. Stress tests are carried out on a fictitious bank to show the sort of useful information and insight they can give. Journal: North American Actuarial Journal Pages: 66-71 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595801 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595801 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:66-71 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Ho Author-X-Name-First: Thomas Author-X-Name-Last: Ho Title: A Var Model of an Investment Cycle Abstract: This paper extends the vast body of research literature on financial modeling to business control. Though important to business management, this area is often ignored by the field of financial research. The author also recommends that VaR not be confined to merely assessing the risk of a single portfolio or a trading floor, but be applied to an entire investment cycle for the purposes of risk management. Journal: North American Actuarial Journal Pages: 57-65 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595800 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595800 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:57-65 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Twinney Author-X-Name-First: Marc Author-X-Name-Last: Twinney Title: “Social Security, Productivity, and Demographics”, Committee on Social Security–Retirement and Disability Income, April, 1999 Journal: North American Actuarial Journal Pages: 149-149 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595814 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595814 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:149-149 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sze Author-X-Name-First: Michael Author-X-Name-Last: Sze Title: “Social Security, Productivity, and Demographics”, Committee on Social Security–Retirement and Disability Income, April, 1999 Journal: North American Actuarial Journal Pages: 148-148 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595813 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595813 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:148-148 Template-Type: ReDIF-Article 1.0 Author-Name: Teri Geske Author-X-Name-First: Teri Author-X-Name-Last: Geske Title: Evaluating the Risks of Modeling Assumptions Used in Risk Measurement Abstract: Over the past few years, risk measurement has become an important, high-profile responsibility for most firms in the financial services industry. With advances in academic theory and in technology, financial risk modeling has grown increasingly sophisticated. Most firms rely on a number of models to analyze their market risks (for example, sensitivity to changes in interest rates, exchange rates, commodity prices, and so on) for asset/liability management. But it is critical to recognize that even the most sophisticated models must make assumptions about key parameters that affect the results of the analysis. This so-called “model risk” reflects the fact that in the real world risk factors are unstable and the historical data upon which many modeling inputs are based can change. This paper discusses model risk, gives specific examples of how model risk can affect fixed-income portfolio valuation, and explains why risk measurement should involve stress testing of key modeling assumptions. If the results of a valuation or asset/liability analysis change dramatically given a small change in a modeling assumption, management may wish to reduce the firm’s exposure to that risk factor, as absolute certainty in financial modeling is an unobtainable goal. Journal: North American Actuarial Journal Pages: 42-47 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595798 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595798 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:42-47 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheidon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheidon Lin Title: Klugman, S.A., Panjer, H.H., and Willmot, G.E., 1998, Journal: North American Actuarial Journal Pages: 150-151 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595816 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595816 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:150-151 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Griffin Author-X-Name-First: Mark Author-X-Name-Last: Griffin Author-Name: Rick Boomgaard Author-X-Name-First: Rick Author-X-Name-Last: Boomgaard Title: Enterprise Risk and Return Management for Financial Institutions Abstract: It is important to include both risk and return in finding the optimal balance of assets and liabilities for financial institutions. Insurance companies, with their range of sophisticated assets and liabilities, are perhaps the best example of the value of such an approach. Examples in the paper refer to the insurance industry, but parallels to other types of financial institutions are easily drawn. The analysis in the paper shows that a comprehensive approach to risk and return produces some interesting conclusions with respect to asset allocation, active versus passive asset management, and the mix and pricing of liabilities. Journal: North American Actuarial Journal Pages: 48-56 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595799 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595799 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:48-56 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Luenberger, David G., 1997, Journal: North American Actuarial Journal Pages: 150-150 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595815 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595815 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:150-150 Template-Type: ReDIF-Article 1.0 Author-Name: Allan Brender Author-X-Name-First: Allan Author-X-Name-Last: Brender Title: Cash-Flow Valuation and Value at Risk Abstract: The cash-flow valuation method (CFVM) has been developed in Canada for the valuation of insurance company annuity products. Its range of application is expected to be extended shortly to the valuation of most other life insurance company products. The CFVM is based on the use of “best-guess” assumptions, supplemented by specific provisions for adverse deviations. In this paper, special attention is paid to the calculation of the provision for adverse deviations with respect to the interest rate risk. We show that the determination of this provision is the analog for life insurance and annuity policy liabilities of the calculation by banks of Value at Risk (VaR) with respect to portfolios of securities held for trading. Journal: North American Actuarial Journal Pages: 26-29 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595796 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595796 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:26-29 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Guest Editorial Journal: North American Actuarial Journal Pages: iv-vii Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595817 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595817 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:iv-vii Template-Type: ReDIF-Article 1.0 Author-Name: Paul Embrechts Author-X-Name-First: Paul Author-X-Name-Last: Embrechts Author-Name: Sidney Resnick Author-X-Name-First: Sidney Author-X-Name-Last: Resnick Author-Name: Gennady Samorodnitsky Author-X-Name-First: Gennady Author-X-Name-Last: Samorodnitsky Title: Extreme Value Theory as a Risk Management Tool Abstract: The financial industry, including banking and insurance, is undergoing major changes. The (re)insurance industry is increasingly exposed to catastrophic losses for which the requested cover is only just available. An increasing complexity of financial instruments calls for sophisticated risk management tools. The securitization of risk and alternative risk transfer highlight the convergence of finance and insurance at the product level. Extreme value theory plays an important methodological role within risk management for insurance, reinsurance, and finance. Journal: North American Actuarial Journal Pages: 30-41 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595797 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595797 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:30-41 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Panjer Author-X-Name-First: Harry Author-X-Name-Last: Panjer Title: Overview Journal: North American Actuarial Journal Pages: 9-10 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595794 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595794 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:9-10 Template-Type: ReDIF-Article 1.0 Author-Name: Philippe Artzner Author-X-Name-First: Philippe Author-X-Name-Last: Artzner Title: Application of Coherent Risk Measures to Capital Requirements in Insurance Abstract: Risk measurements go hand in hand with setting of capital minima by companies as well as by regulators. We review the properties of coherent risk measures and examine their implications for capital requirement in insurance. We also comment on the specific risk-based capital computations. Journal: North American Actuarial Journal Pages: 11-25 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595795 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595795 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:11-25 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Linda Heacox Author-X-Name-First: Linda Author-X-Name-Last: Heacox Title: Credibility Theory Abstract: The North American Actuarial Journal is honoring the Society of Actuaries on its golden anniversary in 1999 by publishing a series of articles on the contributions of actuaries to the development of ideas. In this issue, the second of the series, we explore the development of the credibility idea and the relationships of this development to deep issues in the methodology of science. We begin with a short essay by James C. Hickman and continue with comments by three actuaries who were deeply involved with the development of credibility: Robert A. Bailey, Hans Buühlmann, and Charles C. Hewitt. Journal: North American Actuarial Journal Pages: 1-8 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595793 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595793 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:1-8 Template-Type: ReDIF-Article 1.0 Author-Name: Bernard Dussault Author-X-Name-First: Bernard Author-X-Name-Last: Dussault Title: “Social Security, Productivity, and Demographics”, Committee on Social Security–Retirement and Disability Income, April, 1999 Journal: North American Actuarial Journal Pages: 146-147 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595810 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595810 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:146-147 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: “Social Security, Productivity, and Demographics”, Committee on Social Security–Retirement and Disability Income, April, 1999 Journal: North American Actuarial Journal Pages: 147-147 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595811 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595811 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:147-147 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Klieber Author-X-Name-First: Eric Author-X-Name-Last: Klieber Title: “Social Security, Productivity, and Demographics”, Committee on Social Security–Retirement and Disability Income, April, 1999 Journal: North American Actuarial Journal Pages: 147-148 Issue: 2 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595812 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595812 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:2:p:147-148 Template-Type: ReDIF-Article 1.0 Author-Name: Yuchen Mei Author-X-Name-First: Yuchen Author-X-Name-Last: Mei Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Title: Improving Risk Sharing and Borrower Incentives in Mortgage Design Abstract: In a traditional fixed rate mortgage, the borrower pays a fixed amount each period regardless of the value of the mortgaged property. One problem with this contract is that the borrower is less willing to pay when the house value falls. This was clearly seen in the 2008 financial crisis and its aftermath when mortgage default rates and foreclosures skyrocketed as the housing market crashed. A more efficient contract design should link payments to house prices so that the borrower’s incentive to pay is not undermined by a decline in property value. In addition, this design can save the lender the deadweight foreclosure costs. In this article, we examine two proposed index linked mortgages that have this risk sharing feature. We analyze the effect of both designs on borrower incentives in a multiperiod setting. Journal: North American Actuarial Journal Pages: 485-511 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1634594 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1634594 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:485-511 Template-Type: ReDIF-Article 1.0 Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Title: Agricultural Insurance Ratemaking: Development of a New Premium Principle Abstract: Determining the appropriate premium to charge for the underlying risk is central to delivering a sustainable agricultural insurance program. Though this is fundamental to all types of insurance, in agriculture this is a particularly challenging task given systemic risk, information asymmetry, and a number of multifaceted factors pertaining to the loss experience data, including scarcity and credibility. The objective of this article is to formally introduce premium principles to the agricultural insurance literature, with a focus on a new premium principle approach based on the multivariate weighted distribution. The multivariate weighted premium principle (MWPP) formalizes the reweighting of historical loss experience using auxiliary factors in order to refine the agricultural insurance pricing. These auxiliary factors may reflect systemic risk and include material information, such as economic and market conditions, weather, soil, etc. In the empirical study, a unique reinsurance data set from the province of Manitoba, Canada, is used to evaluate a number of potential premium principles. With the flexibility of the MWPP, the empirical results indicate that the MWPP approach can be a viable premium principle for pricing agricultural insurance. Furthermore, the MWPP redistributes premium rates and assigns increased loadings to higher risk layers, helping reinsurers manage their reserves and achieve improved sustainability in the long term. Journal: North American Actuarial Journal Pages: 512-534 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1618340 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1618340 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:512-534 Template-Type: ReDIF-Article 1.0 Author-Name: Azar Ghahari Author-X-Name-First: Azar Author-X-Name-Last: Ghahari Author-Name: Nathaniel K. Newlands Author-X-Name-First: Nathaniel K. Author-X-Name-Last: Newlands Author-Name: Vyacheslav Lyubchich Author-X-Name-First: Vyacheslav Author-X-Name-Last: Lyubchich Author-Name: Yulia R. Gel Author-X-Name-First: Yulia R. Author-X-Name-Last: Gel Title: Deep Learning at the Interface of Agricultural Insurance Risk and Spatio-Temporal Uncertainty in Weather Extremes Abstract: Challenges in risk estimation for agricultural insurance bring to the fore statistical problems of modeling complex weather and climate dynamics, analyzing massive multi-resolution, multi-source data. Nonstationary space-time structure of such data also introduces greater complexity when assessing the highly nonlinear relationship between weather events and crop yields. In this setting, conventional parametric statistical and actuarial models may no longer be appropriate. In turn, modern machine learning and artificial intelligence procedures, which allow fast and automatic learning of hidden dependencies and structures, offer multiple operational benefits and now prove to deliver a highly competitive performance in a variety of applications, from credit card fraud detection to the next best product offer and customer segmentation. Yet their potential in actuarial sciences, and particularly agricultural insurance, remains largely untapped. In this project, we introduce a modern deep learning methodology into the assessment of climate-induced risks in agriculture and evaluate its potential to deliver a higher predictive accuracy, speed, and scalability. We present a pilot study of deep learning algorithms—specifically, deep belief networks—using historical crop yields, weather station–based records, and gridded weather reanalysis data for Manitoba, Canada from 1996 to 2011. Our findings show that deep learning can attain higher prediction accuracy, based on benchmarking its performance against more conventional approaches, especially in multiscale, heterogeneous data environments of agricultural risk management. Journal: North American Actuarial Journal Pages: 535-550 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1633928 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1633928 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:535-550 Template-Type: ReDIF-Article 1.0 Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Title: A Relational Data Matching Model for Enhancing Individual Loss Experience: An Example from Crop Insurance Abstract: The focus of this article is on predictive analytics regarding data scarcity and credibility, which are major difficulties facing the agricultural insurance sector, often due to limited loss experience data for those infrequent but extreme weather events. A new relational data matching model is presented to predict individual farmer yields in the absence of farm-level data. The relational model defines a similarity measure based on an Euclidean distance metric that considers weather information, farm size, county size, and the coefficient of variation of yield to search for the most “similar” region in a different country to borrow individual loss experience data that are otherwise not available. Detailed farm-level and county-level corn yield data in Canada and the United States are used to empirically evaluate the proposed relational model. Compared to the benchmark model, the empirical results confirm the efficiency of the proposed model in that it yields lower prediction error with smaller variation, and it recovers the actual premium rate more accurately. The proposed relational model provides a new approach for insurers, reinsurers, and governments to enhance individual loss experience, helping to overcome issues (such as data scarcity, credibility, and aggregation bias) that present substantial challenges in risk modeling, pricing, and developing new insurance programs, particularly for developing countries. Journal: North American Actuarial Journal Pages: 551-572 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1634595 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1634595 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:551-572 Template-Type: ReDIF-Article 1.0 Author-Name: Fabio Baione Author-X-Name-First: Fabio Author-X-Name-Last: Baione Author-Name: Davide Biancalana Author-X-Name-First: Davide Author-X-Name-Last: Biancalana Title: An Individual Risk Model for Premium Calculation Based on Quantile: A Comparison between Generalized Linear Models and Quantile Regression Abstract: This article deals with the use of quantile regression and generalized linear models for a premium calculation based on quantiles. A premium principle is a functional that assigns a usually loaded premium to any distribution of claims. The loaded premium is generally greater than the expected value of the loss and the difference is considered to be a risk margin or a safety loading. The failure of a right charge of individual risk rate exposes the insurer to adverse selection and, consequently, to deteriorating financial results. The article aim is to define the individual pure premium rates and the corresponding risk margin in balance with some profit or solvency constraints. We develop a ratemaking process based on a two-part model using quantile regression and a gamma generalized linear model, respectively, in order to estimate the claim’s severity quantiles. Generalized linear models focus on the estimation of the mean of the conditional loss distribution but have some drawbacks in assessing distribution moments other than the mean and are very sensitive to outliers. On the contrary, quantile regression exceeds these limits leading to the estimate of conditional quantiles and is more accurate for a better measurement of the variability of a risk class. The proposed methodology for premium calculation allows us to find further limits of the generalized linear model as the solution we found, under specific assumptions for a generalized linear model, is equivalent to the application of the expected value premium principle. Finally, the methodology we suggest for the two-part quantile regression allows reducing the practical issue of overmodeling and over-parameterization with respect to other proposals on the same topic. Journal: North American Actuarial Journal Pages: 573-590 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1604238 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1604238 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:573-590 Template-Type: ReDIF-Article 1.0 Author-Name: Ishan Muzumdar Author-X-Name-First: Ishan Author-X-Name-Last: Muzumdar Author-Name: Donald Richards Author-X-Name-First: Donald Author-X-Name-Last: Richards Title: Long-Term Implications of the Revenue Transfer Methodology in the Affordable Care Act Abstract: The Affordable Care Act introduced a revenue transfer formula that requires insurance plans with generally healthier enrollees to pay funds into a revenue transfer pool to reimburse plans with generally less healthy enrollees. For a given plan, the issue arises of whether the plan will be a payer into or a receiver from the pool in a chosen future year. To examine that issue, we analyze data from The Actuary Magazine on transfer payments for 2014–2015, and we infer strong evidence of a statistical relationship between year-to-year transfer payments. We also apply to the data a Markov transition model to study annual changes in the payer–receiver statuses of insurance plans. We estimate that the limiting conditional probability that an insurance plan will pay into the pool, given that the plan had paid into the pool in 2014, is 55.6%. Further, that limiting probability is attained quickly because the conditional probability that an insurance plan will pay into the pool in 2024, given that the plan had paid into the pool in 2014, is estimated to be 55.7%. We also find the revenue transfer system to have the disturbing feature that once a plan enters the “state” of paying into the pool, it will stay in that state for an average period of 4.87 years; also, once a plan has received funds from the pool, it will stay in that state for an average period of 3.89 years. Journal: North American Actuarial Journal Pages: 591-597 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1598269 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1598269 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:591-597 Template-Type: ReDIF-Article 1.0 Author-Name: Yang Shen Author-X-Name-First: Yang Author-X-Name-Last: Shen Author-Name: Jianxi Su Author-X-Name-First: Jianxi Author-X-Name-Last: Su Title: Life-Cycle Planning with Ambiguous Economics and Mortality Risks Abstract: In this article, we study the strategic planning problem for a wage earner in a life-cycle model with stochastic lifetime. The wage earner aims to decide on the optimal portfolio choice, consumption, and insurance buying rules over the preretirement and postretirement phases. In addition, the wage earner is concerned about the uncertainty of economic and mortality models. In order to address the concern, the wage earner considers the optimal decisions under the worst-case scenario selected from a set of plausible alternative models. We find that the economic ambiguity and mortality ambiguity have substantially different impacts on the optimal decisions. Specifically, though the worst-case economic scenario depends only on the economic environment, the design of the worst-case mortality scenario is determined by the intricate interplays between the wage earner’s personal profile (e.g., health status, income dynamics, risk aversion, etc.) and the evolution of the economic environment. Moreover, the study of mortality ambiguity is also closely related to the value of statistical life, which can be positive and negative in general. Such a complicated theoretical structure underlying the study of mortality ambiguity can sometimes even overturn the direction of its impacts on the optimal decisions. Our article highlights the importance as well as the complexity for modeling ambiguity aversion in optimal planning studies, which desire more serious and critical treatments from the community of actuarial professionals. Journal: North American Actuarial Journal Pages: 598-625 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1634596 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1634596 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:598-625 Template-Type: ReDIF-Article 1.0 Author-Name: Linda L. Golden Author-X-Name-First: Linda L. Author-X-Name-Last: Golden Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Title: Efficiency Analysis of Health Insurers’ Scale of Operations and Group Affiliation with a Perspective Toward Health Insurers’ Mergers and Acquisitions Effects Abstract: This research uses an indirect methodology to examine the effects of health insurance mergers and acquisitions by analyzing the impact of insurers’ scale of operations and group affiliation status on benefits, costs, and efficiency from the perspective of various stakeholders. The analysis can provide insights related to federal and state governments’ antitrust scrutiny and regulations, and can inform the public debate over mergers and acquisitions in the health insurance industry. We find that stakeholders in this process (consumers, regulators, health care providers, society at large) are inconsistent regarding the assessment of what constitutes efficiency with respect to scale of operations and group affiliation status, depending upon their viewpoint (choice) of most appropriate inputs and outputs to the health care market dynamics. In this study, big-sized insurers (those in the top 20% of insurers by member month enrollment) and small groups (those affiliated with a group with fewer than 10 member insurers) are the most efficient from the societal input–output perspective, From a composite perspective that combines the input–output choices relevant from the societal perspective and from the insurers’ perspective, big-sized insurers and big groups (those affiliated with a group with 10 or more member insurers) are found to be the most efficient. Additionally, we find most insurers are scale inefficient. The analysis of scale (dis)economies provides some guidelines regarding the appropriate scale of operations for the scale efficiency, and informs discussion of mergers and acquisitions among health insurers. Journal: North American Actuarial Journal Pages: 626-645 Issue: 4 Volume: 23 Year: 2019 Month: 10 X-DOI: 10.1080/10920277.2019.1626252 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1626252 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:4:p:626-645 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Quinn Author-X-Name-First: Joseph Author-X-Name-Last: Quinn Title: Retirement Trends and Patterns among Older American Workers Journal: North American Actuarial Journal Pages: 125-126 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595965 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595965 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:125-126 Template-Type: ReDIF-Article 1.0 Author-Name: Tapen Sinha Author-X-Name-First: Tapen Author-X-Name-Last: Sinha Author-Name: Rebecca Benedict Author-X-Name-First: Rebecca Author-X-Name-Last: Benedict Title: Marketing Compulsory Pension Plans as a Service Journal: North American Actuarial Journal Pages: 127-128 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595966 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595966 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:127-128 Template-Type: ReDIF-Article 1.0 Author-Name: Pamela Ostuw Author-X-Name-First: Pamela Author-X-Name-Last: Ostuw Author-Name: Bill Pierron Author-X-Name-First: Bill Author-X-Name-Last: Pierron Author-Name: Paul Yakoboski Author-X-Name-First: Paul Author-X-Name-Last: Yakoboski Title: The Evolution of Retirement Journal: North American Actuarial Journal Pages: 121-122 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595963 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595963 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:121-122 Template-Type: ReDIF-Article 1.0 Author-Name: Thornton Parker Author-X-Name-First: Thornton Author-X-Name-Last: Parker Title: Can the Stocks-for-Retirement Cycle Work? Abstract: Journal: North American Actuarial Journal Pages: 123-124 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595964 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595964 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:123-124 Template-Type: ReDIF-Article 1.0 Author-Name: Roberto Ham-Chande Author-X-Name-First: Roberto Author-X-Name-Last: Ham-Chande Author-Name: José Salas-Lizaur Author-X-Name-First: José Author-X-Name-Last: Salas-Lizaur Title: Retirement Pensions in Mexico Journal: North American Actuarial Journal Pages: 118-118 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595961 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595961 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:118-118 Template-Type: ReDIF-Article 1.0 Author-Name: Catherine Hill Author-X-Name-First: Catherine Author-X-Name-Last: Hill Author-Name: Lois Shaw Author-X-Name-First: Lois Author-X-Name-Last: Shaw Author-Name: Heidi Hartmann Author-X-Name-First: Heidi Author-X-Name-Last: Hartmann Title: Trends in Social Security and Pension Policy—Implications for Women Journal: North American Actuarial Journal Pages: 119-119 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595962 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595962 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:119-119 Template-Type: ReDIF-Article 1.0 Author-Name: Dennis Coleman Author-X-Name-First: Dennis Author-X-Name-Last: Coleman Title: Baby Boom to Baby Bust Journal: North American Actuarial Journal Pages: 116-117 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595960 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595960 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:116-117 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Applebaum Author-X-Name-First: Joseph Author-X-Name-Last: Applebaum Title: Discussion of the Papers by Thornton Parker; Roberto Ham-Chande and José Luis Salas-Lizaur; and Larry Willmore Journal: North American Actuarial Journal Pages: 133-134 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595969 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595969 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:133-134 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Yakoboski Author-X-Name-First: Paul Author-X-Name-Last: Yakoboski Author-Name: Pamela Ostuw Author-X-Name-First: Pamela Author-X-Name-Last: Ostuw Author-Name: Bill Pierron Author-X-Name-First: Bill Author-X-Name-Last: Pierron Title: The 1999 Small Employer Retirement Survey Journal: North American Actuarial Journal Pages: 131-132 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595968 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595968 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:131-132 Template-Type: ReDIF-Article 1.0 Author-Name: Larry Willmore Author-X-Name-First: Larry Author-X-Name-Last: Willmore Title: Public Versus Private Provision of Pensions Journal: North American Actuarial Journal Pages: 129-130 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595967 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595967 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:129-130 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Clark Author-X-Name-First: Robert Author-X-Name-Last: Clark Author-Name: Fred Munzenmaier Author-X-Name-First: Fred Author-X-Name-Last: Munzenmaier Title: Impact of Replacing a Defined Benefit Pension with a Defined Contribution Plan or a Cash Balance Plan Abstract: Four pension plan conversions are examined to determine the impact on retirement benefits of workers. The study was based on interviews with top management, employee surveys, and actuarial analysis of retirement benefits under the old and new pension plans. In general, workers who leave the firm prior to the age of early retirement can expect increased benefits under the new defined contribution and cash balance plans, whereas older, more senior workers can expect to accrue smaller benefits after the plan conversions. Recognizing these potential adverse effects, the employers in our studies provided various types of transition benefits to existing workers or gave employees the choice of remaining in the old defined benefit plan. Employee surveys reveal that younger workers are more supportive of the new pension plans than are older workers. These case studies also indicate that communication by managements with their employees is very important to the successful implementation of plan conversions. Journal: North American Actuarial Journal Pages: 32-56 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595952 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595952 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:32-56 Template-Type: ReDIF-Article 1.0 Author-Name: Moshe Arye Milevsky Author-X-Name-First: Moshe Arye Author-X-Name-Last: Milevsky Title: Optimal Annuitization Policies Abstract: At, or about, the age of retirement, most individuals must decide what additional fraction of their marketable wealth, if any, should be annuitized. Annuitization means purchasing a nonrefundable life annuity from an insurance company, which then guarantees a lifelong consumption stream that cannot be outlived. The decision of whether or not to annuitize additional liquid assets is a difficult one, since it is clearly irreversible and can prove costly in hindsight. Obviously, for a large group of people, the bulk of financial wealth is forcefully annuitized, for example, company pensions and social security. For others, especially as it pertains to personal pension plans, such as 401(k), 403(b), and IRA plans as well as variable annuity contracts, there is much discretion in the matter.The purpose of this paper is to focus on the question of when and if to annuitize. Specifically, my objective is to provide practical advice aimed at individual retirees and their advisors. My main conclusions are as follows:• Annuitization of assets provides unique and valuable longevity insurance and should be actively encouraged at higher ages. Standard microeconomic utility-based arguments indicate that consumers would be willing to pay a substantial “loading” in order to gain access to a life annuity.• The large adverse selection costs associated with life annuities, which range from 10% to 20%, might serve as a strong deterrent to full annuitization.• Retirees with a (strong) bequest motive might be inclined to self-annuitize during the early stages of retirement. Indeed, it appears that most individuals—faced with expensive annuity products—can effectively “beat” the rate of return from a fixed immediate annuity until age 75�80. I call this strategy consume term and invest the difference.• Variable immediate annuities (VIAs) combine equity market participation together with longevity insurance. This financial product is currently underutilized (and not available in certain jurisdictions) and can only grow in popularity. Journal: North American Actuarial Journal Pages: 57-69 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595953 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595953 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:57-69 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Title: “Excess Mortality in Asia Associated with Cigarette Smoking,” Robert J. Pokorski, April 2000 Journal: North American Actuarial Journal Pages: 157-158 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595978 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595978 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:157-158 Template-Type: ReDIF-Article 1.0 Author-Name: Cori Uccello Author-X-Name-First: Cori Author-X-Name-Last: Uccello Title: 401(k) Investment Decisions and Social Security Reform Abstract: This paper uses the 1995 Survey of Consumer Finances to show that 401(k) participants with an underlying defined benefit plan are more likely to invest in equities than are participants whose 401(k) is their primary plan. This suggests that workers with a guaranteed source of retirement income are more likely to invest their other retirement assets more aggressively. Removing this guarantee might result in more conservative investment. Therefore, using current 401(k) asset allocation behavior to project income under a Social Security individual account system with reduced guaranteed benefits could overstate returns to these accounts, thus overstating their attractiveness relative to the current system. Journal: North American Actuarial Journal Pages: 70-79 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595954 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595954 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:70-79 Template-Type: ReDIF-Article 1.0 Author-Name: Jack VanDerhei Author-X-Name-First: Jack Author-X-Name-Last: VanDerhei Author-Name: Craig Copeland Author-X-Name-First: Craig Author-X-Name-Last: Copeland Title: A Behavioral Model for Predicting Employee Contributions to 401(k) Plans Abstract: Previous research on employee contribution behavior to 401(k) plans has often been limited by lack of adequate data. This is primarily because of the types of matching formulas utilized by sponsors. While these formulas are often complicated because of the desire of sponsors to provide sufficient incentives to non-highly compensated employees to contribute in order to comply with technical nondiscrimination testing, this complexity makes it virtually impossible to appropriately analyze the employee’s behavior if we are forced either to observe aggregate plan data or to use information on the plan contribution formulas provided by the participant. The purpose of this paper is to provide preliminary findings introducing new methodology to expand the usefulness of modeling these data as well as a better understanding of contribution behavior by 401(k) plan participants. We utilize a sequential response regression model to allow for the differing incentives faced by the employees at various levels of contributions. Based on findings from 137 distinct matching formulas, we have estimated a behavioral model that is able to control for the tendency of employers to substitute between the amount they match per dollar of employee contribution and the maximum percentage of compensation they are willing to match. Journal: North American Actuarial Journal Pages: 80-94 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595955 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595955 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:80-94 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rappaport Author-X-Name-First: Anna Author-X-Name-Last: Rappaport Title: Setting the Stage Journal: North American Actuarial Journal Pages: 1-11 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595950 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595950 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:1-11 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: Impacts on Economic Security Programs of Rapidly Shifting Demographics Abstract: This paper analyzes in some detail potential impacts on economic security programs—government, employer, and individual—that the aging of the baby boom generation may create. It begins by defining what is meant by “population aging” and concludes that fertility shifts are more important than improving life expectancy. It also argues that calling the baby boom the “postwar baby boom” is inaccurate and will lead to missed targets for product development and marketing. Finally, this section of the paper notes that the most rapidly growing segment of the population will be the oldest old—those age 85 and over, who will also put the greatest stress on the provision of health care and retirement income security.The paper then looks at other demographic shifts of importance, in particular female labor force participation rates. The impact of shifting demographics is reviewed for each sponsor of economic security programs: the government (health care and social security); the employer (pension plans and group benefits); and the individual. Points of concern and offsetting opportunities for the insurance industry are noted. Finally, the paper looks at whether we will be able to “afford” the sudden retirement of the baby boom. The conclusion is that this will be affordable if we can convince a portion of the labor force to stay active longer, and if we have healthy productivity growth rates. The problems of an aging population can all be viewed as opportunities for those who have the map. Journal: North American Actuarial Journal Pages: 12-31 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595951 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595951 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:12-31 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Lunnon Author-X-Name-First: Martin Author-X-Name-Last: Lunnon Author-Name: Aidan Smith Author-X-Name-First: Aidan Author-X-Name-Last: Smith Title: “Social Security—Adequacy, Equity, and Progressiveness: A Review of Criteria Based on Experience in Canada and the United States,” Robert L. Brown and Jeffrey Ip, January 2000 Journal: North American Actuarial Journal Pages: 144-147 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595973 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595973 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:144-147 Template-Type: ReDIF-Article 1.0 Author-Name: Sylvester Schieber Author-X-Name-First: Sylvester Author-X-Name-Last: Schieber Title: Discussion of the Papers By Robert L. Brown and Thomas Trauth Journal: North American Actuarial Journal Pages: 141-143 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595972 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595972 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:141-143 Template-Type: ReDIF-Article 1.0 Author-Name: Ron Gebhardtsbauer Author-X-Name-First: Ron Author-X-Name-Last: Gebhardtsbauer Title: Discussion of the Paper By Catherine Hill, Lois B. Shaw, and Heidi Hartmann Journal: North American Actuarial Journal Pages: 135-136 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595971 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595971 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:135a-136a Template-Type: ReDIF-Article 1.0 Author-Name: Sharon Canner Author-X-Name-First: Sharon Author-X-Name-Last: Canner Title: Discussion of the Papers by Jack VanDerhei and Craig Copeland; Rosa MA. Farell Campa et al.; and Paul Yakoboski, Pamela Ostuw, and Bill Pierron Journal: North American Actuarial Journal Pages: 135-136 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595970 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595970 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:135-136 Template-Type: ReDIF-Article 1.0 Author-Name: Ya-Chun Huang Author-X-Name-First: Ya-Chun Author-X-Name-Last: Huang Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Pricing Dynamic Investment Fund Protection,” Hans U. Gerber and Gérard Pafumi, April 2000 Journal: North American Actuarial Journal Pages: 153-157 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595977 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595977 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:153-157 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Johnson Author-X-Name-First: Richard Author-X-Name-Last: Johnson Author-Name: Anthony Lo Sasso Author-X-Name-First: Anthony Author-X-Name-Last: Lo Sasso Title: Balancing Retirement Security With the Needs of Frail Parents Abstract: Caring for frail elderly parents can interfere with work responsibilities. People who provide care to their parents may need to take time off from work or retire altogether. However, reductions in labor supply at midlife can have serious implications for retirement wealth and, as a result, on economic well-being in later life. This paper examines how family support for the elderly can affect retirement savings by examining the relationship between labor supply, time help to parents, and financial assistance to parents. Using data from the Health and Retirement Study on a nationally representative sample of women ages 53–63, we found that women who helped their parents with personal care assistance worked significantly fewer hours than did those who did not help their parents, whereas those who provided financial assistance worked significantly more hours. Although few persons at midlife presently spend substantial amounts of time helping their elderly parents in any given year, for those who do, the costs can be high. Pressures on families are likely to mount in the near future as falling mortality and fertility rates continue to increase the proportion of the population that is very old and as women continue to play more important roles in the labor market. Journal: North American Actuarial Journal Pages: 104-108 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595957 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595957 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:104-108 Template-Type: ReDIF-Article 1.0 Author-Name: Dennis Radliff Author-X-Name-First: Dennis Author-X-Name-Last: Radliff Title: “Calculating Funding Premiums for Universal Life Insurance,” Calvin Cherry, April 2000 Journal: North American Actuarial Journal Pages: 151-153 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595976 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595976 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:151-153 Template-Type: ReDIF-Article 1.0 Author-Name: Jonathan Forman Author-X-Name-First: Jonathan Author-X-Name-Last: Forman Title: Making Federal Pension Policy Work Abstract: Millions of Americans retire while they are still productive. Of these, many will have the resources to enjoy all of their golden years. Unfortunately, many others will face economic hardships after they have exhausted their own resources but have become too frail to return to work. Part of the problem is that the current pension system is fraught with financial incentives that push ablebodied elderly workers into retirement just when they should instead be encouraged to remain in the workforce to accumulate additional retirement assets. This paper recommends a number of ways to change federal pension laws in order to encourage elderly workers to remain in the workforce. For example, this paper recommends toughening the penalty on premature distributions, repealing the minimum distribution rules, and repealing the exceptions to the Age Discrimination in Employment Act that permit retirement plans to provide early retirement incentives and subsidies.This paper also considers whether the government should require that all retirement plans be neutral as to the timing of retirement. In an age-neutral world, workers would always accrue more benefits if they kept working. Consequently, more workers would remain in the workforce, accumulating additional assets for their eventual retirement.Finally, this paper also considers how federal pension policy could help counteract the tendency of Americans to retire too early because they underestimate their life expectancies, overestimate their financial resources, and fail to understand the deleterious effects of inflation. In particular, this paper recommends that the government require that virtually all retirement plans pay at least a portion of their benefits in the form of an inflation-adjusted annuity. Journal: North American Actuarial Journal Pages: 95-103 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595956 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595956 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:95-103 Template-Type: ReDIF-Article 1.0 Author-Name: Hangsuck Lee Author-X-Name-First: Hangsuck Author-X-Name-Last: Lee Title: “Measuring Foreign Exchange Risk in Insurance Transactions,” John I. Mange, April 2000 Journal: North American Actuarial Journal Pages: 149-151 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595975 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595975 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:149-151 Template-Type: ReDIF-Article 1.0 Author-Name: Rosa Farell Campa Author-X-Name-First: Rosa Author-X-Name-Last: Farell Campa Author-Name: Juan Carlos Padilla Aguilar Author-X-Name-First: Juan Carlos Author-X-Name-Last: Padilla Aguilar Author-Name: Jose Garcia Nuñez Author-X-Name-First: Jose Garcia Author-X-Name-Last: Nuñez Author-Name: Mario Arriaga Parra Author-X-Name-First: Mario Arriaga Author-X-Name-Last: Parra Title: Analysis of the Profiles of Mexican Companies with Respect to Granting a Retirement Pension Plan Journal: North American Actuarial Journal Pages: 114-115 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595959 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595959 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:114-115 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Trauth Author-X-Name-First: Thomas Author-X-Name-Last: Trauth Title: Financing Gaps of Public Pension Schemes and Market Potential for the Private Retirement Market Abstract: Increasing longevity, declining birth rates, and high unemployment severely threaten the financial basis of many public pension plans. These problems are most pronounced in continental Europe, where public pension plans tend to be relatively generous and are usually funded on a pay-as-you-go basis. Given the demographic development, future pension payments exceed the expected contribution payments. The resulting financing gaps can be seen as implicit public debts (net pension liabilities), which often exceed the value of GDP figures and are in many cases higher than the explicit public debt figures. If people would decide to cover these financing gaps via life insurance, life insurance premiums would triple in Germany, more than double in Italy, and double in Canada and France. The increase would be only moderate in the U.S. and particularly small in the U.K. Journal: North American Actuarial Journal Pages: 109-113 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595958 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595958 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:109-113 Template-Type: ReDIF-Article 1.0 Author-Name: Martin le Roux Author-X-Name-First: Martin Author-X-Name-Last: le Roux Title: “Hedging and Reserving for Single-Premium Segregated Fund Contracts,” Mary R. Hardy, April 2000 Journal: North American Actuarial Journal Pages: 147-149 Issue: 1 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10595974 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10595974 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:1:p:147-149 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board EOV Journal: North American Actuarial Journal Pages: ebi-ebi Issue: 4 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.859043 File-URL: http://hdl.handle.net/10.1080/10920277.2013.859043 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: Peng Shi Author-X-Name-First: Peng Author-X-Name-Last: Shi Author-Name: Wei Zhang Author-X-Name-First: Wei Author-X-Name-Last: Zhang Title: Managed Care and Health Care Utilization: Specification of Bivariate Models Using Copulas Abstract: This article studies the effect of managed care on health care utilization compared to traditional fee-for-service plans in private health insurance market. To construct our hypothesis, we build a game-theoretic model to study health care utilization under a two-sided moral hazard: of patients and providers. In econometric modeling, we employ a copula regression to jointly examine individuals’ health plan choice and their utilization of medical care services, because of the endogeneity of insurance choice. The dependence parameter in the copula reflects the relation between the two outcomes, based on which the average treatment effects are further derived. We apply the methodology to a survey data set of the U.S. population and consider three types of curative care and three types of preventive care for the measurement of medical care utilization. We find that managed care is in general associated with higher care utilization. Evidence is also found on the underlying incentives of both patients and medical providers. Journal: North American Actuarial Journal Pages: 306-324 Issue: 4 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.849192 File-URL: http://hdl.handle.net/10.1080/10920277.2013.849192 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:4:p:306-324 Template-Type: ReDIF-Article 1.0 Author-Name: David Ingram Author-X-Name-First: David Author-X-Name-Last: Ingram Author-Name: Elijah Bush Author-X-Name-First: Elijah Author-X-Name-Last: Bush Title: Collective Approaches to Risk in Business: An Introduction to Plural Rationality Theory Abstract: This article initiates a discussion regarding Plural Rationality Theory, which began to be used as a tool for understanding risk 40 years ago in the field of social anthropology. This theory is now widely applied and can provide a powerful paradigm to understand group behaviors. The theory has only recently been utilized in business and finance, where it provides insights into perceptions of risk and the dynamics of firms and markets. Plural Rationality Theory highlights four competing views of risk with corresponding strategies applied in four distinct risk environments. We explain how these rival perspectives are evident on all levels, from roles within organizations to macro level economics. The theory is introduced and the concepts are applied with business terms and examples such as company strategy, where the theory has a particularly strong impact on risk management patterns. The principles are also shown to have been evident in the run up to—and the reactions after—the 2008 financial crisis. Traditional “risk management” is shown to align with only one of these four views of risk, and the consequences of that singular view are discussed. Additional changes needed to make risk management more comprehensive, widely acceptable, and successful are introduced. Journal: North American Actuarial Journal Pages: 297-305 Issue: 4 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.847781 File-URL: http://hdl.handle.net/10.1080/10920277.2013.847781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:4:p:297-305 Template-Type: ReDIF-Article 1.0 Author-Name: M. Boyer Author-X-Name-First: M. Author-X-Name-Last: Boyer Author-Name: Charles Nyce Author-X-Name-First: Charles Author-X-Name-Last: Nyce Title: An Industrial Organization Theory of Risk Sharing Abstract: Examining the global reinsurance market, we propose a new theory of optimal risk sharing that finds its inspiration in the economic theory of the firm. Our model offers a theoretical foundation for two empirical regularities that are observed in the reinsurance market: (1) the choice of specific attachment (the deductible) and detachment points (the policy limits or the retrocession); and (2) the vertical and horizontal tranching of reinsurance contracts. Using a two-factor cost model, we show how reinsurance should be optimally layered (with attachment and detachment points) for a given book of business in order to minimize the cost and total premium associated with catastrophic events. Journal: North American Actuarial Journal Pages: 283-296 Issue: 4 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.839377 File-URL: http://hdl.handle.net/10.1080/10920277.2013.839377 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:4:p:283-296 Template-Type: ReDIF-Article 1.0 Author-Name: Séverine Arnold (-Gaille) Author-X-Name-First: Séverine Author-X-Name-Last: Arnold (-Gaille) Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Forecasting Mortality Trends Allowing for Cause-of-Death Mortality Dependence Abstract: Longevity risk is among the most important factors to consider for pricing and risk management of longevity products. Past improvements in mortality over many years, and the uncertainty of these improvements, have attracted the attention of experts, both practitioners and academics. Since aggregate mortality rates reflect underlying trends in causes of death, insurers and demographers are increasingly considering cause-of-death data to better understand risks in their mortality assumptions. The relative importance of causes of death has changed over many years. As one cause reduces, others increase or decrease. The dependence between mortality for different causes of death is important when projecting future mortality. However, for scenario analysis based on causes of death, the assumption usually made is that causes of death are independent. Recent models, in the form of Vector Error Correction Models (VECMs), have been developed for multivariate dynamic systems and capture time dependency with common stochastic trends. These models include long-run stationary relations between the variables and thus allow a better understanding of the nature of this dependence. This article applies VECMs to cause-of-death mortality rates to assess the dependence between these competing risks. We analyze the five main causes of death in Switzerland. Our analysis confirms the existence of a long-run stationary relationship between these five causes. This estimated relationship is then used to forecast mortality rates, which are shown to be an improvement over forecasts from more traditional ARIMA processes, which do not allow for cause-of-death dependencies. Journal: North American Actuarial Journal Pages: 273-282 Issue: 4 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.838141 File-URL: http://hdl.handle.net/10.1080/10920277.2013.838141 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:4:p:273-282 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoli Zhang Author-X-Name-First: Xiaoli Author-X-Name-Last: Zhang Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Title: The Optimal Write-Down Coefficients in a Percentage for a Catastrophe Bond Abstract: Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. When the aggregate catastrophe loss exceeds a specified amount by the maturity, the CAT bond is triggered and the future bond payments are reduced. This article first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal write-down coefficients in a percentage, implemented by Monte Carlo simulations, which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal write-down coefficients in a percentage help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it demonstrates how the number of coupon payments, loss share, retention level, strike price, maturity, frequency, and severity parameters of the catastrophe loss process and different interest rate models affect the optimal write-down coefficients in a percentage with numerical examples for illustrations. Journal: North American Actuarial Journal Pages: 1-21 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1283236 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1283236 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:1-21 Template-Type: ReDIF-Article 1.0 Author-Name: Luís Portugal Author-X-Name-First: Luís Author-X-Name-Last: Portugal Author-Name: Athanasios A. Pantelous Author-X-Name-First: Athanasios A. Author-X-Name-Last: Pantelous Author-Name: Hirbod Assa Author-X-Name-First: Hirbod Author-X-Name-Last: Assa Title: Claims Reserving with a Stochastic Vector Projection Abstract: In the last three decades, a variety of stochastic reserving models have been proposed in the general insurance literature mainly using (or reproducing) the well-known Chain-Ladder claims-reserving estimates. In practice, when the data do not satisfy the Chain-Ladder assumptions, high prediction errors might occur. Thus, in this article, a combined methodology is proposed based on the stochastic vector projection method and uses the regression through the origin approach of Murphy, but with heteroscedastic errors instead, and different from those that used by Mack. Furthermore, the Mack distribution-free model appears to have higher prediction errors when compared with the proposed one, particularly, for data sets with increasing (regular) trends. Finally, three empirical examples with irregular and regular data sets illustrate the theoretical findings, and the concepts of best estimate and risk margin are reported. Journal: North American Actuarial Journal Pages: 22-39 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1353429 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1353429 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:22-39 Template-Type: ReDIF-Article 1.0 Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: Regression Modeling for the Valuation of Large Variable Annuity Portfolios Abstract: Variable annuities are insurance products that contain complex guarantees. To manage the financial risks associated with these guarantees, insurance companies rely heavily on Monte Carlo simulation. However, using Monte Carlo simulation to calculate the fair market values of these guarantees for a large portfolio of variable annuities is extremely time consuming. In this article, we propose the class of GB2 distributions to model the fair market values of guarantees to capture the positive skewness typically observed empirically. Numerical results are used to demonstrate and evaluate the performance of the proposed model in terms of accuracy and speed. Journal: North American Actuarial Journal Pages: 40-54 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1366863 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1366863 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:40-54 Template-Type: ReDIF-Article 1.0 Author-Name: George Tzougas Author-X-Name-First: George Author-X-Name-Last: Tzougas Author-Name: Spyridon Vrontos Author-X-Name-First: Spyridon Author-X-Name-Last: Vrontos Author-Name: Nicholas Frangos Author-X-Name-First: Nicholas Author-X-Name-Last: Frangos Title: Bonus-Malus Systems with Two-Component Mixture Models Arising from Different Parametric Families Abstract: Two-component mixture distributions defined so that the component distributions do not necessarily arise from the same parametric family are employed for the construction of Optimal Bonus-Malus Systems (BMSs) with frequency and severity components. The proposed modeling framework is used for the first time in actuarial literature research and includes an abundance of alternative model choices to be considered by insurance companies when deciding on their Bonus-Malus pricing strategies. Furthermore, we advance one step further by assuming that all the parameters and mixing probabilities of the two component mixture distributions are modeled in terms of covariates. Applying Bayes' theorem we derive optimal BMSs either by updating the posterior probability of the policyholders’ classes of risk or by updating the posterior mean and the posterior variance. The resulting tailor-made premiums are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. The use of the variance principle in a Bonus-Malus ratemaking scheme in a way that takes into consideration both the number and the costs of claims based on both the a priori and the a posterior classification criteria has not yet been proposed and can alter the resulting premiums significantly, providing the actuary with useful alternative tariff structures. Journal: North American Actuarial Journal Pages: 55-91 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1368398 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1368398 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:55-91 Template-Type: ReDIF-Article 1.0 Author-Name: Marie-Pier Bergeron-Boucher Author-X-Name-First: Marie-Pier Author-X-Name-Last: Bergeron-Boucher Author-Name: Violetta Simonacci Author-X-Name-First: Violetta Author-X-Name-Last: Simonacci Author-Name: Jim Oeppen Author-X-Name-First: Jim Author-X-Name-Last: Oeppen Author-Name: Michele Gallo Author-X-Name-First: Michele Author-X-Name-Last: Gallo Title: Coherent Modeling and Forecasting of Mortality Patterns for Subpopulations Using Multiway Analysis of Compositions: An Application to Canadian Provinces and Territories Abstract: Mortality levels for subpopulations, such as countries in a region or provinces within a country, generally change in a similar fashion over time, as a result of common historical experiences in terms of health, culture, and economics. Forecasting mortality for such populations should consider the correlation between their mortality levels. In this perspective, we suggest using multilinear component techniques to identify a common time trend and then use it to forecast coherently the mortality of subpopulations. Moreover, this multiway approach is performed on life table deaths by referring to Compositional Data Analysis (CoDa) methodology. Compositional data are strictly positive values summing to a constant and represent part of a whole. Life table deaths are compositional by definition because they provide the age composition of deaths per year and sum to the life table radix. In bilinear models the use of life table deaths treated as compositions generally leads to less biased forecasts than other commonly used models by not assuming a constant rate of mortality improvement. As a consequence, an extension of this approach to multiway data is here presented. Specifically, a CoDa adaptation of the Tucker3 model is implemented for life table deaths arranged in three-dimensional arrays indexed by time, age, and population. The proposed procedure is used to forecast the mortality of Canadian provinces in a comparative study. The results show that the proposed model leads to coherent forecasts. Journal: North American Actuarial Journal Pages: 92-118 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1377620 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1377620 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:92-118 Template-Type: ReDIF-Article 1.0 Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Author-Name: Björn Löfdahl Author-X-Name-First: Björn Author-X-Name-Last: Löfdahl Title: A Hidden Markov Approach to Disability Insurance Abstract: Point and interval estimation of future disability inception and recovery rates is predominantly carried out by combining generalized linear models with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modeling procedure by fitting the model to Swedish disability claims data. Journal: North American Actuarial Journal Pages: 119-136 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1387570 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1387570 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:119-136 Template-Type: ReDIF-Article 1.0 Author-Name: Hirbod Assa Author-X-Name-First: Hirbod Author-X-Name-Last: Assa Author-Name: Meng Wang Author-X-Name-First: Meng Author-X-Name-Last: Wang Author-Name: Athanasios A. Pantelous Author-X-Name-First: Athanasios A. Author-X-Name-Last: Pantelous Title: Modeling Frost Losses: Application to Pricing Frost Insurance Abstract: The main objective of this article is to model the losses caused by frost events and use it to price frost insurance. Since the data on frost events are either unavailable or rarely available, we have chosen to obtain a model for frost losses based on temperature by using some fundamental agricultural engineering findings on frost damage. The main challenges in modeling frost loss variables are, first, the nonlinearity of the frost losses with respect to the temperature and, second, the fruit resistance to the first few hours of low temperature. We address both issues when introducing our frost loss variable. Then after finding the loss model, we use it to price frost insurance for a general family of insurance contracts that do not generate any risk of moral hazard. In particular, we will find the premiums of stop-loss policies for losses to citrus fruits using Value at Risk, Conditional Value at Risk, and Wang's premium based on temperature data from San Joaquin Drainage in California. Journal: North American Actuarial Journal Pages: 137-159 Issue: 1 Volume: 22 Year: 2018 Month: 1 X-DOI: 10.1080/10920277.2017.1387571 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1387571 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:1:p:137-159 Template-Type: ReDIF-Article 1.0 Author-Name: Ian Duncan Author-X-Name-First: Ian Author-X-Name-Last: Duncan Author-Name: Bryan Beatty Author-X-Name-First: Bryan Author-X-Name-Last: Beatty Author-Name: Brian Day Author-X-Name-First: Brian Author-X-Name-Last: Day Title: A Risk-Based Evaluation Methodology for Cost Effectiveness of Chronic Condition Health Management Programs Abstract: A financial evaluation of the effectiveness of chronic disease health management programs would ideally take into account the health care costs of managed chronic member populations compared against the health care costs of comparable nonmanaged chronic member populations. This paper considers one approach when a comparison chronic member population is not readily available. The approach uses a nonmanaged nonchronic member population as the comparison group, applying a claims normalization methodology to the medical claims costs of the chronic and nonchronic populations. The normalization process includes stratification by demographic and risk factors. The resulting savings factors are then modified to identify expected savings for single-employer groups. The analysis develops savings factors at the book-of-business level, which are then applied to groups to estimate the savings at the group level. Separate savings factors are developed by age and sex, condition, and duration from initial chronic diagnosis. Results are generally intuitively reasonable: Savings are higher for members with longer duration since identification, as well as for members with more costly conditions (e.g., heart disease, comorbid conditions). The effect-on-savings estimates of underlying factors such as age, duration, and condition have not been extensively examined in the health services literature. Our paper adds to the literature by examining the effect of duration, risk, and condition on savings from a management program while providing a methodology that may be followed by other practitioners to examine these effects in other populations. Journal: North American Actuarial Journal Pages: 1-12 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597606 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597606 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:1-12 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Author-Name: Siu-Hung Cheung Author-X-Name-First: Siu-Hung Author-X-Name-Last: Cheung Title: Structural Changes in the Lee-Carter Mortality Indexes Abstract: In recent years mortality has improved considerably faster than had been predicted, resulting in unforeseen mortality losses for annuity and pension liabilities. Actuaries have considered various models to make stochastic mortality projections, one of which is the celebrated Lee-Carter model. In using the Lee-Carter model, mortality forecasts are made on the basis of the assumed linearity of a mortality index, parameter kt, in the model. However, if this index is indeed not linear, forecasts will tend to be biased and inaccurate. A primary objective of this paper is to examine the linearity of this index by rigorous statistical hypothesis tests. Specifically, we consider Zivot and Andrews’ procedure to determine if there are any structural breaks in the Lee-Carter mortality indexes for the general populations of England and Wales and the United States. The results indicate that there exists a statistically significant structural breakpoint in each of the indexes, suggesting that forecasters should be extra cautious when they extrapolate these indexes. Our findings also provide sound statistical evidence for some demographers’ observation of an accelerated mortality decline after the mid-1970s. Journal: North American Actuarial Journal Pages: 13-31 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597607 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:13-31 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Stallard Author-X-Name-First: Eric Author-X-Name-Last: Stallard Title: Estimates of the Incidence, Prevalence, Duration, Intensity, and Cost of Chronic Disability Among the U.S. Elderly Abstract: The objective of this paper is to estimate the burden of chronic disability on the U.S. elderly population, using unisex and sex-specific measures of long-term care (LTC) service use, intensity, and costs. Multistate life-table analysis was performed of adjacent rounds of the National Long-Term Care Survey (NLTCS) from 1984, 1989, and 1994, using criteria introduced in the Health Insurance Portability and Accountability Act (HIPAA) of 1996 to stratify the disabled population according to level of disability based on ADL and cognitive impairment criteria. Rates of transition to and from nondisabled to disabled states and from all states to death were computed and analyzed for differences by age and sex. Rates of service use, intensity, and costs were computed conditional on age and sex. It was found that approximately 20% of the residual life expectancy at age 65 for males and 30% for females were spent in a state of chronic disability. For both sexes, the years of chronic disability above age 65 were split evenly between mild/moderate and severe disability. The expected costs of purchased LTC services were $59,000 (includes home/community care and institutional care, in constant 2000 dollars), with substantial sex differences: $29,000 for males versus $82,000 for females. For both sexes, the overwhelming majority (92%) of the LTC costs were incurred during episodes of severe disability, with the remaining (8%) incurred during episodes of mild/moderate disability. Residual lifetime unpaid home/community care averaged 3,200 hours for males and 4,000 hours for females, with approximately one-third of those hours incurred during episodes of mild/moderate disability. The criteria for identifying severely disabled persons introduced by HIPAA effectively targeted the high-cost disabled subpopulation. This group accounted for the overwhelming majority of purchased LTC services, and a large majority of unpaid LTC services, over age 65. Sex differences in expected per capita lifetime LTC costs were substantial, with females outspending males 2.8 to 1. Journal: North American Actuarial Journal Pages: 32-58 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597608 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:32-58 Template-Type: ReDIF-Article 1.0 Author-Name: Gabriella Piscopo Author-X-Name-First: Gabriella Author-X-Name-Last: Piscopo Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: The Valuation of Guaranteed Lifelong Withdrawal Benefit Options in Variable Annuity Contracts and the Impact of Mortality Risk Abstract: In light of the growing importance of the variable annuities market, in this paper we introduce a theoretical model for the pricing and valuation of guaranteed lifelong withdrawal benefit (GLWB) options embedded in variable annuity products. As the name suggests, this option offers a lifelong withdrawal guarantee; therefore, there is no limit on the total amount that is withdrawn over the term of the policy because if the account value becomes zero while the insured is still alive, he or she continues to receive the guaranteed amount annually until death. Any remaining account value at the time of death is paid to the beneficiary as a death benefit. We offer a specific framework to value the GLWB option in a market-consistent manner under the hypothesis of a static withdrawal strategy, according to which the withdrawal amount is always equal to the guaranteed amount. The valuation approach is based on the decomposition of the product into living and death benefits. The model makes use of the standard no-arbitrage models of mathematical finance, which extend the Black-Scholes framework to insurance contracts, assuming the fund follows a geometric Brownian motion and the insurance fee is paid, on an ongoing basis, as a proportion of the assets. We develop a sensitivity analysis, which shows how the value of the product varies with the key parameters, including the age of the policyholder at the inception of the contract, the guaranteed rate, the risk-free rate, and the fund volatility. We calculate the fair fee, using Monte Carlo simulations under different scenarios. We give special attention to the impact of mortality risk on the value of the option, using a flexible model of mortality dynamics, which allows for the possible perturbations by mortality shock of the standard mortality tables used by practitioners. Moreover, we evaluate the introduction of roll-up and step-up options and the effect of the decision to delay withdrawing. Empirical analyses are performed, and numerical results are provided. Journal: North American Actuarial Journal Pages: 59-76 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597609 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597609 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:59-76 Template-Type: ReDIF-Article 1.0 Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Author-Name: Jose Garrido Author-X-Name-First: Jose Author-X-Name-Last: Garrido Title: Actuarial Applications of Epidemiological Models Abstract: The risk of a global avian flu or influenza A (H1 N1) pandemic and the emergence of the worldwide SARS epidemic in 2002–2003 have led to a revived interest in the study of infectious diseases. Mathematical models have become important tools in analyzing the transmission dynamics and in measuring the effectiveness of controlling strategies. Research on infectious diseases in the actuarial literature goes only so far in setting up epidemiological models that better reflect the transmission dynamics. This paper attempts to build a bridge between epidemiological and actuarial modeling and set up an actuarial model that provides financial arrangements to cover the expenses resulting from the medical treatments of infectious diseases.Based on classical epidemiological compartment models, the first part of this paper proposes insurance policies and models to quantify the risk of infection and formulates financial arrangements, between an insurer and insureds, using actuarial methodology. For practical purposes, the second part employs a variety of numerical methods to calculate premiums and reserves. The last part illustrates the methods by designing insurance products for two well-known epidemics: the Great Plague in England and the SARS epidemic in Hong Kong. Journal: North American Actuarial Journal Pages: 112-136 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597612 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597612 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:112-136 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Arthur Renshaw Author-X-Name-First: Arthur Author-X-Name-Last: Renshaw Title: Longevity-Indexed Life Annuities Abstract: This paper addresses the problem of the sharing of longevity risk between an annuity provider and a group of annuitants. An appropriate longevity index is designed in order to adapt the amount of the periodic payments in life annuity contracts. This accounts for unexpected longevity improvements experienced by a given reference population. The approach described in the present paper is in contrast with group self-annuitization, where annuitants bear their own risk. Here the annuitants bear only the nondiversifiable risk that the future mortality trend departs from that of the reference forecast. In that respect, the life annuities discussed in this paper are substitutes for reinsurance and securitization of longevity risk. Journal: North American Actuarial Journal Pages: 97-111 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597611 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597611 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:97-111 Template-Type: ReDIF-Article 1.0 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Mateusz Maj Author-X-Name-First: Mateusz Author-X-Name-Last: Maj Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Title: Improving the Design of Financial Products in a Multidimensional Black-Scholes Market Abstract: Using various techniques, authors have shown that in one-dimensional markets, complex (path-dependent) contracts are generally not optimal for rational consumers. In this paper we generalize these results to a multidimensional Black-Scholes market. In such a market, we discuss optimal contracts for investors who prefer more to less and have a fixed investment horizon T > 0. First, given a desired probability distribution, we give an explicit form of the optimal contract that provides this distribution to the consumer. Second, in the case of risk-averse investors, we are able to propose two ways of improving the design of financial products. In all cases, the optimal payoff can be seen as a path-independent European option that is written on the so-called market portfolio. We illustrate the theory with a few well-known securities and strategies. For example, we show that a buy-and-hold investment strategy can be dominated by a series of power options written on the underlying market portfolio. We also analyze the inefficiency of a widely used portfolio insurance strategy called Constant Proportion Portfolio Insurance. Journal: North American Actuarial Journal Pages: 77-96 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597610 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597610 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:77-96 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Cowell Author-X-Name-First: Michael Author-X-Name-Last: Cowell Title: “Mortality Projections for Social Security Programs in the United States,” Alice H. Wade, Vol. 14, No. 3, 2010 Journal: North American Actuarial Journal Pages: 137-139 Issue: 1 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597613 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597613 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:137-139 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin Abstract: I study the problem of how individuals should invest their wealth in a risky financial market to minimize the probability that they outlive their wealth, also known as the probability of lifetime ruin. Specifically, I determine the optimal investment strategy of an individual who targets a given rate of consumption and seeks to minimize the probability of lifetime ruin. Two forms of the consumption function are considered: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of his or her wealth. The first is arguably more realistic, but the second has a close connection with optimal consumption in Merton’s model of optimal consumption and investment under power utility.For constant force of mortality, I determine (a) the probability that individuals outlive their wealth if they follow the optimal investment strategy; (b) the corresponding optimal investment rule that tells individuals how much money to invest in the risky asset for a given wealth level; (c) comparative statics for the functions in (a) and (b); (d) the distribution of the time of lifetime ruin, given that ruin occurs; and (e) the distribution of bequest, given that ruin does not occur. I also include numerical examples to illustrate how the formulas developed in this paper might be applied. Journal: North American Actuarial Journal Pages: 106-126 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596174 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596174 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:106-126 Template-Type: ReDIF-Article 1.0 Author-Name: Yong Yao Author-X-Name-First: Yong Author-X-Name-Last: Yao Title: Efficient Factor Models For Yield Curve Dynamics Abstract: This paper derives a class of efficient factor models that bridge a gap between factor models and Heath-Jarrow-Morton models. These efficient factor models provide arbitrage-free dynamics for the yield curve, can be readily extended to fit the current yield curve, and have closed-form formulas for pricing default-free zero-coupon bonds. The short rate is a state variable in these efficient factor models. There are no restrictions imposed on the functional form of the volatility of the short rate except for certain technical conditions to ensure the solvability of the associated stochastic differential equations. The stochastic volatility of the short rate can be one of the state variables. The paper also presents a closed-form solution for default-free discount bond prices in the Malkiel model and provides a new method to derive the Ritchken-Sankarasubramanian model. Journal: North American Actuarial Journal Pages: 90-105 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596173 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596173 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:90-105 Template-Type: ReDIF-Article 1.0 Author-Name: Manuel Morales Author-X-Name-First: Manuel Author-X-Name-Last: Morales Title: On A Surplus Process Under A Periodic Environment Abstract: The problem of modeling claims occurring in periodic random environments is discussed in this paper. In the classical approach of risk theory, the occurrence of claims is modeled by counting processes that do not account for claims following a periodic pattern. The author discusses how the use of the classical approach to model a periodic portfolio might lead to the miscalculation of important risk indices, namely the associated ruin probability.He presents a periodic model, in terms of nonhomogeneous Poisson processes, that has potential practical applications. The discussion is based on some properties of the modeled periodic intensities. Existing simulation techniques are adapted to this periodic model, which provides a practical way to evaluate ruin probabilities. Journal: North American Actuarial Journal Pages: 76-89 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596172 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596172 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:76-89 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: Julia Wirch Author-X-Name-First: Julia Author-X-Name-Last: Wirch Title: The Iterated Cte Abstract: In this paper we present a method for defining a dynamic risk measure from a static risk measure, by backwards iteration. We apply the method to the conditional tail expectation (CTE) risk measure to construct a new, dynamic risk measure, the iterated CTE (ICTE). We show that the ICTE is coherent, consistent, and relevant according to the definitions of Riedel (2003), and we derive formulae for the ICTE for the case where the loss process is lognormal. Finally, we demonstrate the practical implementation of the ICTE to an equity-linked insurance contract with maturity and death benefit guarantees. Journal: North American Actuarial Journal Pages: 62-75 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596171 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596171 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:62-75 Template-Type: ReDIF-Article 1.0 Author-Name: Wei Zhou Author-X-Name-First: Wei Author-X-Name-Last: Zhou Title: “Martingale Valuation of Cash Flows for Insurance and Interest Models”, J. F. Carriére, July 2004 Journal: North American Actuarial Journal Pages: 152-153 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596178 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596178 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:152-153 Template-Type: ReDIF-Article 1.0 Author-Name: Bartholomew Leung Author-X-Name-First: Bartholomew Author-X-Name-Last: Leung Author-Name: H. W. J. Lee Author-X-Name-First: H. W. J. Author-X-Name-Last: Lee Author-Name: Chi Kin Chan Author-X-Name-First: Chi Kin Author-X-Name-Last: Chan Title: “Martingale Valuation of Cash Flows for Insurance and Interest Models”, J. F. Carriére, July 2004 Journal: North American Actuarial Journal Pages: 150-152 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596177 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596177 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:150-152 Template-Type: ReDIF-Article 1.0 Author-Name: Tom Hoedemakers Author-X-Name-First: Tom Author-X-Name-Last: Hoedemakers Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Title: “Risk and Discounted Loss Reserves,” Greg Taylor, January 2004 Abstract: Journal: North American Actuarial Journal Pages: 146-149 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596176 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596176 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:146-149 Template-Type: ReDIF-Article 1.0 Author-Name: Adam Kolkiewicz Author-X-Name-First: Adam Author-X-Name-Last: Kolkiewicz Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Title: Volatility Risk For Regime-Switching Models Abstract: Regime-switching models have proven to be well-suited for capturing the time series behavior of many financial variables. In particular, they have become a popular framework for pricing equity-linked insurance products. The success of these models demonstrates that realistic modeling of financial time series must allow for random changes in volatility. In the context of valuation of contingent claims, however, random volatility poses additional challenges when compared with the standard Black-Scholes framework. The main reason is the incompleteness of such models, which implies that contingent claims cannot be hedged perfectly and that a unique identification of the correct risk-neutral measure is not possible.The objective of this paper is to provide tools for managing the volatility risk. First we present a formula for the expected value of a shortfall caused by misspecification of the realized cumulative variance. This, in particular, leads to a closed-form expression for the expected shortfall for any strategy a hedger may use to deal with the stochastic volatility. Next we identify a method of selection of the initial volatility that minimizes the expected shortfall. This strategy is the same as delta hedging based on the cumulative volatility that matches the Black-Scholes model with the stochastic volatility model. We also discuss methods of managing the volatility risk under model uncertainty. In these cases, super-hedging is a possible strategy but it is expensive. The results presented enable a more accurate analysis of the trade-off between the initial cost and the risk of a shortfall. Journal: North American Actuarial Journal Pages: 127-145 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596175 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596175 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:127-145 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Steven Prus Author-X-Name-First: Steven Author-X-Name-Last: Prus Title: Social Transfers And Income Inequality In Old Age Abstract: This paper examines variation in old-age income inequality between industrialized nations with modern welfare systems. The analysis of income inequality across countries with different retirement income systems provides a perspective on public pension policy choices and designs and their distributional implications. Because of the progressive nature of public pension programs, we hypothesize that there is an inverse relationship between the quality of public pension benefits and old-age income inequality—that is, countries with comprehensive, universal, and generous public pension systems will exhibit more equal distributions of income in old age.Luxembourg Income Study data indeed show that cross-national variation in old-age income inequality is partly explained by differences in the percentage of seniors’ total income derived from public pension transfers. Sweden, for example, has the highest level of government transfers and the lowest level of old-age income inequality, while Israel and the United States have the lowest levels of dependency on government transfers and the highest levels of income inequality. A notable exception is Canada, where public transfers represent only a moderate portion of elderly income, yet old-age income inequality is relatively low. These findings suggest that quality of public pension benefits does indeed play a role in explaining differences in old-age income inequality between industrialized nations, yet these variations are also likely influenced by other factors. Journal: North American Actuarial Journal Pages: 30-36 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596169 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596169 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:30-36 Template-Type: ReDIF-Article 1.0 Author-Name: Howard Bolnick Author-X-Name-First: Howard Author-X-Name-Last: Bolnick Title: A Framework For Long-Term Actuarial Projections Of Health Care Costs Abstract: Ever-expanding life expectancy is increasing the size of elderly populations with profound social and economic consequences for developed nations, including future cost of their health care systems. Most existing long-term health care cost projections are driven mainly by changing demographics (aging populations). This simplified approach fails to recognize the many variables, and complicated interactions among them, affecting the future of health, health care, and health care costs. This study presents a framework incorporating key health care cost drivers. Using the framework, the study then introduces three plausible futures for health care along with broad, nonmodeled estimates of their costs that point to a very wide range of potential future costs. By taking the next step and building actuarial models based on the framework presented in this study, actuaries and health economists can create a powerful tool for health policymakers and health officials to better understand the long-term consequences of decisions taken during their stewardship of health care systems. Journal: North American Actuarial Journal Pages: 1-29 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596168 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596168 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:1-29 Template-Type: ReDIF-Article 1.0 Author-Name: X. Lin Author-X-Name-First: X. Author-X-Name-Last: Lin Title: Cairns, Andrew J. G., 2004, Journal: North American Actuarial Journal Pages: 154-155 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596179 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596179 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:154-155 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Panjer Author-X-Name-First: Harry Author-X-Name-Last: Panjer Title: Continuing the Tradition Journal: North American Actuarial Journal Pages: iii-iii Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596180 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596180 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Author-Name: Albert Wong Author-X-Name-First: Albert Author-X-Name-Last: Wong Author-Name: Howell Tong Author-X-Name-First: Howell Author-X-Name-Last: Tong Title: Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use Abstract: This paper introduces nonlinear threshold time series modeling techniques that actuaries can use in pricing insurance products, analyzing the results of experience studies, and forecasting actuarial assumptions. Basic “self-exciting” threshold autoregressive (SETAR) models, as well as heteroscedastic and multivariate SETAR processes, are discussed. Modeling techniques for each class of models are illustrated through actuarial examples. The methods that are described in this paper have the advantage of being direct and transparent. The sequential and iterative steps of tentative specification, estimation, and diagnostic checking parallel those of the orthodox Box-Jenkins approach for univariate time series analysis. Journal: North American Actuarial Journal Pages: 37-61 Issue: 4 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596170 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596170 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:37-61 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Author-Name: Ričardas Zitikis Author-X-Name-First: Ričardas Author-X-Name-Last: Zitikis Title: Empirical Estimation of Risk Measures and Related Quantities Abstract: The authors present an alternative representation of risk measures originally defined in terms of expectations with respect to distorted probabilities. They also show that the right-tail, left-tail, and two-sided deviations/indices suggested by Wang (1998) can be represented in this alternative form. Empirical estimators for these quantities are proposed and their properties explored. Journal: North American Actuarial Journal Pages: 44-54 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596117 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596117 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:44-54 Template-Type: ReDIF-Article 1.0 Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Author-Name: Emiliano Valdez Author-X-Name-First: Emiliano Author-X-Name-Last: Valdez Title: Tail Conditional Expectations for Elliptical Distributions Abstract: Significant changes in the insurance and financial markets are giving increasing attention to the need for developing a standard framework for risk measurement. Recently, there has been growing interest among insurance and investment experts to focus on the use of a tail conditional expectation because it shares properties that are considered desirable and applicable in a variety of situations. In particular, it satisfies requirements of a “coherent” risk measure in the spirit developed by Artzner et al. (1999). This paper derives explicit formulas for computing tail conditional expectations for elliptical distributions, a family of symmetric distributions that includes the more familiar normal and student-t distributions. The authors extend this investigation to multivariate elliptical distributions allowing them to model combinations of correlated risks. They are able to exploit properties of these distributions, naturally permitting them to decompose the conditional expectation, and allocate the contribution of individual risks to the aggregated risks. This is meaningful in practice, particularly in the case of computing capital requirements for an institution that may have several lines of correlated business and is concerned about fairly allocating the total capital to these constituents. Journal: North American Actuarial Journal Pages: 55-71 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596118 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596118 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:55-71 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: “Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends,” Hans U. Gerber and Elias S. W. Shiu, July 2003 - Discussion by John A. Beekman Journal: North American Actuarial Journal Pages: 102-103 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596124 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596124 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:102-103 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheldon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheldon Lin Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates Abstract: This paper considers the pricing of equity-indexed annuities (EIAs). Traditionally, the values of the guarantees embedded in these contracts are priced by modeling the underlying index fund while keeping the interest rates constant. The assumption of constant interest rates becomes unrealistic in pricing and hedging the EIAs since the embedded guarantees are often of much longer maturity. To solve this problem, the authors propose an economic model that has the flexibility of modeling the underlying index fund as well as the interest rates. Some popular EIAs are illustrated to assess the implication of the proposed model. Journal: North American Actuarial Journal Pages: 72-91 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596119 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596119 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:72-91 Template-Type: ReDIF-Article 1.0 Author-Name: Hélène Cossette Author-X-Name-First: Hélène Author-X-Name-Last: Cossette Author-Name: Thierry Duchesne Author-X-Name-First: Thierry Author-X-Name-Last: Duchesne Author-Name: Étienne Marceau Author-X-Name-First: Étienne Author-X-Name-Last: Marceau Title: Modeling Catastrophes and their Impact on Insurance Portfolios Abstract: The authors propose a general individual catastrophe risk model that allows damage ratios to be random functions of the catastrophe intensity. They derive some distributional properties of the insured risks and of the aggregate catastrophic loss under this model. Through the model and ruin probability calculations, they formally illustrate the well-known fact that the catastrophe risk cannot be diversified through premium collection alone, as is the case with the usual “day-to-day” risk, even for an arbitrary large portfolio. They also derive some risk orderings between different catastrophe portfolios and show that the risk level of a realistic portfolio falls between that of a portfolio of comonotonic risks and that of a portfolio of independent risks. Finally, the authors illustrate their findings with a numerical example inspired from earthquake insurance. Journal: North American Actuarial Journal Pages: 1-22 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596114 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596114 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:1-22 Template-Type: ReDIF-Article 1.0 Author-Name: Hon-Kwok Fung Author-X-Name-First: Hon-Kwok Author-X-Name-Last: Fung Author-Name: Leong Kwan Li Author-X-Name-First: Leong Author-X-Name-Last: Kwan Li Title: Pricing Discrete Dynamic Fund Protections Abstract: The authors investigate the pricing of discretely monitored dynamic fund protections when the fund price follows a lognormal process or a constant elasticity of variance (CEV) process. A backward recursive pricing formula is derived. By employing a numerical technique that combines function approximation and numerical quadrature, the authors demonstrate how to complete each recursion level efficiently. Numerical experiments show that the results compare favorably with those obtained by other pricing methods. Journal: North American Actuarial Journal Pages: 23-31 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596115 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596115 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:23-31 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Author-Name: Ann De Schepper Author-X-Name-First: Ann Author-X-Name-Last: De Schepper Author-Name: David Vyncke Author-X-Name-First: David Author-X-Name-Last: Vyncke Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Rob Kaas Author-X-Name-First: Rob Author-X-Name-Last: Kaas Title: Stable Laws and the Present Value of Fixed Cash Flows Abstract: In this paper, the authors consider the present value of a series of fixed cash flows under stochastic interest rates. To model these interest rates, they don’t use the common lognormal model, but stable laws, which better fit in with reality. Their main intention is to derive a result for the distribution function of such a present value. However, due to the dependencies between successive discounted payments, the calculation of an exact analytical distribution is impossible. Therefore, use is made of the methodology of comonotonic random variables and the convex ordering of risks, introduced by the same authors in some previous papers.The present paper starts with a brief overview of properties and features of stable laws, and of the possible application of the concept of convex ordering to sums of risks, which is also the situation for a present value of future payments. Afterwards, the authors show how, for the present value under investigation, an approximation in the form of a convex upper bound can be derived. This upper bound has an easier structure than the original present value, and they derive elegant calculation formulas for the distribution of this bound. Finally, they provide some numerical examples that illustrate the precision of the approximation. Due to the design of the present value and the construction of the upper bound, these illustrations show great promise concerning the accuracy of the approximation. Journal: North American Actuarial Journal Pages: 32-43 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596116 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596116 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:32-43 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 Journal: North American Actuarial Journal Pages: 96-101 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596122 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596122 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:96-101 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Title: “Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends,” Hans U. Gerber and Elias S. W. Shiu, July 2003 Journal: North American Actuarial Journal Pages: 102-102 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596123 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596123 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:102-102 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Decamps Author-X-Name-First: Marc Author-X-Name-Last: Decamps Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Title: “Pricing Lookback Options and Dynamic Guarantees,” Hans U. Gerber and Elias S. W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 94-95 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596120 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596120 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:94-95 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: “Pricing Lookback Options and Dynamic Guarantees,” Hans U. Gerber and Elias S. W. Shiu, January 2003 - Discussion by Marc Decamps; Marc J. Goovaerts Journal: North American Actuarial Journal Pages: 95-96 Issue: 4 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596121 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596121 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:95-96 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Bauer Author-X-Name-First: Daniel Author-X-Name-Last: Bauer Author-Name: Jin Gao Author-X-Name-First: Jin Author-X-Name-Last: Gao Author-Name: Thorsten Moenig Author-X-Name-First: Thorsten Author-X-Name-Last: Moenig Author-Name: Eric R. Ulm Author-X-Name-First: Eric R. Author-X-Name-Last: Ulm Author-Name: Nan Zhu Author-X-Name-First: Nan Author-X-Name-Last: Zhu Title: Policyholder Exercise Behavior in Life Insurance: The State of Affairs Abstract: The article presents a review of structural models of policyholder behavior in life insurance. We first discuss underlying drivers of policyholder behavior in theory and survey the implications of different models. We then turn to empirical behavior and appraise how well different drivers explain observations. The key contributions lie in the synthesis and the systematic categorization of different approaches. The article should provide a foundation for future studies, and we describe some important directions for future research in the conclusion. Journal: North American Actuarial Journal Pages: 485-501 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1314816 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1314816 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:485-501 Template-Type: ReDIF-Article 1.0 Author-Name: Maciej Augustyniak Author-X-Name-First: Maciej Author-X-Name-Last: Augustyniak Author-Name: Mathieu Boudreault Author-X-Name-First: Mathieu Author-X-Name-Last: Boudreault Title: Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk Abstract: Variable annuities are investment vehicles offered by insurance companies that combine a life insurance policy with long-term financial guarantees. These guarantees expose the insurer to market risks, such as volatility and interest rate risks, which can be managed only with a hedging strategy. The objective of this article is to study the effectiveness of dynamic delta-rho hedging strategies for mitigating interest rate risk in variable annuities with either a guaranteed minimum death benefit or guaranteed minimum withdrawal benefit rider. Our analysis centers on three important practical issues: (1) the robustness of delta-rho hedging strategies to model uncertainty, (2) the impact of guarantee features (maturity versus withdrawal benefits) on the performance of the hedging strategy, and (3) the importance of hedging interest rate risk in either a low and stable or rising interest rate environment. Overall, we find that the impact of interest rate risk is equally felt for the two types of products considered, and that interest rate hedges do lead to a significant risk reduction for the insurer, even when the ongoing low interest rate environment is factored in. Journal: North American Actuarial Journal Pages: 502-525 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1316210 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1316210 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:502-525 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: Insurance Portfolio Risk Retention Abstract: In this article, I introduce a statistic for managing a portfolio of insurance risks. This tool is based on changes in the risk profile when changes in a risk parameter, such as a deductible, coinsurance, or upper policy limit, are made. I refer to the new statistic as a risk measure relative marginal change and denote it as RM2. By examining data from the Wisconsin Local Government Property Fund, I show how it can be used by an insurer to identify the “best” and “worst” risks in terms of opportunities for risk management. The RM2 changes reflect the underlying dependence structure of risks; I use an elliptical copula framework to demonstrate the sensitivity of risk mitigation strategy to the dependence structure. Journal: North American Actuarial Journal Pages: 526-551 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1317272 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1317272 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:526-551 Template-Type: ReDIF-Article 1.0 Author-Name: Stefan Cutajar Author-X-Name-First: Stefan Author-X-Name-Last: Cutajar Author-Name: Helena Smigoc Author-X-Name-First: Helena Author-X-Name-Last: Smigoc Author-Name: Adrian O’Hagan Author-X-Name-First: Adrian Author-X-Name-Last: O’Hagan Title: Actuarial Risk Matrices: The Nearest Positive Semidefinite Matrix Problem Abstract: The manner in which a group of insurance risks are interrelated is commonly presented via a correlation matrix. Actuarial risk correlation matrices are often constructed using output from disparate modeling sources and can be subjectively adjusted, for example, increasing the estimated correlation between two risk sources to confer reserving prudence. Hence, while individual elements still obey the assumptions of correlation values, the overall matrix is often not mathematically valid (not positive semidefinite). This can prove problematic in using the matrix in statistical models. The first objective of this article is to review existing techniques that address the nearest positive semidefinite matrix problem in a very general setting. The chief approaches studied are Semidefinite Programming (SDP) and the Alternating Projections Method (APM). The second objective is to finesse the original problem specification to consider imposition of a block structure on the initial risk correlation matrix. This commonly employed technique identifies off-diagonal subsets of the matrix where values can or should be set equal to some constant. This may be due to similarity of the underlying risks and/or with the goal of increasing computational efficiency for processes involving large matrices. Implementation of further linear constraints of this nature requires adaptation of the standard SDP and APM algorithms. In addition, a new Shrinking Method is proposed to provide an alternative solution in the context of this increased complexity. “Nearness” is primarily considered in terms of two summary measures for differences between matrices: the Chebychev Norm (maximum element distance) and the Frobenius Norm (sum of squared element distances). Among the existing methods, adapted to function appropriately for actuarial risk matrices, APM is extremely efficient in producing solutions that are optimal in the Frobenius norm. An efficient algorithm that would return a positive semidefinite matrix that is optimal in Chebychev norm is currently unknown. However, APM is used to highlight the existence of matrices close to such an optimum and exploited, via the Shrinking Method, to find high-quality solutions. All methods are shown to work well both on artificial and real actuarial risk matrices provided under collaboration with Tokio Marine Kiln (TMK). Convergence speeds are calculated and compared and sample data and MATLAB code is provided. Ultimately the APM is identified as being superior in Frobenius distance and convergence speed. The Shrinking Method, building on the output of the APM algorithm, is demonstrated to provide excellent results at low computational cost for minimizing Chebychev distance. Journal: North American Actuarial Journal Pages: 552-564 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1317273 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1317273 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:552-564 Template-Type: ReDIF-Article 1.0 Author-Name: Daniël Linders Author-X-Name-First: Daniël Author-X-Name-Last: Linders Author-Name: Fan Yang Author-X-Name-First: Fan Author-X-Name-Last: Yang Title: Aggregating Risks with Partial Dependence Information Abstract: We consider the problem of aggregating dependent risks in the presence of partial dependence information. More concretely, we assume that the risks involved belong to independent subgroups and the dependence structure within each group is unknown. A sharp convex upper bound exists in this setting, and this constrained upper bound improves the existing, unconstrained, comonotonic upper bound in convex order. Moreover, we prove the uniqueness of this constrained upper bound and provide a characterization in terms of the distribution of its sum. Numerical illustrations are provided to show the improvement of the new upper bound. Journal: North American Actuarial Journal Pages: 565-579 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1317603 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1317603 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:565-579 Template-Type: ReDIF-Article 1.0 Author-Name: Patrice Gaillardetz Author-X-Name-First: Patrice Author-X-Name-Last: Gaillardetz Author-Name: Mehran Moghtadai Author-X-Name-First: Mehran Author-X-Name-Last: Moghtadai Title: Partial Hedging for Equity-Linked Products Using Risk-Minimizing Strategies Abstract: In this article, we consider the pricing and hedging of equity-indexed annuities (EIAs) using local risk-minimizing strategies as well as evaluating the capital requirement for these products. Since these products involve mortality as well as financial risks, we integrate mortality risk and propose partial hedging strategies that protect the insurer based on risk measures. The framework we present makes use of sequential local risk-minimizing strategies to take into account all intermediate requirements. To demonstrate the flexibility of this framework we present numerical examples featuring point-to-point EIAs with a two-state regime-switching equity model. Journal: North American Actuarial Journal Pages: 580-593 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1318707 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1318707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:580-593 Template-Type: ReDIF-Article 1.0 Author-Name: Zixi Li Author-X-Name-First: Zixi Author-X-Name-Last: Li Author-Name: Adam W. Shao Author-X-Name-First: Adam W. Author-X-Name-Last: Shao Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: The Impact of Systematic Trend and Uncertainty on Mortality and Disability in a Multistate Latent Factor Model for Transition Rates Abstract: Multiple state functional disability models do not generally include systematic trend and uncertainty. We develop and estimate a multistate latent factor intensity model with transition and recovery rates depending on a stochastic frailty factor to capture trend and uncertainty. We estimate the model parameters using U.S. Health and Retirement Study data between 1998 and 2012 with Monte Carlo maximum likelihood estimation method. The model shows significant reductions in disability and mortality rates during this period and allows us to quantify uncertainty in transition rates arising from the stochastic frailty factor. Recovery rates are very sensitive to the stochastic frailty. There is an increase in expected future lifetimes as well as an increase in future healthy life expectancy. The proportion of lifetime spent in disability on average remains stable with no strong support in the data for either morbidity compression or expansion. The model has widespread application in costing of government-funded aged care and pricing and risk management of long-term-care insurance products. Journal: North American Actuarial Journal Pages: 594-610 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1330157 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1330157 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:594-610 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Title: Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development Abstract: This article proposes a new loss reserving approach, inspired from the collective model of risk theory. According to the collective paradigm, we do not relate payments to specific claims or policies, but we work within a frequency-severity setting, with a number of payments in every cell of the run-off triangle, together with the corresponding paid amounts. Compared to the Tweedie reserving model, which can be seen as a compound sum with Poisson-distributed number of terms and Gamma-distributed summands, we allow here for more general severity distributions, typically mixture models combining a light-tailed component with a heavier-tailed one, including inflation effects. The severity model is fitted to individual observations and not to aggregated data displayed in run-off triangles with a single value in every cell. In that respect, the modeling approach appears to be a powerful alternative to both the crude traditional aggregated approach based on triangles and the extremely detailed individual reserving approach developing each and every claim separately. A case study based on a motor third-party liability insurance portfolio observed over 2004–2014 is used to illustrate the relevance of the proposed approach. Journal: North American Actuarial Journal Pages: 611-619 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1353428 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1353428 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:611-619 Template-Type: ReDIF-Article 1.0 Author-Name: Gee Y. Lee Author-X-Name-First: Gee Y. Author-X-Name-Last: Lee Title: General Insurance Deductible Ratemaking Abstract: Insurance claims have deductibles, which must be considered when pricing for insurance premium. The deductible may cause censoring and truncation to the insurance claims. However, modeling the unobserved response variable using maximum likelihood in this setting may be a challenge in practice. For this reason, a practitioner may perform a regression using the observed response, in order to calculate the deductible rates using the regression coefficients. A natural question is how well this approach performs, and how it compares to the theoretically correct approach to rating the deductibles. Also, a practitioner would be interested in a systematic review of the approaches to modeling the deductible rates. In this article, an overview of deductible ratemaking is provided, and the pros and cons of two deductible ratemaking approaches are compared: the regression approach and the maximum likelihood approach. The regression approach turns out to have an advantage in predicting aggregate claims, whereas the maximum likelihood approach has an advantage when calculating theoretically correct relativities for deductible levels beyond those observed by empirical data. For demonstration, loss models are fit to the Wisconsin Local Government Property Insurance Fund data, and examples are provided for the ratemaking of per-loss deductibles offered by the fund. The article discovers that the regression approach is actually a single-parameter approximation to the true relativity curve. A comparison of selected models from the generalized beta family discovers that the usage of long-tail severity distributions may improve the deductible rating, while advanced frequency models such as 01-inflated models may have limited advantages due to estimation issues under censoring and truncation. In addition, in this article, models for specific peril types are combined to improve the ratemaking. Journal: North American Actuarial Journal Pages: 620-638 Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1353430 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1353430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:620-638 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board EOV Journal: North American Actuarial Journal Pages: ebi-ebi Issue: 4 Volume: 21 Year: 2017 Month: 10 X-DOI: 10.1080/10920277.2017.1406267 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1406267 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: Shi-jie Jiang Author-X-Name-First: Shi-jie Author-X-Name-Last: Jiang Title: Voluntary Termination of Life Insurance Policies Abstract: In this paper, one error-correction model (ECM) that is able to avoid the problem of producing noise within traditional multiple cointegration vectors has been employed to explore the dynamics of surrender behavior. The evidence shows that both the emergency fund hypothesis and interest rate hypothesis are sustained in the short run as well as in the long run. A unique cointegration relationship within the surrender dynamics has been validated. In addition, a new hypothesis test that stresses the competition for the withdrawal of life insurance policy cash values has also been conducted. Such a crowding-out effect between policy loans and policy surrenders might be attributed to the motivation that keeps a life policy in force, the existence of surrender charges, and the automatic premium loan provision. Journal: North American Actuarial Journal Pages: 369-380 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597596 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597596 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:369-380 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Title: Developing Mortality Improvement Formulas Abstract: Longevity improvements have contributed to widespread underfunding of pension plans and losses in insured annuity portfolios. Insurers might reasonably expect some upside from the effect of lower mortality on their life business. Although mortality improvement scales, such as the Society of Actuaries Scale AA, are widely employed in pension and annuity valuation, the derivation of these scales appears heuristic, leading to problems in deriving meaningful measures of uncertainty. We explore the evidence on mortality trends for the Canadian life insurance companies, data, using stochastic models. We use the more credible population data to benchmark the insured lives data. Finally, we derive a practical, model-based formula for actuaries to incorporate mortality improvement and the associated uncertainty into their calculations. Journal: North American Actuarial Journal Pages: 381-399 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597597 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597597 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:381-399 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Hans U. Gerber Author-X-Name-First: Hans U. Author-X-Name-Last: Gerber Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Authors’ Reply: A Direct Approach to the Discounted Penalty Function - Discussion by Volkmar Lautscham; Yi Lu; Eric C. K. Cheung Journal: North American Actuarial Journal Pages: 445-447 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597603 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597603 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:445-447 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Title: “A Direct Approach to the Discounted Penalty Function”, Hansjörg Albrecher, Hans U. Gerber, and Hailiang Yang, Volume 14, No. 4, 2010 Journal: North American Actuarial Journal Pages: 441-445 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597602 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597602 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:441-445 Template-Type: ReDIF-Article 1.0 Author-Name: Kaiqi Yu Author-X-Name-First: Kaiqi Author-X-Name-Last: Yu Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Author-Name: David Stanford Author-X-Name-First: David Author-X-Name-Last: Stanford Title: The Moments of the Time of Ruin in Markovian Risk Models Abstract: We present an approach based on matrix-analytic methods to find moments of the time of ruin in Markovian risk models. The approach is applicable when claims occur according to a Markovian arrival process (MAP) and claim sizes are phase distributed with parameters that depend on the state of the MAP. The method involves the construction of a sample-path-equivalent Markov-modulated fluid flow for the risk model. We develop an algorithm for moments of the time of ruin and prove the algorithm is convergent. Examples show that the proposed approach is computationally stable. Journal: North American Actuarial Journal Pages: 464-471 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597605 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597605 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:464-471 Template-Type: ReDIF-Article 1.0 Author-Name: Werner Hürlimann Author-X-Name-First: Werner Author-X-Name-Last: Hürlimann Title: Biometric Solvency Risk for Portfolios of General Life Contracts. I. The Single-Life Multiple Decrement Case Abstract: Solvency II splits life insurance risk into seven risk classes consisting of three biometric risks (mortality risk, longevity risk, and disability/morbidity risk) and four nonbiometric risks (lapse risk, expense risk, revision risk, and catastrophe risk). The best estimate liabilities for the biometric risks are valued with biometric life tables (mortality and disability tables), while those of the nonbiometric risks require alternative valuation methods. The present study is restricted to biometric risks encountered in traditional single-life insurance contracts with multiple causes of decrement. Based on the results of quantitative impact studies, process risk was deemed to be not significant enough to warrant an explicit calculation. It was therefore assumed to be implicitly included in the systematic/parameter risk, resulting in a less complex standard formula. For the purpose of internal models and improved risk management, it appears important to capture separately or simultaneously all risk components of biometric risks. Besides its being of interest for its own sake, this leads to a better understanding of the standard approach and its application extent. Based on a total balance sheet approach we express the liability risk solvency capital of an insurance portfolio as value-at-risk and conditional value-at-risk of the prospective liability risk understood as random present value of future cash flows at a given time. The proposed approach is then applied to determine the biometric solvency capital for a portfolio of general life contracts. Using the conditional mean and variance of a portfolio’s prospective liability risk and a gamma distribution approximation we obtain simple solvency capital formulas as well as corresponding solvency capital ratios. To account for the possibility of systematic/parameter risk, we propose either to shift the biometric life tables or to apply a stochastic biometric model, which allows for random biometric rates. A numerical illustration for a cohort of immediate life annuities in arrears reveals the importance of process risk in the assessment of longevity risk solvency capital. Journal: North American Actuarial Journal Pages: 400-419 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597598 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597598 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:400-419 Template-Type: ReDIF-Article 1.0 Author-Name: P. W. A. Dayananda Author-X-Name-First: P. W. A. Author-X-Name-Last: Dayananda Author-Name: John Kemper Author-X-Name-First: John Author-X-Name-Last: Kemper Title: Fair Terms and Fair Pricing for Multiple Warrant Issues Abstract: Some firms utilize one or more tranches of warrant issues to supplement their capital base. Unlike exchange-traded options, the exercise of warrants requires the issuance of stock by the company, resulting in a form of dilution. Some previous studies of warrant valuation relied on “the value of the firm,” which is nonobservable, making it difficult to apply the corresponding valuation formula. This paper derives closed-form formulas to value single and multiple tranches of warrants based on the underlying stock price, its volatility, and other known parameter values. The paper first establishes the equivalence of the Black-Scholes formula for both call options and warrants in the case of a single tranche. Thereafter, it considers the impact on the value of previously issued warrants that results when a new tranche of warrants is subsequently issued, showing in each case that fair treatment of the first-issued warrant holders requires an adjustment (due to dilution) in the terms of those warrants and a corresponding modification in the warrants’ value once a second tranche of warrants is issued. To promote such fair treatment, terms of a warrant indenture would specify the nature of the adjustment required when future warrants are issued or exercised, analogous to the antidilution terms related, for example, to stock dividends. Unlike multiple issues of traded options, which are valued independently of one another, multiple warrant issues will be shown to have prices dependent on other warrants outstanding. Also examined is the sensitivity of the fair-value adjustment to changes in the underlying variables, and the theoretical fair-value prices are compared with Black-Scholes prices and with market prices of warrants in the case of two publicly traded companies, each with two warrant issues outstanding. As warrant issues modify the equity structure of a firm, the methodology of valuing warrants presented here will be useful to investment actuaries in situations in which a comprehensive market value for all of a firm’s securities is called for. In addition, risk management practices may sometimes include the use of warrant transactions to hedge stock positions similar to the way that call options are used for that purpose. This may include hedging the risk in equity-linked insurance contracts when the equity position includes stock in companies that have one or more warrant issues that are traded. The methods developed here are also applicable to multiple issues of executive stock options (ESOs) or to combinations of warrant issues and ESOs. Journal: North American Actuarial Journal Pages: 448-463 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597604 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597604 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:448-463 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: A Direct Approach to the Discounted Penalty Function Abstract: This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods. Journal: North American Actuarial Journal Pages: 420-434 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597599 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597599 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:420-434 Template-Type: ReDIF-Article 1.0 Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Title: “A Direct Approach to the Discounted Penalty Function”, Hansjörg Albrecher, Hans U. Gerber, and Hailiang Yang, Volume 14, No. 4, 2010 Journal: North American Actuarial Journal Pages: 438-441 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597601 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597601 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:438-441 Template-Type: ReDIF-Article 1.0 Author-Name: Volkmar Lautscham Author-X-Name-First: Volkmar Author-X-Name-Last: Lautscham Title: “A Direct Approach to the Discounted Penalty Function”, Hansjörg Albrecher, Hans U. Gerber, and Hailiang Yang, Volume 14, No. 4, 2010 Journal: North American Actuarial Journal Pages: 434-438 Issue: 4 Volume: 14 Year: 2010 X-DOI: 10.1080/10920277.2010.10597600 File-URL: http://hdl.handle.net/10.1080/10920277.2010.10597600 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:14:y:2010:i:4:p:434-438 Template-Type: ReDIF-Article 1.0 Author-Name: François Dufresne Author-X-Name-First: François Author-X-Name-Last: Dufresne Title: Discussion on “On Cramér’s First Contributions to Ruin Theory,” by Ennio Badolati and Sandra Ciccone, Volume 21(2) Journal: North American Actuarial Journal Pages: 321-321 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1616965 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1616965 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:321-321 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Canudas-Romo Author-X-Name-First: Vladimir Author-X-Name-Last: Canudas-Romo Author-Name: Heather Booth Author-X-Name-First: Heather Author-X-Name-Last: Booth Author-Name: Marie-Pier Bergeron-Boucher Author-X-Name-First: Marie-Pier Author-X-Name-Last: Bergeron-Boucher Title: Minimum Death Rates and Maximum Life Expectancy: The Role of Concordant Ages Abstract: Only five populations have achieved maximum life expectancy (or best practice population) more than occasionally since 1900. The aim of this article is to understand how maximum life expectancy is achieved in the context of mortality transition. We explore this aim using the concepts of potential life expectancy, based on minimum rates at each age among all high longevity populations, and concordant ages. Concordant ages are defined as ages at which the minimum death rate occurs in the population with the maximum life expectancy. The results show the extent to which maximum life expectancy could increase through the realization of demonstrably achievable minimum rates. Concordant ages are concentrated at increasingly older ages over time, but they have produced more than half of the change in maximum life expectancy in almost all periods since 1900. This finding is attributed to their quantity and position whereby concordant ages are concentrated at the ages that have the greatest impact on mortality decline in a particular period. Based on mortality forecasts, we expect that concordant ages will continue to lead increases in female maximum life expectancy, but that they will play a weaker role in male maximum life expectancy. Journal: North American Actuarial Journal Pages: 322-334 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2018.1519448 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1519448 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:322-334 Template-Type: ReDIF-Article 1.0 Author-Name: Qing Liu Author-X-Name-First: Qing Author-X-Name-Last: Liu Author-Name: Chen Ling Author-X-Name-First: Chen Author-X-Name-Last: Ling Author-Name: Liang Peng Author-X-Name-First: Liang Author-X-Name-Last: Peng Title: Statistical Inference for Lee-Carter Mortality Model and Corresponding Forecasts Abstract: Although the Lee-Carter model has become a benchmark in modeling mortality rates, forecasting mortality risk, and hedging longevity risk, some serious issues exist on its inference and interpretation in the actuarial science literature. After pointing out these pitfalls, this article proposes a modified Lee-Carter model, provides a rigorous statistical inference, and derives the asymptotic distributions of the proposed estimators and unit root test when the mortality index is nearly integrated and errors in the model satisfy some mixing conditions. After a unit root hypothesis is not rejected, future mortality forecasts can be obtained via the proposed inference. An application of the proposed unit root test to U.S. mortality rates rejects the unit root hypothesis for the female and combined mortality rates but does not reject the unit root hypothesis for the male mortality rates. Journal: North American Actuarial Journal Pages: 335-363 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2018.1556702 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1556702 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:335-363 Template-Type: ReDIF-Article 1.0 Author-Name: Zhiyi Shen Author-X-Name-First: Zhiyi Author-X-Name-Last: Shen Author-Name: Yukun Liu Author-X-Name-First: Yukun Author-X-Name-Last: Liu Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Title: Nonparametric Inference for VaR, CTE, and Expectile with High-Order Precision Abstract: Value-at-Risk and Conditional Tail Expectation are the two most frequently applied risk measures in quantitative risk management. Recently expectile has also attracted much attention as a risk measure because of its elicitability property. This article establishes empirical likelihood–based estimation with high-order precision for these three risk measures. The superiority of the estimation is justified both in theory and via simulation studies. Extensive simulation studies confirm that our method significantly improves the coverage probabilities for interval estimation of the three risk measures, compared to three competing methods available in the literature. Journal: North American Actuarial Journal Pages: 364-385 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1566075 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1566075 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:364-385 Template-Type: ReDIF-Article 1.0 Author-Name: Whitney Schwark Pratt Author-X-Name-First: Whitney Author-X-Name-Last: Schwark Pratt Author-Name: Zhenxiang Zhao Author-X-Name-First: Zhenxiang Author-X-Name-Last: Zhao Author-Name: Beth Mitchell Author-X-Name-First: Beth Author-X-Name-Last: Mitchell Author-Name: Kevin Ashpole Author-X-Name-First: Kevin Author-X-Name-Last: Ashpole Author-Name: Karl J. Gregor Author-X-Name-First: Karl J. Author-X-Name-Last: Gregor Title: Diabetes Payer-Addressable Burden: An Actuarial Analysis Abstract: The Payer-Addressable Burden (PAB) analysis describes the total allowed cost of care curve and seeks to identify opportunities to address those costs. The objective of this study is to describe health plan financials from an actuarial perspective for members with diabetes, including members with serious emergent hypoglycemic events. Data were obtained from Optum’s proprietary database, and medical and prescription claims were evaluated using an episode grouper program, Symmetry® Episode Treatment Groups, to aggregate allowed claim costs from the claims. The aggregated allowed costs were summed to produce a total allowed cost for a specific episode of care (EOC) for each patient. Analyses were conducted across three successive 12-month periods, from April 2013 to March 2016, and described allowed costs with EOCs based on commercial and Medicare Advantage Part D (MAPD) plans, type 1 diabetes (T1DM) and type 2 diabetes (T2DM), and hypoglycemic events. Three areas of allowed claims costs were analyzed: diabetes-specific PAB (dPAB), comorbidity-associated PAB, and total PAB (tPAB). A health plan actuarial and financial perspective was used and focused on average annual allowed cost per member with diabetes. A total of 631,888 commercial members and 549,960 MAPD members had both medical and pharmacy benefits and were included in the analyses. The tPAB costs were two to three times higher than the dPAB costs at each study year for both commercial and MAPD members, but the annual trend in average cost per EOC was higher for dPAB than for tPAB. A higher proportion of commercial and MAPD T2DM members with a claim for a hypoglycemic event were in the highest dPAB cost category versus members without a claim for a hypoglycemic event (commercial: 56% vs. 2%, respectively; MAPD: 75% vs. 2%,respectively). Comorbidities cost an average of 31.2% or 28.0% more when commercial or MAPD members, respectively, had diabetes versus not having diabetes. The average annual dPAB and tPAB were noticeably higher for members with a claim for a hypoglycemic event versus those without a claim for a hypoglycemic event. Because of a much higher prevalence and aggregate allowed cost impact of T2DM members, actuaries may focus more on T2DM members when making financial decisions, despite the fact that T1DM average annual allowed costs per member are much more expensive than T2DM average annual allowed costs per member. Return on investment analyses should be conducted to better understand the addressability of diabetes costs. Journal: North American Actuarial Journal Pages: 386-394 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1566077 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1566077 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:386-394 Template-Type: ReDIF-Article 1.0 Author-Name: K. P. Sapna Isotupa Author-X-Name-First: K. P. Sapna Author-X-Name-Last: Isotupa Author-Name: Mary Kelly Author-X-Name-First: Mary Author-X-Name-Last: Kelly Author-Name: Anne Kleffner Author-X-Name-First: Anne Author-X-Name-Last: Kleffner Title: Experience-Rating Mechanisms in Auto Insurance: Implications for High-Risk, Low-Risk, and Novice Drivers Abstract: Using a unique data set that rates a cohort of drivers on two distinct experience-rating mechanisms, we examine the impact of these experience-rating mechanism on premiums charged to low-risk, high-risk, and novice drivers. The first mechanism is a pure no-claims discount that classifies drivers by 0 to 6 or more years of at-fault claims-free driving. The second is a bonus-malus system with 32 driving record (DR) classes. Using standard stochastic modeling techniques, we find that having a greater number of DR classes does not result in lower prices for the new drivers nor does it create significant savings to the lowest risk drivers. And, not surprisingly, with an increasing number of malus DR classes, the highest risk insureds pay a substantially higher premium that may not be sustainable over time. Due to its mandatory nature in most countries, monitoring the fairness of the classification mechanism and the affordability and availability of auto insurance are common regulatory goals. Charging novice drivers excessively high premiums may conflict with affordability and fairness objectives. Thus, we conclude with an examination of other pricing mechanisms that can be used for novice drivers. Journal: North American Actuarial Journal Pages: 395-411 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1572524 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1572524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:395-411 Template-Type: ReDIF-Article 1.0 Author-Name: Milton Boyd Author-X-Name-First: Milton Author-X-Name-Last: Boyd Author-Name: Brock Porth Author-X-Name-First: Brock Author-X-Name-Last: Porth Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Author-Name: Daniel Turenne Author-X-Name-First: Daniel Author-X-Name-Last: Turenne Title: The Impact of Spatial Interpolation Techniques on Spatial Basis Risk for Weather Insurance: An Application to Forage Crops Abstract: Weather index insurance for crops is at the developmental stage, however, this type of insurance is particularly susceptible to the problem of spatial basis risk. Spatial basis risk occurs when the weather observed at weather stations does not match the weather experienced on the farmer’s property, causing improper indemnities to be paid to the farmer. However, spatial basis risk may be reduced through the use of averaging and spatial interpolation techniques, such as inverse distance weighting and kriging. These techniques make it possible to incorporate multiple weather stations in the estimation process rather than using only the single closest station, potentially resulting in more accurate estimations and thereby reducing spatial basis risk. Therefore, the objective of this study is to examine the extent to which the choice of spatial interpolation techniques can influence the amount of spatial basis risk in a weather-based insurance model. Using forage crops from the province of Ontario, Canada, as an example, a weather insurance index is developed based on cooling degree days. The weather index represents the heat stress that the crops receive over the growing season. This insurance index is used to determine to what extent spatial basis risk can be reduced by the insurer’s choice of spatial interpolation technique. Seven different interpolation methods are applied to temperature data from Ontario, and theoretical indemnities are calculated for forage producers across the province. By analyzing the correlation between the estimated indemnities and reported forage yields, the amount of spatial basis risk in each model is quantified. The results of this study highlight the importance of choosing an appropriate method based on the characteristics of the target region (and data). Operationally this is important because insurers typically apply the same interpolation methods across an entire region. While one finding of this research may suggest that governments and/or insurance companies may wish to invest in additional weather stations to improve the accuracy of the interpolation method and index, this may not be feasible in practice. Given this, future research may consider utilizing satellite-based remote sensing weather estimates to augment the weather station data and reduce basis risk. Journal: North American Actuarial Journal Pages: 412-433 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1566074 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1566074 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:412-433 Template-Type: ReDIF-Article 1.0 Author-Name: Jose M. Pavía Author-X-Name-First: Jose M. Author-X-Name-Last: Pavía Author-Name: Francisco G. Morillas Author-X-Name-First: Francisco G. Author-X-Name-Last: Morillas Author-Name: Juan Carlos Bosch-Rodríguez Author-X-Name-First: Juan Carlos Author-X-Name-Last: Bosch-Rodríguez Title: Using Parametric Bootstrap to Introduce and Manage Uncertainty: Replicated Loaded Insurance Life Tables Abstract: Insurance companies develop loaded life tables to protect themselves against deviations, for example, in the number of expected deaths or in the (residual) expectation of life of their insured. In doing so, however, the single random vector of experience crude death rates from which loaded tables are constructed is treated as deterministic or, at best, as a single realization of an underlying stochastic process, omitting the fact that it is estimated and subject to error and uncertainty. This can result in serious consequences for the insurer. To solve this problem, we follow the example of other researchers and propose a method to replicate loaded life tables using parametric bootstrap. We focus on estimating period-loaded life tables from company portfolios, where the sizes of the exposed-to-risk populations are significantly smaller than those of general populations. If we have a set of B loaded life tables, the average behavior and some extreme values can be computed and subsequently used in managing premiums or reserves. This article offers life insurers a simple way of incorporating the experience uncertainty in actuarial tasks (for example, in pricing) by comparing the limits of the confidence intervals obtained between parametric bootstrap and classical approaches (such as limit theorems). Journal: North American Actuarial Journal Pages: 434-446 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1596820 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1596820 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:434-446 Template-Type: ReDIF-Article 1.0 Author-Name: Peter A. Forsyth Author-X-Name-First: Peter A. Author-X-Name-Last: Forsyth Author-Name: Kenneth R. Vetzal Author-X-Name-First: Kenneth R. Author-X-Name-Last: Vetzal Author-Name: Graham Westmacott Author-X-Name-First: Graham Author-X-Name-Last: Westmacott Title: Management of Portfolio Depletion Risk through Optimal Life Cycle Asset Allocation Abstract: Members of defined contribution (DC) pension plans must take on additional responsibilities for their investments, compared to participants in defined benefit (DB) pension plans. The transition from DB to DC plans means that more employees are faced with these responsibilities. We explore the extent to which DC plan members can follow financial strategies that have a high chance of resulting in a retirement scenario that is fairly close to that provided by DB plans. Retirees in DC plans typically must fund spending from accumulated savings. This leads to the risk of depleting these savings, that is, portfolio depletion risk. We analyze the management of this risk through life cycle optimal dynamic asset allocation, including the accumulation and decumulation phases. We pose the asset allocation strategy as an optimal stochastic control problem. Several objective functions are tested and compared. We focus on the risk of portfolio depletion at the terminal date, using such measures as conditional value at risk (CVAR) and probability of ruin. A secondary consideration is the median terminal portfolio value. The control problem is solved using a Hamilton-Jacobi-Bellman formulation, based on a parametric model of the financial market. Monte Carlo simulations that use the optimal controls are presented to evaluate the performance metrics. These simulations are based on both the parametric model and bootstrap resampling of 91 years of historical data. The resampling tests suggest that target-based approaches that seek to establish a safety margin of wealth at the end of the decumulation period appear to be superior to strategies that directly attempt to minimize risk measures such as the probability of portfolio depletion or CVAR. The target-based approaches result in a reasonably close approximation to the retirement spending available in a DB plan. There is a small risk of depleting the retiree’s funds, but there is also a good chance of accumulating a buffer that can be used to manage unplanned longevity risk or left as a bequest. Journal: North American Actuarial Journal Pages: 447-468 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1570469 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1570469 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:447-468 Template-Type: ReDIF-Article 1.0 Author-Name: Iqbal Owadally Author-X-Name-First: Iqbal Author-X-Name-Last: Owadally Author-Name: Feng Zhou Author-X-Name-First: Feng Author-X-Name-Last: Zhou Author-Name: Rasaq Otunba Author-X-Name-First: Rasaq Author-X-Name-Last: Otunba Author-Name: Jessica Lin Author-X-Name-First: Jessica Author-X-Name-Last: Lin Author-Name: Douglas Wright Author-X-Name-First: Douglas Author-X-Name-Last: Wright Title: Time Series Data Mining with an Application to the Measurement of Underwriting Cycles Abstract: Underwriting cycles are believed to pose a risk management challenge to property-casualty insurers. The classical statistical methods that are used to model these cycles and to estimate their length assume linearity and give inconclusive results. Instead, we propose to use novel time series data Mining algorithms to detect and estimate periodicity on U.S. property-casualty insurance markets. These algorithms are in increasing use in data science and are applied to Big Data. We describe several such algorithms and focus on two periodicity detection schemes. Estimates of cycle periods on industry-wide loss ratios, for all lines combined and for four specific lines, are provided. One of the methods appears to be robust to trends and to outliers. Journal: North American Actuarial Journal Pages: 469-484 Issue: 3 Volume: 23 Year: 2019 Month: 7 X-DOI: 10.1080/10920277.2019.1570468 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1570468 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:3:p:469-484 Template-Type: ReDIF-Article 1.0 Author-Name: Jeremy Gold Author-X-Name-First: Jeremy Author-X-Name-Last: Gold Title: Retirement Benefits, Economics and Accounting: Moral Hazard and Frail Benefit Designs Abstract: This paper uses economic principles to analyze alternative recognition schemes for end-of-period retirement plan liabilities; the candidates, using U.S. nomenclature, are the vested benefit obligation (VBO), the accumulated benefit obligation (ABO) and the projected benefit obligation (PBO).In competitive employment markets with rational contracting we are unable to justify projected costing (PBO-based) for typical pay-related defined benefit plans. Projected costing misrepresents the economic obligations incurred by shareholders and invites moral hazard.Employee exposure to moral hazard may be minimized by exit costing (VBO-based) which recognizes only those benefits to which an exiting employee is entitled under the explicit benefit contract. But exit costing may not fully inform shareholders about the obligations that they have incurred under implicit contracts that extend beyond the plan document. Accrued costing (represented in the United States by the ABO) may better measure shareholders’ economic commitments.Small differences between the ABO and the VBO may measure a human capital asset incented by delayed vesting and benefit eligibility. Large differences are a marker for frail benefit design and potential moral hazard.Moral hazard options exercised by employers disappoint employees and may lead to unwelcome ex-post results-oriented repairs imposed by legislators, regulators and courts. Journal: North American Actuarial Journal Pages: 88-111 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596186 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596186 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:88-111 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Petertil Author-X-Name-First: Jeffrey Author-X-Name-Last: Petertil Title: Measuring Terminable Postretirement Obligations Abstract: New approaches are needed to value benefit plans subject to unilateral changes or termination. The paper focuses on postretirement health benefits, but the thesis may be relevant to any flow not guaranteed by law or accumulating funds.Retiree health benefits have usually been extended to participating active employees only in concert with a reserved right by the plan sponsor to control the design and, by implication, the cash flow. Over the course of the last fifteen years, this reserved extension of benefits has almost invariably led to reductions in benefits, when compared to the plan of benefits at an earlier period. In most cases, such reductions were anticipated under the circumstances that came to prevail (high health care cost increases), but were not taken into account by most of the projection and discounting methods of the time.Current actuarial and accounting methods generate present values for terminable retiree health plans that have little credibility as measures of the beneficiary’s asset or the sponsor’s liability. Improvements are needed that will expand the actuarial toolbox and provide solutions to economic and accounting problems.This paper provides a basis for discussion of assumptions that are appropriate when the plan sponsor can unilaterally and dramatically change future cash flows. The paper discusses how actuaries might best approach measurement situations where further plan reductions, or outright terminations, are to be anticipated. It introduces refinements and briefly discusses how each would fit with the usual actuarial model and how differences might affect behavior. These ideas are related to financial economics and the Bader-Gold paper “Reinventing Pension Actuarial Science.” Before concluding, the wider topic of discount rate selection is briefly addressed. Journal: North American Actuarial Journal Pages: 112-119 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596187 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596187 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:112-119 Template-Type: ReDIF-Article 1.0 Author-Name: Shane Whelan Author-X-Name-First: Shane Author-X-Name-Last: Whelan Title: “Equity Risk Premium: Expectations Great and Small,” Richard A. Derrig and Elisha D. Orr, January 2004 Journal: North American Actuarial Journal Pages: 120-124 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596188 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596188 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:120-124 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: “Authors’ Reply: Equity Risk Premium: Expectations Great and Small,” Richard A. Derrig and Elisha D. Orr, January 2004 - Discussion by Shane F. Whelan Journal: North American Actuarial Journal Pages: 124-126 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596189 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596189 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:124-126 Template-Type: ReDIF-Article 1.0 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Author-Name: Howard Waters Author-X-Name-First: Howard Author-X-Name-Last: Waters Author-Name: Chessman Wekwete Author-X-Name-First: Chessman Author-X-Name-Last: Wekwete Title: A Model for Coronary Heart Disease and Stroke with Applications to Critical Illness Insurance Underwriting I: The Model Abstract: In Part I we construct a model for the development of coronary heart disease (CHD) or stroke that either incorporates, or includes pathways through, the major risk factors of interest when underwriting for critical illness insurance. Our main purpose is to develop a model that could be used to assess the impact on insurance underwriting of genetic information relevant to CHD and/or stroke. Our model is parameterized using data from the Framingham Heart Study in the United States. In Part II we extend this model to include other critical illnesses, for example, cancers and kidney failure, and describe some applications of the model. Journal: North American Actuarial Journal Pages: 13-40 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596182 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596182 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:13-40 Template-Type: ReDIF-Article 1.0 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Author-Name: Howard Waters Author-X-Name-First: Howard Author-X-Name-Last: Waters Author-Name: Chessman Wekwete Author-X-Name-First: Chessman Author-X-Name-Last: Wekwete Title: A Model for Coronary Heart Disease and Stroke with Applications to Critical Illness Insurance Underwriting II: Applications Abstract: In Part I we constructed a model for the development of coronary heart disease (CHD) or stroke that either incorporates, or includes pathways through, the major risk factors of interest when underwriting for critical illness (CI) insurance. In Part II we extend this model to include other critical illnesses, for example, cancers and kidney failure, and describe some applications of the model. In particular, we discuss CI premium ratings for applicants with combinations of some or all of high body mass index, smoking, high blood pressure, high cholesterol, and diabetes. We also consider the possible effect on CI premium ratings of genetic conditions that increase the likelihood of high blood pressure, high cholesterol, diabetes, CHD event, or stroke. Journal: North American Actuarial Journal Pages: 41-56 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596183 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596183 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:41-56 Template-Type: ReDIF-Article 1.0 Author-Name: Kristen Moore Author-X-Name-First: Kristen Author-X-Name-Last: Moore Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Optimal Design of a Perpetual Equity-Indexed Annuity Abstract: We find the participation rate, guaranteed death benefit, guaranteed surrender benefit, and initial and maintenance fees that most appeal to a buyer of a perpetual equity-indexed annuity (EIA) from the standpoint of maximizing the buyer’s expected discounted utility of wealth at death, also called bequest, while still allowing the issuer of the EIA to (at least) break even on the basis of the expected discounted value of the issuer’s payout. In calculating the buyer’s expected utility, we use the physical probability faced by the buyer. However, in calculating the expected value of the issuer’s payout, we use a type of risk-neutral probability by assuming that the issuer sells many independent policies. We demonstrate our method with an illustrative numerical example. Journal: North American Actuarial Journal Pages: 57-72 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596184 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596184 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:57-72 Template-Type: ReDIF-Article 1.0 Author-Name: Jeremy Gold Author-X-Name-First: Jeremy Author-X-Name-Last: Gold Title: The Times They are a-Changin’ Journal: North American Actuarial Journal Pages: iii-vi Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596193 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596193 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:iii-vi Template-Type: ReDIF-Article 1.0 Author-Name: C. Jon Exley Author-X-Name-First: C. Author-X-Name-Last: Jon Exley Title: Pension Funds and the U.K. Economy Abstract: The paper considers the impact of U.K. defined benefit (DB) pension plan unding and investment on the U.K. economy. It suggests that many conventional theories are based on incomplete or inconsistent economics. In particular, the author suggests that:• An economy cannot really gain competitive advantage from high returns on the domestic assets in which pension funds invest.• DB liabilities are essentially similar for most schemes and can be closely matched with bonds.• Funding pension liabilities has no primary impact on individuals’ consumption and saving or on firms’ capital investment.• Pension funds are not natural investors in the equity of new ventures.The conclusion of the paper is that the most significant impact of pension funds on the U.K. economy relates to the costs imposed by extreme mismatching between their financial assets and liabilities. The author argues that such risks can, in essence, “crowd out” entrepreneurial risk. He asserts that the U.K. economy would gain from greater focus on the matching of these assets and liabilities, and that the best way to stimulate enterprise is by eliminating the frictional costs in the economy arising from current practices. Journal: North American Actuarial Journal Pages: 73-87 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596185 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596185 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:73-87 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Title: “Further Analysis of Future Canadian Health Care Costs,” Robert L. Brown and Uma Suresh, April 2004 Journal: North American Actuarial Journal Pages: 126-127 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596190 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596190 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:126-127 Template-Type: ReDIF-Article 1.0 Author-Name: Timothy Ross Author-X-Name-First: Timothy Author-X-Name-Last: Ross Title: “Disruption of a Managed Competition Environment by Low-Ball Premium Bids: The Minnesota State Employees Group Insurance Program,” Harry Sutton, Roger Feldman, and Bryan Dowd, April 2004 Journal: North American Actuarial Journal Pages: 128-128 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596192 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596192 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:128a-128a Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Title: “A Note on the Myers and Read Capital Allocation Formula” Stephen J. Mildenhall, April 2004 Journal: North American Actuarial Journal Pages: 128-128 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596191 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596191 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:128-128 Template-Type: ReDIF-Article 1.0 Author-Name: Gilbert Fellingham Author-X-Name-First: Gilbert Author-X-Name-Last: Fellingham Author-Name: H. Dennis Tolley Author-X-Name-First: H. Author-X-Name-Last: Dennis Tolley Author-Name: Thomas Herzog Author-X-Name-First: Thomas Author-X-Name-Last: Herzog Title: Comparing Credibility Estimates of Health Insurance Claims Costs Abstract: We fit a linear mixed model and a Bayesian hierarchical model to data provided by an insurance company located in the Midwest. We used models fit to the 1994 data to predict health insurance claims costs for 1995. We implemented the linear mixed model in SAS and used two different prediction methods to predict 1995 costs. In the linear mixed model we assumed a normal likelihood. In the hierarchical Bayes model, we used Markov chain Monte Carlo methods to obtain posterior distributions of the parameters, as well as predictive distributions of the next year’s costs. We assumed the likelihood for this model to be a mixture of a gamma distribution for the nonzero costs, with a point mass for the zero costs. All prediction methods use credibility-type estimators that use relevant information from related experience. The linear mixed model was heavily influenced by the skewed nature of the data. The assumed gamma likelihood of the full Bayesian analysis appeared to underestimate the tails of the distributions. All prediction models underestimated costs for 1995. Journal: North American Actuarial Journal Pages: 1-12 Issue: 1 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596181 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596181 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:1-12 Template-Type: ReDIF-Article 1.0 Author-Name: Godfrey Perrott Author-X-Name-First: Godfrey Author-X-Name-Last: Perrott Author-Name: William Hines Author-X-Name-First: William Author-X-Name-Last: Hines Title: Fair Value Accounting Compared to Other Accounting Systems Abstract: It is well known that the total profit generated from an insurance product is fixed (unless the accounting system affects the product management), but the incidence of reported profit varies depending on the accounting system used and the way that assumptions are set and reset. The purpose of this paper is to take a very simple product (a single-premium deferred annuity (SPDA) with no special features) and follow its earnings over a 15-year period. We will examine the volatility of earnings under Fair Value (FV) accounting as proposed by the International Accounting Standards Committee (IASC), as we understand it, and U.S. GAAP and U.S. Statutory accounting. Additionally, we will examine how each of the accounting systems is impacted by the choice of a lapse assumption. We have the additional objective of simplicity, to produce a model that the reader can relate to and whose calculations can be reproduced with nominal effort. Journal: North American Actuarial Journal Pages: 62-87 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596029 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596029 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:62-87 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: The Coming Revolution in Insurance Accounting Abstract: This paper briefly examines some trends that could affect future financial reporting for insurance companies and will explore some of the fundamental issues being discussed. Topics covered include: what needs to be fixed at the national and international level, the factors that contribute to the changes, evaluation of a new or enhanced financial reporting system, and the big issues in financial reporting of insurance. Journal: North American Actuarial Journal Pages: 1-11 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596026 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596026 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:1-11 Template-Type: ReDIF-Article 1.0 Author-Name: Edward (Jed) Frees Author-X-Name-First: Edward Author-X-Name-Last: (Jed) Frees Title: Continuing a Tradition Journal: North American Actuarial Journal Pages: iii-iii Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596038 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596038 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: “Author’s Reply: A Regime-Switching Model of Long-Term Stock Returns” by Mary Hardy, April 2001 - Discussion by Gordon E. Klein Journal: North American Actuarial Journal Pages: 173-176 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596037 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596037 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:173-176 Template-Type: ReDIF-Article 1.0 Author-Name: Marsha Wallace Author-X-Name-First: Marsha Author-X-Name-Last: Wallace Title: Performance Reporting under Fair Value Accounting Abstract: This paper compares performance measurement under fair value accounting vs. U.S. GAAP accounting. As illustrated in the paper, the main difference between fair value accounting and U.S. GAAP accounting lies in the treatment of gains and losses on both assets and liabilities. Fair value accounting would report all gains and losses on both assets and liabilities in the period in which they arise. U.S. GAAP on the other hand, recognizes gains and losses over the life of the block of business (or at the time of a transaction). When net gains and losses on assets and liabilities are immaterial, the pattern of earnings under both systems can be quite similar. However, If a company is generating significant gains or losses on its net book of business (such as in the case of an asset/liability mismatch), fair value accounting will reveal this much sooner than U.S. GAAP. When the full impact of its actions (including gains and losses) is reported in the current period, management is in a better position to understand how the value of the company is changing and adjust its decisions accordingly. This is one of the main reasons for moving to a fair value system and is expected to be a major benefit if fair value accounting is ultimately adopted. Journal: North American Actuarial Journal Pages: 28-61 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596028 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596028 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:28-61 Template-Type: ReDIF-Article 1.0 Author-Name: Gordon Klein Author-X-Name-First: Gordon Author-X-Name-Last: Klein Title: “A Regime-Switching Model of Long-Term Stock Returns” by Mary Hardy, April 2001 Journal: North American Actuarial Journal Pages: 171-173 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596036 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596036 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:171-173 Template-Type: ReDIF-Article 1.0 Author-Name: David Babbel Author-X-Name-First: David Author-X-Name-Last: Babbel Author-Name: Jeremy Gold Author-X-Name-First: Jeremy Author-X-Name-Last: Gold Author-Name: Craig Merrill Author-X-Name-First: Craig Author-X-Name-Last: Merrill Title: Fair Value of Liabilities: The Financial Economics Perspective Abstract: In this paper we present the fundamental approaches of financial economics to valuation. Three methods are demonstrated by which financial economists account for risk. We illustrate how these methods relate to one another and how they can be applied in the valuation of risky corporate bonds, guaranteed investment contracts (GICs) with and without interest rate contingencies, and whole life insurance. Next, we discuss how these models treat orthogonal risks, such as the kind often covered by insurance contracts. Demand side and supply side diversification are treated, and liquidity risk is then considered. We conclude with a summary of the benefits of decomposition and transparency. Journal: North American Actuarial Journal Pages: 12-27 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596027 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596027 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:12-27 Template-Type: ReDIF-Article 1.0 Author-Name: Heekyung Youn Author-X-Name-First: Heekyung Author-X-Name-Last: Youn Author-Name: Arkady Shemyakin Author-X-Name-First: Arkady Author-X-Name-Last: Shemyakin Author-Name: Edwin Herman Author-X-Name-First: Edwin Author-X-Name-Last: Herman Title: A Re-Examination of the Joint Mortality Functions Abstract: Mortality analysis involving multiple lives is easily one of the more complicated aspects in the theory of life contingencies. In this paper, we re-investigate joint mortality functions and in particular, we examine an assertion that relates the joint-life and last-survivor random variables. This common assertion states that the sum of the lifetimes of the joint-life and the last-survivor statuses is equal to the sum of the lifetimes of the single statuses. However, we show that this assertion is not precisely correct. We therefore offer a modification to the statuses definitions so that this common assertion holds. Journal: North American Actuarial Journal Pages: 166-170 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596035 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596035 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:166-170 Template-Type: ReDIF-Article 1.0 Author-Name: M. Zaki Khorasanee Author-X-Name-First: M. Author-X-Name-Last: Zaki Khorasanee Title: A Cash-Flow Approach to Pension Funding Abstract: The problem of how to fund a defined-benefit pension plan is detached from the problem of how the cost of such a plan should be recognized. An approach to funding based on the projection of aggregate cash flows and the explicit modeling of new entrants is presented. It is shown that commonly used funding methods can be derived from the cash-flow approach. A generalized funding method for a plan subject to a stationary distribution of new entrants is derived. It is concluded that plan actuaries might need to modify existing funding methods to incorporate useful information about the expected number and distribution of future entrants. Journal: North American Actuarial Journal Pages: 137-165 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596034 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596034 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:137-165 Template-Type: ReDIF-Article 1.0 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: Implementation of Four Models for Outstanding Liabilities in Winbugs: A Discussion of a Paper by Ntzoufras and Dellaportas Abstract: Ntzoufras and Dellaportas (2002) described four models for outstanding claim amounts of the “reported but not settled” variety. Two of the models incorporated claim-counts data in addition to the claim amounts themselves in order to add a hierarchical stage in the usual log-normal and state-space models. The purpose of this discussion is to describe how the models presented in Ntzoufras and Dellaportas may be implemented using WinBUGS. The use of WinBUGS to implement the Bayesian analysis of a number of other actuarial models was considered by Scollnik (2001). Journal: North American Actuarial Journal Pages: 128-136 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596033 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596033 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:128-136 Template-Type: ReDIF-Article 1.0 Author-Name: Ioannis Ntzoufras Author-X-Name-First: Ioannis Author-X-Name-Last: Ntzoufras Author-Name: Petros Dellaportas Author-X-Name-First: Petros Author-X-Name-Last: Dellaportas Title: Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty Abstract: This paper deals with the prediction of the amount of outstanding automobile claims that an insurance company will pay in the near future. We consider various competing models using Bayesian theory and Markov chain Monte Carlo methods. Claim counts are used to add a further hierarchical stage in the model with log-normally distributed claim amounts and its corresponding state space version. This way, we incorporate information from both the outstanding claim amounts and counts data resulting in new model formulations. Implementation details and illustrations with real insurance data are provided. Journal: North American Actuarial Journal Pages: 113-125 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596032 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596032 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:113-125 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Wong Author-X-Name-First: Johnny Author-X-Name-Last: Wong Title: A Comparison of Solvency Requirements and Early Warning Systems for Life Insurance Companies in China With Representative World Practices Abstract: The People’s Republic of China has experienced substantial growth in insurance demand over the last decade. However, development of the related laws and regulations has not kept pace with the development of the insurance industry there. This paper reports on a pioneering study comparing different statutory reserve, solvency, and early warning systems in a sample of countries and regions in three of the world’s important economic regions–Asia, North America, and Europe. It begins with the construction of a model office applicable to the People’s Republic of China’s regulatory framework and unique market environment. Reserve standards and solvency measurement systems in different supervisory frameworks then are applied to the model office. The results are analyzed as a comparative study of the People’s Republic of China’s total assets required for the reserves and solvency margins under the practices of other jurisdictions. Early warning systems also are discussed. Journal: North American Actuarial Journal Pages: 91-112 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596031 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596031 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:91-112 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Freedman Author-X-Name-First: Mark Author-X-Name-Last: Freedman Title: “Fair Value Accounting Compared to Other Accounting Systems”, Godfrey Perrott and William Hines, January 2002 Journal: North American Actuarial Journal Pages: 87-90 Issue: 1 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596030 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596030 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:1:p:87-90 Template-Type: ReDIF-Article 1.0 Author-Name: Moshe Milevsky Author-X-Name-First: Moshe Author-X-Name-Last: Milevsky Author-Name: Chris Robinson Author-X-Name-First: Chris Author-X-Name-Last: Robinson Title: Self-Annuitization and Ruin in Retirement Abstract: At retirement, most individuals face a choice between voluntary annuitization and discretionary management of assets with systematic withdrawals for consumption purposes. Annuitization–buying a life annuity from an insurance company–assures a lifelong consumption stream that cannot be outlived, but it is at the expense of a complete loss of liquidity. On the other hand, discretionary management and consumption from assets–self-annuitization–preserves flexibility but with the distinct risk that a constant standard of living will not be maintainable.In this paper we compute the lifetime and eventual probability of ruin (PoR) for an individual who wishes to consume a fixed periodic amount–a self-constructed annuity–from an initial endowment invested in a portfolio earning a stochastic (lognormal) rate of return. The lifetime PoR is the probability that net wealth will hit zero prior to a stochastic date of death. The eventual PoR is the probability that net wealth will ever hit zero for an infinitely lived individual.We demonstrate that the probability of ruin can be represented as the probability that the stochastic present value (SPV) of consumption is greater than the initial investable wealth. The lifetime and eventual probabilities of ruin are then obtained by evaluating one minus the cumulative density function of the SPV at the initial wealth level. In that eventual case, we offer a precise analytical solution because the SPV is known to be a reciprocal gamma distribution. For the lifetime case, using the Gompertz law of mortality, we provide two approximations. Both involve “moment matching” techniques that are motivated by results in Arithmetic Asian option pricing theory. We verify the accuracy of these approximations using Monte Carlo simulations. Finally, a numerical case study is provided using Canadian mortality and capital market parameters. It appears that the lifetime probability of ruin–for a consumption rate that is equal to the life annuity payout–is at its lowest with a well-diversified portfolio. Journal: North American Actuarial Journal Pages: 112-124 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595940 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595940 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:112-124 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Warshawsky Author-X-Name-First: Mark Author-X-Name-Last: Warshawsky Title: “Self-Annuitization and Ruin in Retirement”, Moshe Arye Milevsky and Chris Robinson, October 2000 Journal: North American Actuarial Journal Pages: 127-129 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595943 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595943 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:127-129 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Pokorski Author-X-Name-First: Robert Author-X-Name-Last: Pokorski Author-Name: Ulrike Ohlmer Author-X-Name-First: Ulrike Author-X-Name-Last: Ohlmer Title: Use of a Markov Model to Estimate Long-Term Insured Lives’ Mortality Risk Associated With BRCA1 and BRCA2 Gene Mutations Abstract: There is uncertainty regarding the degree of insurance risk associated with BRCA1/2, the gene mutations associated with breast cancer. Most reports to date have been based on high-risk populations selected from families with multiple and/or early-onset cancers; more favorable data have been reported in studies without this selection bias.This paper discusses use of a Markov model to estimate mortality risk associated with BRCA1/2 gene mutations in female life insurance applicants. The goal is to derive a range of risk estimates based on different assumptions of breast and ovarian cancer incidence. A particular strength of the model is that transition probabilities after cancer diagnosis vary with age and cancer stage, as do excess hazard rates.Data calculated by the model indicate that no single mortality curve characterizes risk for all life insurance applicants with a BRCA1/2 mutation. Rather, mortality risk depends on breast and ovarian cancer incidence rates and subsequent mortality rates, and on the method used to deal with competing breast and ovarian cancer incidence and mortality rates. Further refinement of risk estimates will depend on better incidence data and on resolution of complex statistical problems, such as informative censoring.Widespread use of genetic information by insurance consumers could have important economic implications. For companies that sell individually underwritten products, profitability might decrease. Consumers might find higher prices and reduced availability, with a corresponding decrease in quantity of insurance purchased. Insurance and consumer ramifications would vary by cover, with living-benefit products, such as critical-illness insurance, most adversely affected. Societal choices are limited. Given assumptions in the cited scenario, it is likely premiums would rise and quantity of insurance purchased would decrease even with no change in existing social policy; attempted legal or regulatory remedies would further accentuate price increases and reductions in quantity purchased. Journal: North American Actuarial Journal Pages: 130-148 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595944 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595944 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:130-148 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Author-Name: Rob Kaas Author-X-Name-First: Rob Author-X-Name-Last: Kaas Title: “Self-Annuitization and Ruin in Retirement”, Moshe Arye Milevsky and Chris Robinson, October 2000 Journal: North American Actuarial Journal Pages: 124-126 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595941 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595941 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:124-126 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Brown Author-X-Name-First: Jeffrey Author-X-Name-Last: Brown Title: “Self-Annuitization and Ruin in Retirement”, Moshe Arye Milevsky and Chris Robinson, October 2000 Journal: North American Actuarial Journal Pages: 126-127 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595942 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595942 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:126-127 Template-Type: ReDIF-Article 1.0 Author-Name: Tiong Serena Author-X-Name-First: Tiong Author-X-Name-Last: Serena Title: Author’s Reply: Valuing Equity-Indexed Annuities - Discussion by G. Thomas Mitchell; Hans U. Gerber; Elias S. W. Shiu Journal: North American Actuarial Journal Pages: 169-170 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595948 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595948 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:169-170 Template-Type: ReDIF-Article 1.0 Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Title: Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution Abstract: Estimation of the tail index parameter of a single-parameter Pareto model has wide application in actuarial and other sciences. Here we examine various estimators from the standpoint of two competing criteria: efficiency and robustness against upper outliers. With the maximum likelihood estimator (MLE) being efficient but nonrobust, we desire alternative estimators that retain a relatively high degree of efficiency while also being adequately robust. A new generalized median type estimator is introduced and compared with the MLE and several well-established estimators associated with the methods of moments, trimming, least squares, quantiles, and percentile matching. The method of moments and least squares estimators are found to be relatively deficient with respect to both criteria and should become disfavored, while the trimmed mean and generalized median estimators tend to dominate the other competitors. The generalized median type performs best overall. These findings provide a basis for revision and updating of prevailing viewpoints. Other topics discussed are applications to robust estimation of upper quantiles, tail probabilities, and actuarial quantities, such as stop-loss and excess-of-loss reinsurance premiums that arise concerning solvency of portfolios. Robust parametric methods are compared with empirical nonparametric methods, which are typically nonrobust. Journal: North American Actuarial Journal Pages: 12-27 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595935 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595935 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:12-27 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Valuing Equity-Indexed Annuities”, Serena Tiong, October 2000 Journal: North American Actuarial Journal Pages: 164-169 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595947 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595947 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:164-169 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Beal Author-X-Name-First: Robert Author-X-Name-Last: Beal Title: Bridging the Gap Between Roe and IRR Abstract: Internal rate of return (IRR) measures the level annual return over the life of an investment, whereas return on equity (ROE) measures the return over each accounting period. This paper develops the relationships between IRR and ROE by presenting and proving four algebraic theorems involving IRR and ROE. These theorems are developed using generic investment terminology that does not rely on any specific accounting basis. The relationships are then expressed using U.S. statutory and GAAP terminology. The paper demonstrates that IRR is not just a statutory concept and ROE is not just a GAAP concept. Financial projections for a hypothetical insurance product illustrate these relationships. Journal: North American Actuarial Journal Pages: 1-11 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595934 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595934 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:1-11 Template-Type: ReDIF-Article 1.0 Author-Name: Maria Bruno Author-X-Name-First: Maria Author-X-Name-Last: Bruno Author-Name: Emanuela Camerini Author-X-Name-First: Emanuela Author-X-Name-Last: Camerini Author-Name: Alvaro Tomassetti Author-X-Name-First: Alvaro Author-X-Name-Last: Tomassetti Title: Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates Abstract: We refer to a recent paper by G. Parker (1997) in which the risk of a portfolio of life insurance policies (namely the risk related to the entire contractual life) is studied by separating the demographic component from the financial component. In our paper, after making a brief summary of Parker’s model, we propose two additional contributions:We first give the problem a different formalization, thus allowing a portfolio risk analysis by management periods and a study of the risk due to the interactions among years;We elaborate on a powerful and flexible algorithm for calculating the probability distribution of the sum of random variables that proves useful to solve not only the problems discussed in this paper concerning the risk analysis but also various other problems.In the paper, we also show, for both contributions, some applications made under the same financial and demographic assumptions taken by Parker; we also compare our results with Parker’s results. Journal: North American Actuarial Journal Pages: 44-55 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595937 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595937 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:44-55 Template-Type: ReDIF-Article 1.0 Author-Name: G. Thomas Mitchell Author-X-Name-First: G. Thomas Author-X-Name-Last: Mitchell Title: “Valuing Equity-Indexed Annuities”, Serena Tiong, October 2000 Journal: North American Actuarial Journal Pages: 163-164 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595946 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595946 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:163-164 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Robin Damm Author-X-Name-First: Robin Author-X-Name-Last: Damm Author-Name: Ishmael Sharara Author-X-Name-First: Ishmael Author-X-Name-Last: Sharara Title: Including Homemakers in Social Security Abstract: For some time, many people have felt that homemaking and/or childcare duties should be classified as “work,” and as such, these people should be included in social security systems. This paper analyzes the current provision for homemakers in the Canada and Québec Pension Plans (C/QPP), along with three other methods aimed at improving C/QPP benefits for homemakers. It concludes that splitting incomes between married couples on a voluntary basis has several desirable characteristics. However, due to a reduction in income taxes payable, the Canadian government(s) would likely reject this approach. To analyze further alternatives, the paper also reviews a study presented by the U.S. Subcommittee on Social Security that looked at various earnings sharing schemes within the Old Age, Survivors and Disability Insurance (OASDI) scheme. Due to the complexity of OASDI, it would not be possible to modify benefits for homemakers without affecting other groups (such as divorced persons and widow(er)s). As such, the subcommittee had several standards for analyzing any potential modifications to OASDI. However, none of the plans presented ccomplished all of the goals set out by the subcommittee. In addition, there would be vast administrative difficulties associated with implementing any of the earnings sharing schemes. Even if these problems could be overcome, the two national security systems are very different, so proposed solutions under the U.S. system might not be appropriate to the Canadian system. Journal: North American Actuarial Journal Pages: 28-43 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595936 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595936 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:28-43 Template-Type: ReDIF-Article 1.0 Author-Name: Serena Tiong Author-X-Name-First: Serena Author-X-Name-Last: Tiong Title: Valuing Equity-Indexed Annuities Abstract: Equity-indexed annuities have generated a great deal of interest and excitement among both insurers and their customers since they were first introduced to the marketplace in early 1995. Because of the embedded options in these products, the insurers are presented with some challenging mathematical problems when it comes to the pricing and management of equity indexed annuities. This paper explores the pricing aspect of three of the most common product designs: the point-to-point, the cliquet, and the lookback. Based on certain assumptions, we are able to present the pricing formulas in closed form for the three product designs. The method of Esscher transforms is the fundamental tool for pricing such deferred annuities. Journal: North American Actuarial Journal Pages: 149-163 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595945 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595945 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:149-163 Template-Type: ReDIF-Article 1.0 Author-Name: Barbara Kalben Author-X-Name-First: Barbara Author-X-Name-Last: Kalben Title: Why Men Die Younger Abstract: It is generally accepted that, on average, women live longer than men. Few, however, are aware that there is an underlying and consistent pattern of factors contributing to the sex mortality differential. This paper attempts to synthesize the evidence supporting and refuting the hypotheses for the sex mortality differential. The extent of the sex mortality differential is examined. It has existed since at least 1750; it occurs at all age groups, even prenatally, in nearly all animal species studied and for almost every major cause of death. Evidence supports both the biological/genetic and the social/cultural/environmental/behavioral schools of hypotheses, as well as interactions between the two, but the determining component may revolve around the differing chromosomes and hormones between the sexes. Behavioral distinctions, especially cigarette smoking, also affect the sex mortality differential. Journal: North American Actuarial Journal Pages: 83-111 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595939 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595939 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:83-111 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Author-Name: Hal Pedersen Author-X-Name-First: Hal Author-X-Name-Last: Pedersen Title: Catastrophe Risk Bonds Abstract: This article examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore, the pricing of catastrophe risk bonds requires an incomplete markets setting, and this creates special difficulties in the pricing methodology. The authors briefly discuss the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities. Journal: North American Actuarial Journal Pages: 56-82 Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595938 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595938 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:56-82 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: Switching Regimes Journal: North American Actuarial Journal Pages: iii-iv Issue: 4 Volume: 4 Year: 2000 X-DOI: 10.1080/10920277.2000.10595949 File-URL: http://hdl.handle.net/10.1080/10920277.2000.10595949 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:4:y:2000:i:4:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: Zhiwei Zhu Author-X-Name-First: Zhiwei Author-X-Name-Last: Zhu Author-Name: Zhi Li Author-X-Name-First: Zhi Author-X-Name-Last: Li Author-Name: David Wylde Author-X-Name-First: David Author-X-Name-Last: Wylde Author-Name: Michael Failor Author-X-Name-First: Michael Author-X-Name-Last: Failor Author-Name: George Hrischenko Author-X-Name-First: George Author-X-Name-Last: Hrischenko Title: Logistic Regression for Insured Mortality Experience Studies Abstract: Properly adapted statistical modeling methodology can be a powerful tool for coping with a broad range of challenges related to life and annuity insurance industries' experience studies. In this article, we present a logistic regression model based on U.S. insured mortality experience study with a focus on gaining study efficiency and effectiveness by addressing multiple analytical predicaments within one statistical modeling framework. These predicaments include but are not limited to (a) testing statistical significances or credibility of potential mortality drivers, (b) estimation of normalized mortality, slopes, and differentials, (c) quantification of study reliability, and (d) extrapolation for under-experienced mortality, smoothing between select and ultimate estimations, and development of basic experience tables. Journal: North American Actuarial Journal Pages: 241-255 Issue: 4 Volume: 19 Year: 2015 Month: 10 X-DOI: 10.1080/10920277.2015.1039135 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1039135 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:4:p:241-255 Template-Type: ReDIF-Article 1.0 Author-Name: Xudong Zeng Author-X-Name-First: Xudong Author-X-Name-Last: Zeng Author-Name: Yuling Wang Author-X-Name-First: Yuling Author-X-Name-Last: Wang Author-Name: James M. Carson Author-X-Name-First: James M. Author-X-Name-Last: Carson Title: Dynamic Portfolio Choice with Stochastic Wage and Life Insurance Abstract: We study optimal insurance, consumption, and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing constant absolute risk aversion utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance decision is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses life insurance and investment portfolio choice to hedge stochastic wage risk. Journal: North American Actuarial Journal Pages: 256-272 Issue: 4 Volume: 19 Year: 2015 Month: 10 X-DOI: 10.1080/10920277.2015.1041987 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1041987 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:4:p:256-272 Template-Type: ReDIF-Article 1.0 Author-Name: Els Godecharle Author-X-Name-First: Els Author-X-Name-Last: Godecharle Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Title: Reserving by Conditioning on Markers of Individual Claims: A Case Study Using Historical Simulation Abstract: This article explores the use of claim specific characteristics, so-called claim markers, for loss reserving with individual claims. Starting from the approach of Rosenlund and using the technique of historical simulation we develop a stochastic Reserve by Detailed Conditioning method that is applicable to a microlevel data set with detailed information on individual claims. We construct the predictive distribution of the outstanding loss reserve by simulating future payments of a claim, given its claim markers. We demonstrate the performance of the method on a portfolio of general liability insurance policies for private individuals from a European insurance company. Hereby we explore how to incorporate different kinds of claim markers and evaluate the impact of the set of markers and their specification on the predictive distribution of the outstanding reserve. Journal: North American Actuarial Journal Pages: 273-288 Issue: 4 Volume: 19 Year: 2015 Month: 10 X-DOI: 10.1080/10920277.2015.1046607 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1046607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:4:p:273-288 Template-Type: ReDIF-Article 1.0 Author-Name: Jimmy Poon Author-X-Name-First: Jimmy Author-X-Name-Last: Poon Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Title: A Spatial Cross-Sectional Credibility Model with Dependence Among Risks Abstract: A Bühlmann-Straub type credibility model with dependence structure among risk parameters and conditional spatial cross-sectional dependence is studied. Predictors of future losses for the model under both types of dependence are derived by minimizing the expected quadratic loss function, and nonparametric estimators of structural parameters are considered in the spatial statistics context. Predictions and estimations made for the proposed model are examined and compared to other models in an application with crop insurance data and in a simulation study. Journal: North American Actuarial Journal Pages: 289-310 Issue: 4 Volume: 19 Year: 2015 Month: 10 X-DOI: 10.1080/10920277.2015.1063441 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1063441 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:4:p:289-310 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoqiang Cai Author-X-Name-First: Xiaoqiang Author-X-Name-Last: Cai Author-Name: Limin Wen Author-X-Name-First: Limin Author-X-Name-Last: Wen Author-Name: Xianyi Wu Author-X-Name-First: Xianyi Author-X-Name-Last: Wu Author-Name: Xian Zhou Author-X-Name-First: Xian Author-X-Name-Last: Zhou Title: Credibility Estimation of Distribution Functions with Applications to Experience Rating in General Insurance Abstract: This article presents a new credibility estimation of the probability distributions of risks under Bayes settings in a completely nonparametric framework. In contrast to the Ferguson's Bayesian nonparametric method, it does not need to specify a mathematical form of the prior distribution (such as a Dirichlet process). We then show the applications of the method in general insurance premium pricing, a procedure commonly known as experience rating, which utilizes the insured's claim experience to calculate a proper premium under a given premium principle (referred to as a risk measure). As this method estimates the probability distributions of losses, not just the means and variances, it provides a unified nonparametric framework to experience rating for arbitrary premium principles. This encompasses the advantages of the well-known Bühlmann's and Ferguson's approaches, while it overcomes their drawbacks. We first establish a linear Bayes method and prove its strong consistency in nonparametric settings that require only knowledge of the first two moments of the loss distributions considered as a stochastic process. Then an empirical Bayes method is developed for the more general situation where a portfolio of risks is observed but no knowledge is available or assumed on their loss and prior distributions, including their moments. It is shown to be asymptotically optimal. The performance of our estimates in comparison with traditional methods is also evaluated through theoretical analysis and numerical studies, which show that our approach produces premium estimates close to the optima. Journal: North American Actuarial Journal Pages: 311-335 Issue: 4 Volume: 19 Year: 2015 Month: 10 X-DOI: 10.1080/10920277.2015.1057649 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1057649 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:4:p:311-335 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board EOV Journal: North American Actuarial Journal Pages: ebi-ebi Issue: 4 Volume: 19 Year: 2015 Month: 10 X-DOI: 10.1080/10920277.2015.1117845 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1117845 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:19:y:2015:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Empirical Estimation of Risk Measures and Related Quantities - Discussion by Vytaras Brazauskas; Thomas Kaiser Journal: North American Actuarial Journal Pages: 117-118 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596156 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:117-118 Template-Type: ReDIF-Article 1.0 Author-Name: Marsha Wallace Author-X-Name-First: Marsha Author-X-Name-Last: Wallace Title: “Credit Standing and the Fair Value of Liabilities: A Critique,” by Philip Heckman, January 2004 Journal: North American Actuarial Journal Pages: 125-129 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596161 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596161 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:125-129 Template-Type: ReDIF-Article 1.0 Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Author-Name: Thomas Kaiser Author-X-Name-First: Thomas Author-X-Name-Last: Kaiser Title: “Empirical Estimation of Risk Measures and Related Quantities,” Bruce L. Jones and Ricǎrdas Zitikis, October 2003 Journal: North American Actuarial Journal Pages: 114-117 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596155 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596155 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:114-117 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Valuation of Equity-Indexed Annuities under Stochastic Interest Rates - Discussion by Mark D. J. Evans Journal: North American Actuarial Journal Pages: 124-125 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596160 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596160 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:124-125 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Response to Author: Credit Standing and the Fair Value of Liabilities: A Critique by Philip Heckman, January 2004 Journal: North American Actuarial Journal Pages: 131-132 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596163 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596163 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:131-132 Template-Type: ReDIF-Article 1.0 Author-Name: John Ralfe Author-X-Name-First: John Author-X-Name-Last: Ralfe Author-Name: Cliff Speed Author-X-Name-First: Cliff Author-X-Name-Last: Speed Author-Name: Jon Palin Author-X-Name-First: Jon Author-X-Name-Last: Palin Title: Pensions and Capital Structure Abstract: This paper considers the pension plan as part of the capital structure of the sponsoring employer. This enables lessons from financial theory concerning capital structure to be used to answer the question, “What assets should a pension fund hold?” The standard Modigliani-Miller framework is expanded on to consider the implications of corporate tax. This leads to the conclusion that bond investment for pension plans has tangible advantages over holding risky assets (e.g., equities). The paper considers a case study of the pension plan of the Boots Company, a U.K. pharmacy retailer with a pension fund of around £2.3 billion ($3.5 billion), where these ideas were put into practice. Finally, the paper discusses the value released to shareholders and the extra security members of the pension fund have derived from putting theory into practice. Journal: North American Actuarial Journal Pages: 103-113 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596154 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596154 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:103-113 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Credit Standing and the Fair Value of Liabilities: A Critique - Discussion by Marsha Wallace Journal: North American Actuarial Journal Pages: 129-131 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596162 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596162 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:129-131 Template-Type: ReDIF-Article 1.0 Author-Name: Tony Day Author-X-Name-First: Tony Author-X-Name-Last: Day Title: Financial Economics and Actuarial Practice Abstract: Starting in the United Kingdom and continuing through the U.S. and Canadian actuarial professions, proponents of financial economics have been forcefully promoting a review of traditional actuarial practices and training. In particular, the financial theories first proposed by Modigliani and Miller and subsequently developed by others have been used to highlight serious weaknesses in typical actuarial thinking. In summary, it is claimed that much actuarial advice wrongly specifies value, that guidelines and standards need radical revision, and that traditional actuarial intuition suffers in comparison to newer modes of thought adopted by other professions.This paper examines concepts from both financial economics and actuarial science as applied to defined benefit schemes using a simple discounted cash-flow framework as a reference point. The general finding is that many standard modes of actuarial thought are, in fact, indefensible when examined with the tools and techniques of financial economics. The call for revision of actuarial training and practices is credible and necessary.However, the paper also touches upon areas where a heavy-handed application of finance theory could be misguided due to limitations in the simple financial economic models presented. It concludes that financial economics should be carefully integrated into actuarial thought rather than appended to existing actuarial theory or inserted as a wholesale replacement. Journal: North American Actuarial Journal Pages: 90-102 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596153 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596153 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:90-102 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Seydel, Rüdiger, 2003, Journal: North American Actuarial Journal Pages: 137-137 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596165 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596165 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:137-137 Template-Type: ReDIF-Article 1.0 Author-Name: R. J. Verrall Author-X-Name-First: R. J. Author-X-Name-Last: Verrall Title: A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving Abstract: This paper shows how Bayesian models within the framework of generalized linear models can be applied to claims reserving. The author demonstrates that this approach is closely related to the Bornhuetter-Ferguson technique. Benktander (1976) and Mack (2000) previously studied the Bornhuetter-Ferguson technique and advocated using credibility models. The present paper uses a Bayesian parametric model within the framework of generalized linear models. Journal: North American Actuarial Journal Pages: 67-89 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596152 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596152 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:67-89 Template-Type: ReDIF-Article 1.0 Author-Name: Frank Bensics Author-X-Name-First: Frank Author-X-Name-Last: Bensics Title: Hardy, Mary R. 2003, Journal: North American Actuarial Journal Pages: 133-136 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596164 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596164 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:133-136 Template-Type: ReDIF-Article 1.0 Author-Name: Heath Windcliff Author-X-Name-First: Heath Author-X-Name-Last: Windcliff Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Title: The 1/ Pension Investment Puzzle Abstract: This paper examines the so-called 1/n investment puzzle that has been observed in defined contribution plans whereby some participants divide their contributions equally among the available asset classes. It has been argued that this is a very naive strategy since it contradicts the fundamental tenets of modern portfolio theory. We use simple arguments to show that this behavior is perhaps less naive than it at first appears. It is well known that the optimal portfolio weights in a mean-variance setting are extremely sensitive to estimation errors, especially those in the expected returns. We show that when we account for estimation error, the 1/n rule has some advantages in terms of robustness; we demonstrate this with numerical experiments. This rule can provide a risk-averse investor with protection against very bad outcomes. Journal: North American Actuarial Journal Pages: 32-45 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596151 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596151 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:32-45 Template-Type: ReDIF-Article 1.0 Author-Name: Faye Albert Author-X-Name-First: Faye Author-X-Name-Last: Albert Title: Irwin Vanderhoof 1927 – 2000 Journal: North American Actuarial Journal Pages: 141-143 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596167 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596167 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:141-143 Template-Type: ReDIF-Article 1.0 Author-Name: J. F. Carrière Author-X-Name-First: J. F. Author-X-Name-Last: Carrière Title: Martingale Valuation of Cash Flows for Insurance and Interest Models Abstract: Using a pricing axiom from financial economics, a martingale valuation method is presented with the properties of numeraire invariance and no arbitrage. The pricing method is then applied to cash flows in actuarial models like loans, bonds, insurances, annuities, reserves, and surplus processes. Special emphasis is given to portfolios of defaultable bonds, where new modeling results are given. Also, an optimal repayment analysis of a common loan arrangement reveals that the book and market interest rates have to be equal. Journal: North American Actuarial Journal Pages: 1-16 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596150 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596150 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:1-16 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Title: E. J. Moorhead (1910 – 2004) Journal: North American Actuarial Journal Pages: 138-140 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596166 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596166 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:138-140 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Evans Author-X-Name-First: Mark Author-X-Name-Last: Evans Title: “Valuation of Equity-Indexed Annuities under Stochastic Interest Rates,” X. Sheldon Lin and Ken Seng Tan, October 2003 Journal: North American Actuarial Journal Pages: 123-124 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596159 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596159 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:123-124 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Tail Conditional Expectations for Elliptical Distributions - Discussion by Martin Bilodeau Journal: North American Actuarial Journal Pages: 122-123 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596158 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596158 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:122-123 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Bilodeau Author-X-Name-First: Martin Author-X-Name-Last: Bilodeau Title: “Tail Conditional Expectations for Elliptical Distributions,” Zinoviy M. Landsman and Emiliano A. Valdez, October 2003 Journal: North American Actuarial Journal Pages: 118-122 Issue: 3 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596157 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596157 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:118-122 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rita Bacinello Author-X-Name-First: Anna Rita Author-X-Name-Last: Bacinello Title: Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option Abstract: This paper analyzes a life insurance endowment policy, paid by annual premiums, in which the benefit is annually adjusted according to the performance of a special investment portfolio and a minimum return is guaranteed to the policyholder. In particular, the author considers both the case in which the annual premium is constant and the case in which the premium also is adjusted according to the performance of the reference portfolio. Moreover, the policy under scrutiny is characterized by the presence of a surrender option, that is, of an American-style put option that enables the policyholder to give up the contract and receive the surrender value. The aim of the paper is to give sufficient conditions under which there exists a (unique) fair premium. This premium is implicitly defined by an equation (or, alternatively, can be viewed as a fixed point of a suitable function) based on a recursive binomial tree àla Cox, Ross, and Rubinstein (1979). An iterative algorithm is then implemented in order to compute it. Journal: North American Actuarial Journal Pages: 1-17 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596097 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596097 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:1-17 Template-Type: ReDIF-Article 1.0 Author-Name: Ana Cebrián Author-X-Name-First: Ana Author-X-Name-Last: Cebrián Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Philippe Lambert Author-X-Name-First: Philippe Author-X-Name-Last: Lambert Title: Generalized Pareto Fit to the Society of Actuaries’ Large Claims Database Abstract: This paper discusses a statistical modeling strategy based on extreme value theory to describe the behavior of an insurance portfolio, with particular emphasis on large claims. The strategy is illustrated using the 1991–92 group medical claims database maintained by the Society of Actuaries. Using extreme value theory, the modeling strategy focuses on the “excesses over threshold” approach to fit generalized Pareto distributions. The proposed strategy is compared to standard parametric modeling based on gamma, lognormal, and log-gamma distributions. Extreme value theory outperforms classical parametric fits and allows the actuary to easily estimate high quantiles and the probable maximum loss from the data. Journal: North American Actuarial Journal Pages: 18-36 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596098 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596098 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:18-36 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends Abstract: In this paper asset and liability values are modeled by geometric Brownian motions. In the first part of the paper we consider a pension plan sponsor with the funding objective that the pension asset value is to be within a band that is proportional to the pension liability value. Whenever the asset value is about to fall below the lower barrier or boundary of the band, the sponsor will provide sufficient funds to prevent this from happening. If, on the other hand, the asset value is about to exceed the upper barrier of the band, the assets are reduced by the potential overflow and returned to the sponsor. This paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In particular we are interested in situations where these two expected values are equal. In the second part of the paper the refunds at the upper barrier are interpreted as the dividends paid to the shareholders of a company according to a barrier strategy. However, if the (modified) asset value ever falls to the liability value, which is the lower barrier, “ruin” takes place, and no more dividends can be paid. We derive an explicit expression for the expected discounted dividends before ruin. From this we find an explicit expression for the proportionality constant of the upper barrier that maximizes the expected discounted dividends. If the initial asset value is the optimal upper barrier, there is a particularly simple and intriguing expression for the expected discounted dividends, which can be interpreted as the present value of a deterministic perpetuity with exponentially growing payments. Journal: North American Actuarial Journal Pages: 37-51 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596099 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596099 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:37-51 Template-Type: ReDIF-Article 1.0 Author-Name: Thierry Duchesne Author-X-Name-First: Thierry Author-X-Name-Last: Duchesne Author-Name: Jacques Rioux Author-X-Name-First: Jacques Author-X-Name-Last: Rioux Title: “Efficient and Robust Fitting of Lognormal Distributions,” Robert Serfling, October 2002 Journal: North American Actuarial Journal Pages: 112-116 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596108 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596108 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:112-116 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Title: Authors’ Reply: “Efficient and Robust Fitting of Lognormal Distributions,” Robert Serfling, October 2002 - Discussion by Thierry Duchesne; Jacques Rioux Journal: North American Actuarial Journal Pages: 116-116 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596109 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596109 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:116-116 Template-Type: ReDIF-Article 1.0 Author-Name: Linda Smith Brothers Author-X-Name-First: Linda Smith Author-X-Name-Last: Brothers Title: An Individual’s Chosen Retirement Age: When is the Economically Feasible Retirement Age Chosen over the Anchor Provided by Known Others? Abstract: Do individuals make rational, well-planned retirement age decisions? Evidence is not conclusive; some decisions seem to be quite reasonable, while others, including the long-term trends generated by these decisions, seem irrational. In order to be able to predict and influence these important decisions, the process leading up to making them needs to be better understood. The process an individual uses to make a retirement decision may be influenced by a rational allocation of money, time, and effort, as suggested by a utility-maximizing Household Production approach. Alternately, the decision process may be strongly influenced by an anchor, defined by the retirement ages chosen by friends, neighbors, relatives, and colleagues, as suggested by Anchoring and Prospect Theory. Studies investigating anchoring and risk-seeking or risk-aversion behavior, which results when a target is seen as a loss or a gain from the anchor, have found that individuals make irrational decisions under many different circumstances. A set of retirement decision propositions, which hypothesize that the heuristic of Anchoring and the resulting cognitive biases described by Prospect Theory will influence the chosen retirement age, are developed in this paper. Retirement information provided by the employer is a possible moderator that may reduce the influence of the anchor on the retirement decision; a set of moderator hypotheses are also developed in this paper. Propositions strongly supported by existing research predict that, unless sufficient information regarding retirement issues is used by an individual, he or she is likely to choose an inappropriate retirement age. Journal: North American Actuarial Journal Pages: 87-110 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596106 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596106 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:87-110 Template-Type: ReDIF-Article 1.0 Author-Name: T. P. Hutchinson Author-X-Name-First: T. P. Author-X-Name-Last: Hutchinson Title: “Mortality of the Extreme Aged in the United States in the 1990s, Based on Improved Medicare Data” by Bert Kestenbaum and B. Reneé Ferguson, July 2002 Journal: North American Actuarial Journal Pages: 111-112 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596107 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596107 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:111-112 Template-Type: ReDIF-Article 1.0 Author-Name: Carisa Yu Author-X-Name-First: Carisa Author-X-Name-Last: Yu Title: “Pricing Lookback Options and Dynamic Guarantees,” Hans U. Gerber and Elias S. W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 124-127 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596113 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596113 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:124-127 Template-Type: ReDIF-Article 1.0 Author-Name: Yung-Ping Chen Author-X-Name-First: Yung-Ping Author-X-Name-Last: Chen Author-Name: John Scott Author-X-Name-First: John Author-X-Name-Last: Scott Title: Gradual Retirement: An Additional Option in Work and Retirement Abstract: Aging of the population raises many questions and issues for individuals, families, and society: economic, political, social, psychological, medical, ethical, moral, religious, and legal, all of which bear on the quality of life in its many dimensions. Economic security in old age is one rubric under which many of the problems and their possible solutions may be discussed. How a society arranges for its members to work and retire is an important facet in the provision for old-age economic security.This article is concerned with the implications of demographic and labor force changes for work and retirement. It discusses the role of gradual (or phased) retirement in introducing flexibility into the range of choices between work and retirement.Section 1 explains the rationale for gradual retirement. Section 2 spells out the barriers to implementing gradual retirement programs, including legal barriers and barriers relating to pension plan objectives. Section 3 discusses some possible solutions for implementing gradual retirement programs. Section 4 describes some selected examples of gradual retirement programs, and Section 5 contains concluding remarks. Journal: North American Actuarial Journal Pages: 62-74 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596104 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596104 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:62-74 Template-Type: ReDIF-Article 1.0 Author-Name: Jonathan Barry Forman Author-X-Name-First: Jonathan Barry Author-X-Name-Last: Forman Author-Name: Patricia Scahill Author-X-Name-First: Patricia Author-X-Name-Last: Scahill Title: Issues for Implementing Phased Retirement in Defined Benefit Plans Abstract: U.S. society is aging. The nature of work has changed from work that requires physical strength to work based on knowledge. As a result, workers are beginning to phase into retirement rather than going directly from full-time work to full retirement. From a retirement income perspective, many final-average-pay defined benefit plans have features that make phased retirement difficult at best and detrimental at worst. U.S. pension law and regulations present barriers to phased retirement if the phased retiree wants to receive a portion of available pension benefits during phased retirement.This paper examines private sector options to encourage phased retirement and to eliminate the disincentives that currently affect defined benefit plans. It offers alternative calculations of final average pay that do not penalize the part-time worker. It also demonstrates that the plan’s early retirement reduction and late retirement increase can be set to maintain actuarial equity throughout phased retirement. The paper presents benefit calculations with equal actuarial values for various payout patterns.The paper discusses the coordination between phased retirement and subsidized early retirement. Finally, the paper notes some of the changes in ERISA that will be needed to facilitate phased retirement in defined benefit plans, especially for participants who want to receive pension distributions while working part time. Journal: North American Actuarial Journal Pages: 75-84 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596105 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596105 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:75-84 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends - Discussion by X. Sheldon Lin; Marc Decamps; Marc Goovaerts Journal: North American Actuarial Journal Pages: 55-56 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596102 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596102 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:55-56 Template-Type: ReDIF-Article 1.0 Author-Name: Rob Kaas Author-X-Name-First: Rob Author-X-Name-Last: Kaas Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Title: Note on the Tail Behavior of Random Walk Maxima with Heavy Tails and Negative Drift Abstract: This paper investigates the asymptotic tail behavior of maxima of a random walk with negative mean and heavy-tailed increment distribution. A simple proof is given to improve the related result in Ng et al. (2002). Journal: North American Actuarial Journal Pages: 57-61 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596103 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596103 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:57-61 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheldon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheldon Lin Title: “Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends”, Hans U. Gerber and Elias S. W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 51-53 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596100 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596100 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:51-53 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 Journal: North American Actuarial Journal Pages: 117-119 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596110 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596110 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:117-119 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Decamps Author-X-Name-First: Marc Author-X-Name-Last: Decamps Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Title: “Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends”, Hans U. Gerber and Elias S. W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 54-55 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596101 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596101 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:54-55 Template-Type: ReDIF-Article 1.0 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 Journal: North American Actuarial Journal Pages: 119-122 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596111 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596111 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:119-122 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheldon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheldon Lin Title: “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 Journal: North American Actuarial Journal Pages: 122-124 Issue: 3 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596112 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596112 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:122-124 Template-Type: ReDIF-Article 1.0 Author-Name: Laslo Bollmann Author-X-Name-First: Laslo Author-X-Name-Last: Bollmann Author-Name: Matthias Scherer Author-X-Name-First: Matthias Author-X-Name-Last: Scherer Title: Modeling Influenza-Like Illness Activity in the United States Abstract: Influenza causes yearly costs for hospitalization and outpatient visits of more than $10 billion in the United States. The prediction of influenza epidemics is thus relevant for health insurance providers and public health facilities, among others. A useful piece of information is the probability distribution of influenza epidemics occurring within a given time horizon of one or two years. We present a model that delivers confidence intervals for future influenza activity in different regions in the United States. The model takes into account the specific statistical characteristics of influenza activity such as volatility clusters, seasonal effects, and dependencies between different regions. Confidence intervals for the regions are obtained using ARMA-GARCH models, and regional dependencies are captured by a pair-copula construction, describing jointly the residuals of the ARMA-GARCH models. Our model allows us to simulate influenza activity over a future time horizon. Journal: North American Actuarial Journal Pages: 323-342 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1284001 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1284001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:323-342 Template-Type: ReDIF-Article 1.0 Author-Name: George Mavros Author-X-Name-First: George Author-X-Name-Last: Mavros Author-Name: Andrew J. G. Cairns Author-X-Name-First: Andrew J. G. Author-X-Name-Last: Cairns Author-Name: George Streftaris Author-X-Name-First: George Author-X-Name-Last: Streftaris Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Title: Stochastic Mortality Modeling: Key Drivers and Dependent Residuals Abstract: This article proposes an alternative framework for modeling the stochastic dynamics of mortality rates. A simple age basis combined with two stochastic period factors is used to explain the key mortality drivers, while the remaining structure is modeled via a multivariate autoregressive residuals model. The latter captures the stationary mortality dynamics and introduces dependencies between adjacent age-period cells of the mortality matrix that, among other things, can be structured to capture cohort effects in a transparent manner and incorporate across ages correlations in a natural way. Our approach is compared with models with and without a univariate cohort process. The age- and period-related latent states of the mortality basis are more robust when the residuals surface is modeled via the multivariate time-series model, implying that the process indeed acts independently of the assumed mortality basis. Under the Bayesian paradigm, the posterior distribution of the models is considered to explore coherently the extent of parameter uncertainty. Samples from the posterior predictive distribution are used to project mortality, and an in-depth sensitivity analysis is conducted. The methodology is easily extendable in multiple ways that give a different form and degree of significance to the different components of mortality dynamics. Journal: North American Actuarial Journal Pages: 343-368 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1286992 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1286992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:343-368 Template-Type: ReDIF-Article 1.0 Author-Name: Eric R. Ulm Author-X-Name-First: Eric R. Author-X-Name-Last: Ulm Title: On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds Abstract: Guaranteed funds with crediting rates for fixed periods determined by a pension provider or insurance company are common features of accumulation annuity contracts. Policyholders can transfer money back and forth between these accounts and money market accounts that give them features similar to demand deposits, and yet they frequently credit a higher rate than the money market. Transfer restrictions are commonly employed to prevent arbitrage. In this article, we model the interaction between company and policyholder as a multiperiod game in which the company maximizes risk-neutral expected present value of profits and the policyholder maximizes his expected discounted utility. We find that the optimal strategy on the part of the company is to credit a rate higher than the money market rate in the first period to entice the policyholder to invest in the guaranteed fund. The company then credits the floor in the remaining periods as the policyholder transfers out the maximum amount. This does better for the policyholder in low interest rate environments and worse in high interest rate environments and acts as a type of “interest rate insurance” for the policyholder. Journal: North American Actuarial Journal Pages: 369-381 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1298449 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1298449 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:369-381 Template-Type: ReDIF-Article 1.0 Author-Name: Shinichi Kamiya Author-X-Name-First: Shinichi Author-X-Name-Last: Kamiya Author-Name: George Zanjani Author-X-Name-First: George Author-X-Name-Last: Zanjani Title: Egalitarian Equivalent Capital Allocation Abstract: We apply Moulin's notion of egalitarian equivalent cost sharing of a public good to the problem of insurance capitalization and capital allocation where the liability portfolio is fixed. We show that this approach yields overall capitalization and cost allocations that are Pareto efficient, individually rational, and, unlike other mechanisms, stable in the sense of adhering to cost monotonicity. Journal: North American Actuarial Journal Pages: 382-396 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1298450 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1298450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:382-396 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel Gbari Author-X-Name-First: Samuel Author-X-Name-Last: Gbari Author-Name: Michel Poulain Author-X-Name-First: Michel Author-X-Name-Last: Poulain Author-Name: Luc Dal Author-X-Name-First: Luc Author-X-Name-Last: Dal Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Extreme Value Analysis of Mortality at the Oldest Ages: A Case Study Based on Individual Ages at Death Abstract: In this article, the force of mortality at the oldest ages is studied using the statistical tools from extreme value theory. A unique data basis recording all individual ages at death above 95 for extinct cohorts born in Belgium between 1886 and 1904 is used to illustrate the relevance of the proposed approach. No leveling off in the force of mortality at the oldest ages is found, and the analysis supports the existence of an upper limit to human lifetime for these cohorts. Therefore, assuming that the force of mortality becomes ultimately constant, that is, that the remaining lifetime tends to the Negative Exponential distribution as the attained age grows is a conservative strategy for managing life annuities. Journal: North American Actuarial Journal Pages: 397-416 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1301260 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1301260 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:397-416 Template-Type: ReDIF-Article 1.0 Author-Name: Yichun Chi Author-X-Name-First: Yichun Author-X-Name-Last: Chi Author-Name: X. Sheldon Lin Author-X-Name-First: X. Sheldon Author-X-Name-Last: Lin Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle Abstract: In this article, an optimal reinsurance problem is formulated from the perspective of an insurer, with the objective of minimizing the risk-adjusted value of its liability where the valuation is carried out by a cost-of-capital approach and the capital at risk is calculated by either the value-at-risk (VaR) or conditional value-at-risk (CVaR). In our reinsurance arrangement, we also assume that both insurer and reinsurer are obligated to pay more for a larger realization of loss as a way of reducing ex post moral hazard. A key contribution of this article is to expand the research on optimal reinsurance by deriving explicit optimal reinsurance solutions under an economic premium principle. It is a rather general class of premium principles that includes many weighted premium principles as special cases. The advantage of adopting such a premium principle is that the resulting reinsurance premium depends not only on the risk ceded but also on a market economic factor that reflects the market environment or the risk the reinsurer is facing. This feature appears to be more consistent with the reinsurance market. We show that the optimal reinsurance policies are piecewise linear under both VaR and CVaR risk measures. While the structures of optimal reinsurance solutions are the same for both risk measures, we also formally show that there are some significant differences, particularly on the managing tail risk. Because of the integration of the market factor (via the reinsurance pricing) into the optimal reinsurance model, some new insights on the optimal reinsurance design could be gleaned, which would otherwise be impossible for many of the existing models. For example, the market factor has a nontrivial effect on the optimal reinsurance, which is greatly influenced by the changes of the joint distribution of the market factor and the loss. Finally, under an additional assumption that the market factor and the loss have a copula with quadratic sections, we demonstrate that the optimal reinsurance policies admit relatively simple forms to foster the applicability of our theoretical results, and a numerical example is presented to further highlight our results. Journal: North American Actuarial Journal Pages: 417-432 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1302346 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1302346 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:417-432 Template-Type: ReDIF-Article 1.0 Author-Name: Adam W. Kolkiewicz Author-X-Name-First: Adam W. Author-X-Name-Last: Kolkiewicz Author-Name: Fangyuan Sally Lin Author-X-Name-First: Fangyuan Sally Author-X-Name-Last: Lin Title: Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes Abstract: This article presents a numerical method of pricing the surrender risk in Ratchet equity-index annuities (EIAs). We assume that log-returns of the underlying fund belong to a class of regime-switching models where the parameters are allowed to change randomly according to a hidden Markov chain. The defining feature of these models is the fact that in each regime the characteristic function of log-returns is assumed to have an analytical form. The presented method provides an unified pricing framework within this class and includes the recently developed COS method as a particular case. This aspect of the method is particularly useful when pricing Ratchet options embedded in EIAs, for which the COS method exhibits a low rate of convergence. Our numerical results confirm that for models considered in this article the proposed approach improves convergence of the COS method without increasing the computational burden. Journal: North American Actuarial Journal Pages: 433-457 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1302804 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1302804 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:433-457 Template-Type: ReDIF-Article 1.0 Author-Name: Zhenyu Cui Author-X-Name-First: Zhenyu Author-X-Name-Last: Cui Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Author-Name: Anne MacKay Author-X-Name-First: Anne Author-X-Name-Last: MacKay Title: Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model Abstract: The Chicago Board of Options Exchange (CBOE) advocates linking variable annuity (VA) fees to its trademark VIX index in a recent white paper. It claims that the VIX-linked fee structure has several advantages over the traditional fixed percentage fee structure. However, the evidence presented is largely based on nonparametric extrapolation of historical data on market prices. Our work lays out a theoretical basis with a parametric model to analyze the impact of the VIX-linked fee structure and to verify some claims from the CBOE. In a Heston-type stochastic volatility setting, we jointly model the dynamics of an equity index (underlying the value of VA policyholders’ accounts) and the VIX index. In this framework, we price a guaranteed minimum maturity benefit with VIX-linked fees. Through numerical examples, we show that the VIX-linked fee reduces the sensitivity of the insurer's liability to market volatility when compared to a VA with the traditional fixed fee rate. Journal: North American Actuarial Journal Pages: 458-483 Issue: 3 Volume: 21 Year: 2017 Month: 7 X-DOI: 10.1080/10920277.2017.1307765 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1307765 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:458-483 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: Chengming Xu Author-X-Name-First: Chengming Author-X-Name-Last: Xu Title: On The Decomposition Of The Ruin Probability For A Jump-Diffusion Surplus Process Compounded By A Geometric Brownian Motion Abstract: If one assumes that the surplus of an insurer follows a jump-diffusion process and the insurer would invest its surplus in a risky asset, whose prices are modeled by a geometric Brownian motion, the resulting surplus for the insurer is called a jump-diffusion surplus process compounded by a geometric Brownian motion. In this resulting surplus process, ruin may be caused by a claim or oscillation. We decompose the ruin probability in the resulting surplus process into the sum of two ruin probabilities: the probability that ruin is caused by a claim, and the probability that ruin is caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When claim sizes are exponentially distributed, asymptotical formulas of the ruin probabilities are derived from the integro-differential equations, and it is shown that all three ruin probabilities are asymptotical power functions with the same orders and that the orders of the power functions are determined by the drift and volatility parameters of the geometric Brownian motion. It is known that the ruin probability for a jump-diffusion surplus process is an asymptotical exponential function when claim sizes are exponentially distributed. The results of this paper further confirm that risky investments for an insurer are dangerous in the sense that either ruin is certain or the ruin probabilities are asymptotical power functions, not asymptotical exponential functions, when claim sizes are exponentially distributed. Journal: North American Actuarial Journal Pages: 120-129 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596255 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596255 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:120-129 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest - Discussion by Nathaniel Smith; Andrew C. Y. Ng; Jinxia Zhu Journal: North American Actuarial Journal Pages: 119-119 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596254 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596254 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:119-119 Template-Type: ReDIF-Article 1.0 Author-Name: Jinxia Zhu Author-X-Name-First: Jinxia Author-X-Name-Last: Zhu Title: “Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest”, Jun Cai, Hans U. Gerber and Hailiang Yang, April 2006 Journal: North American Actuarial Journal Pages: 116-118 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596253 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596253 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:116-118 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Title: “Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest”, Jun Cai, Hans U. Gerber and Hailiang Yang, April 2006 Journal: North American Actuarial Journal Pages: 112-116 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596252 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596252 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:112-116 Template-Type: ReDIF-Article 1.0 Author-Name: Nathaniel Smith Author-X-Name-First: Nathaniel Author-X-Name-Last: Smith Title: “Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest”, Jun Cai, Hans U. Gerber and Hailiang Yang, April 2006 Journal: North American Actuarial Journal Pages: 109-112 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596251 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596251 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:109-112 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest Abstract: In the absence of investment and dividend payments, the surplus is modeled by a Brownian motion. But now assume that the surplus earns investment income at a constant rate of credit interest. Dividends are paid to the shareholders according to a barrier strategy. It is shown how the expected discounted value of the dividends and the optimal dividend barrier can be calculated; Kummer’s confluent hypergeometric differential equation plays a key role in this context. An alternative assumption is that business can go on after ruin, as long as it is profitable. When the surplus is negative, a higher rate of debit interest is applied. Several numerical examples document the influence of the parameters on the optimal dividend strategy. Journal: North American Actuarial Journal Pages: 94-108 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596250 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596250 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:94-108 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: On Optimal Dividend Strategies In The Compound Poisson Model Abstract: The optimal dividend problem goes back to a paper that Bruno De Finetti presented to the International Congress of Actuaries in New York (1957). For a stock company that pays dividends to its shareholders, what is the strategy that maximizes the expectation of the discounted dividends (until possible ruin)? Jeanblanc-Picqué and Shiryaev (1995) and Asmussen and Taksar (1997) solved the problem in the Brownian motion model, when a ceiling is imposed for the dividend rate. Here we study the problem with the Brownian motion generalized to a compound Poisson process. In particular, we derive a rule for deciding between plowback and dividend payout, which is a key issue in corporate finance. Journal: North American Actuarial Journal Pages: 76-93 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596249 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596249 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:76-93 Template-Type: ReDIF-Article 1.0 Author-Name: Chuancun Yin Author-X-Name-First: Chuancun Author-X-Name-Last: Yin Title: “On a Classical Risk Model with a Constant Dividend Barrier”, Xiaowen Zhou, October 2005 Abstract: Journal: North American Actuarial Journal Pages: 139-143 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596259 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596259 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:139-143 Template-Type: ReDIF-Article 1.0 Author-Name: Piet de Jong Author-X-Name-First: Piet Author-X-Name-Last: de Jong Title: Forecasting Runoff Triangles Abstract: This paper deals with the methodology of liability forecasting using the runoff triangle data. Techniques are based on time series models and methods that facilitate the calculation of forecast distributions and the assessment of model fit. The models deal with correlation within triangles. Correlations are critical to proper reserving. The output of the methodology is the complete shape of the liability distribution. Methods are applied to a well-known runoff triangle and results compared to those from previous studies. Journal: North American Actuarial Journal Pages: 28-38 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596246 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596246 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:28-38 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “On a Classical Risk Model with a Constant Dividend Barrier”, Xiaowen Zhou, October 2005 Journal: North American Actuarial Journal Pages: 133-139 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596258 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596258 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:133-139 Template-Type: ReDIF-Article 1.0 Author-Name: Ernesto Schirmacher Author-X-Name-First: Ernesto Author-X-Name-Last: Schirmacher Author-Name: Sholom Feldblum Author-X-Name-First: Sholom Author-X-Name-Last: Feldblum Title: Financial Pricing Models for Property-Casualty Insurance Products Abstract: Insurance companies sell products without knowing what the ultimate costs will be. Moreover, in many cases the time between receipt of premium and the payment of claims could span many years. To manage the risk that companies have assumed, they need special tools to monitor the ongoing profitability of their products.In this paper we introduce one tool—retrospective analysis—to monitor profitability. Retrospective analysis is mainly concerned with incorporating all available information about a block of business to determine the current estimate of profitability and to attribute any differences to the appropriate sources.To illustrate the methods used in retrospective analysis we present a simplified but complete model of an insurance policy. We also introduce two economic accounting systems—the net present value system and the internal rate of return system—and analyze how emerging experience alters the profitability of our insurance policy. We pay special attention to quantifying the changes under both accounting systems. Journal: North American Actuarial Journal Pages: 1-27 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596245 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596245 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:1-27 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Siu Author-X-Name-First: Tak Author-X-Name-Last: Siu Title: Option Pricing Under Autoregressive Random Variance Models Abstract: The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discretetime version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the log-normal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted. Journal: North American Actuarial Journal Pages: 62-75 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596248 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596248 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:62-75 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: On The Decomposition Of The Ruin Probability For A Jump-Diffusion Surplus Process Compounded By A Geometric Brownian Motion - Discussion by Hailiang Yang Journal: North American Actuarial Journal Pages: 129-131 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596257 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596257 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:129-131 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: John van der Hoek Author-X-Name-First: John Author-X-Name-Last: van der Hoek Title: Capital Allocation In Insurance Abstract: The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line. Journal: North American Actuarial Journal Pages: 39-61 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596247 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596247 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:39-61 Template-Type: ReDIF-Article 1.0 Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: “On The Decomposition Of The Ruin Probability For A Jump-Diffusion Surplus Process Compounded By A Geometric Brownian Motion”, Jun Cai and Chengming Xu, April 2006 Journal: North American Actuarial Journal Pages: 129-131 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596256 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596256 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:129a-131a Template-Type: ReDIF-Article 1.0 Author-Name: Jiafeng Sun Author-X-Name-First: Jiafeng Author-X-Name-Last: Sun Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Title: “Toward a Unified Approach to Fitting Loss Models”, Stuart Klugman and Jacques Rioux, January 2006 Journal: North American Actuarial Journal Pages: 147-153 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596261 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596261 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:147-153 Template-Type: ReDIF-Article 1.0 Author-Name: Beda Chan Author-X-Name-First: Beda Author-X-Name-Last: Chan Title: McNeil, Alexander J., Frey, Rüdiger, and Embrechts, Paul, 2005, Journal: North American Actuarial Journal Pages: 154-154 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596262 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596262 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:154-154 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: Authors’ Reply: On a Classical Risk Model with a Constant Dividend Barrier - Discussion by Beda Chan; Hans U. Gerber; Chuancun Yin; Elias S. W. Shiu Journal: North American Actuarial Journal Pages: 143-146 Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596260 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596260 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:143-146 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Title: The Magnificent Seven Journal: North American Actuarial Journal Pages: iii-v Issue: 2 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596263 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596263 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:2:p:iii-v Template-Type: ReDIF-Article 1.0 Author-Name: Bonnie-Jeanne MacDonald Author-X-Name-First: Bonnie-Jeanne Author-X-Name-Last: MacDonald Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Author-Name: Richard Morrison Author-X-Name-First: Richard Author-X-Name-Last: Morrison Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Research and Reality: A Literature Review on Drawing Down Retirement Financial Savings Abstract: How do, could, and should retirees draw down their financial savings? This article reviews over 100 papers on this topic from the perspective of individuals, families, governments, and financial institutions. Three significant conceptual/methodological weaknesses in the existing literature are identified: (1) analysts have examined a limited range of self-managed drawdown strategies; (2) nearly all have ignored home ownership, pensions, debt, and government taxes and transfers when quantitatively evaluating alternative drawdown strategies; and (3) there is a well-acknowledged gap between the behavior implied by economic models and that of real-life individuals, particularly when it comes to voluntary annuitization. Expanding the set of drawdown strategies evaluated (e.g., including larger payouts when life expectancy is reduced after the onset of a significant health condition, or using savings as bridge income to delay the take-up of Social Security payments), refining the income concept used, and more exact modeling of the trade-offs underlying individual decision-making will likely increase the appeal of self-managed drawdown strategies and help resolve the “annuity puzzle” that has long dominated this line of research. It may also lead to advice and financial products that will better meet the needs of retirees. Journal: North American Actuarial Journal Pages: 181-215 Issue: 3 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.821938 File-URL: http://hdl.handle.net/10.1080/10920277.2013.821938 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:3:p:181-215 Template-Type: ReDIF-Article 1.0 Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Author-Name: Zhongyi Yuan Author-X-Name-First: Zhongyi Author-X-Name-Last: Yuan Title: Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation Abstract: Consider a portfolio of n obligors subject to possible default. We propose a new structural model for the loss given default, which takes into account the severity of default. Then we study the tail behavior of the loss given default under the assumption that the losses of the n obligors jointly follow a multivariate regular variation structure. This structure provides an ideal framework for modeling both heavy tails and asymptotic dependence. Multivariate models involving Archimedean copulas and mixtures are revisited. As applications, we derive asymptotic estimates for the value at risk and conditional tail expectation of the loss given default and compare them with the traditional empirical estimates. Journal: North American Actuarial Journal Pages: 253-271 Issue: 3 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.830557 File-URL: http://hdl.handle.net/10.1080/10920277.2013.830557 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:3:p:253-271 Template-Type: ReDIF-Article 1.0 Author-Name: Brian Hartman Author-X-Name-First: Brian Author-X-Name-Last: Hartman Author-Name: Chris Groendyke Author-X-Name-First: Chris Author-X-Name-Last: Groendyke Title: Model Selection and Averaging in Financial Risk Management Abstract: Simulated asset returns are used in many areas of actuarial science. For example, life insurers use them to price annuities, life insurance, and investment guarantees. The quality of those simulations has come under increased scrutiny during the current financial crisis. When simulating the asset price process, properly choosing which model or models to use, and accounting for the uncertainty in that choice, is essential. We investigate how best to choose a model from a flexible set of models. In our regime-switching models the individual regimes are not constrained to be from the same distributional family. Even with larger sample sizes, the standard model-selection methods (AIC, BIC, and DIC) incorrectly identify the models far too often. Rather than trying to identify the best model and limiting the simulation to a single distribution, we show that the simulations can be made more realistic by explicitly modeling the uncertainty in the model-selection process. Specifically, we consider a parallel model-selection method that provides the posterior probabilities of each model being the best, enabling model averaging and providing deeper insights into the relationships between the models. The value of the method is demonstrated through a simulation study, and the method is then applied to total return data from the S&P 500. Journal: North American Actuarial Journal Pages: 216-228 Issue: 3 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.824374 File-URL: http://hdl.handle.net/10.1080/10920277.2013.824374 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:3:p:216-228 Template-Type: ReDIF-Article 1.0 Author-Name: Xiao Wei Author-X-Name-First: Xiao Author-X-Name-Last: Wei Author-Name: Marcellino Gaudenzi Author-X-Name-First: Marcellino Author-X-Name-Last: Gaudenzi Author-Name: Antonino Zanette Author-X-Name-First: Antonino Author-X-Name-Last: Zanette Title: Pricing Ratchet Equity-Indexed Annuities with Early Surrender Risk in a CIR++ Model Abstract: In this article we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique that permits us to obtain a first-order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without a global minimum contract value. Numerical comparisons show the reliability of the proposed methods. Journal: North American Actuarial Journal Pages: 229-252 Issue: 3 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.826126 File-URL: http://hdl.handle.net/10.1080/10920277.2013.826126 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:3:p:229-252 Template-Type: ReDIF-Article 1.0 Author-Name: Grace Skalski Author-X-Name-First: Grace Author-X-Name-Last: Skalski Title: Presidential Addresses 1949–1998 Journal: North American Actuarial Journal Pages: 64-112 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595861 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595861 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:64-112 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: Social Security Abstract: The U.S. Social Security program (Old-Age, Survivors, and Disability Insurance) was enacted in 1935, long after many European nations had instituted similar ones. The driving force for such action was the Great Depression of the early 1930s, which had pushed many persons into poverty. The program was not intended to solve the immediate problem (which instead was handled by federal funding of state public assistance plans), but rather as an initial step of preventive action for the long run.The current financial status of the Social Security program is excellent over the short range, but very likely a significant, although not overwhelming, problem is present as to the long range. Various proposals to remedy the situation are examined, some merely maintaining the existing character of the program but reducing benefit costs and/or increasing its income, and others reducing its scope by partially or wholly privatizing it. Journal: North American Actuarial Journal Pages: 59-63 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595860 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595860 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:59-63 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: John E. O’Connor, Jr. 1942–1999 Journal: North American Actuarial Journal Pages: 113-113 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595863 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595863 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:113a-113a Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Charles L. Trowbridge 1916–1999 Journal: North American Actuarial Journal Pages: 113-113 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595862 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595862 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:113-113 Template-Type: ReDIF-Article 1.0 Author-Name: M. David Brown Author-X-Name-First: M. David Author-X-Name-Last: Brown Title: The Public Role of Actuaries in Private Pensions in Canada Abstract: Actuaries have played prominent public roles in the development of occupational pension plans and social security arrangements in Canada. These roles include advising governments and government-appointed committees about regulatory structures, establishing funding standards, actively participating in regulatory functions, and pioneering valuation work for pension plans covering public sector employees. The formation in 1965 of the Canadian Institute of Actuaries led to the accreditation of actuaries in pension and tax legislation and to the development of actuarial standards of practice for pension work. Journal: North American Actuarial Journal Pages: 28-33 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595856 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595856 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:28-33 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Title: Our Golden Anniversary Journal: North American Actuarial Journal Pages: iii-iv Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595865 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595865 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: Howard Bolnick Author-X-Name-First: Howard Author-X-Name-Last: Bolnick Title: To Sustain a Vital and Vibrant Actuarial Profession Abstract: Insurance markets are different from most other markets. Insurance markets have an inherent self-destructive tendency that can cause market failure. However, insurance markets not only exist, they thrive. This paper explores the essential role that actuaries play in countering problems that can cause market failure. Armed with our mathematical and business skills and strong sense of professionalism, actuaries are essential to the successful growth of insurance companies and insurance markets. The breakdown of barriers among segments of the financial services industry creates an opportunity for actuaries to apply these same skills to noninsurance financial institutions. Actuaries have a strong claim to becoming the profession the public relies upon to ensure that an adequate balance is kept between profits and solvency. The foundation of this claim is not the superiority of our intellectual tools. It is the advantages to society of actuaries as a well-defined, recognized group of trustworthy and professional financial managers. Journal: North American Actuarial Journal Pages: 19-27 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595855 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595855 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:19-27 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Joy and Sadness Journal: North American Actuarial Journal Pages: eb1-eb1 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595864 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595864 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:eb1-eb1 Template-Type: ReDIF-Article 1.0 Author-Name: Dwight Bartlett Author-X-Name-First: Dwight Author-X-Name-Last: Bartlett Title: Measures of Actuarial Status for Social Security Abstract: From the inception of Social Security in 1935 to the present time, a variety of measures for evaluating the actuarial status of the program have been employed. In addition, how the results of these measures have been displayed and interpreted has also evolved. These results have had great influence on policymakers’ and the general public’s perceptions of the financial condition of the program. This paper is intended to be an update of my earlier paper on the same subject, that is, a historical review of the development of these methods and their interpretation. The paper closes with suggestions as to future changes in the measurement methods, in the light of possible future changes in the program itself. Journal: North American Actuarial Journal Pages: 10-18 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595854 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595854 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:10-18 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Linda Heacox Author-X-Name-First: Linda Author-X-Name-Last: Heacox Title: The Actuarial Role in Financial Reporting Abstract: This is the fourth in a series of interviews on the history of ideas published by the NAAJ in commemoration of the fiftieth anniversary of the Society of Actuaries. This contribution to the series covers developments in financial reporting for life insurance companies and for the sponsors of long-term employee benefits. Financial reporting techniques developed in response to the information requirements of efficient capital markets, and they have influenced advances in accounting and actuarial thought. Journal: North American Actuarial Journal Pages: 1-9 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595853 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595853 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:1-9 Template-Type: ReDIF-Article 1.0 Author-Name: Harold Ingraham Author-X-Name-First: Harold Author-X-Name-Last: Ingraham Title: The Society of Actuaries Education and Examination System, 1949–1999 Abstract: The public responsibility of life insurance actuaries has changed from supervisory compliance with detailed state laws to certifying adherence to more general regulatory objectives complemented by actuarial standards of practice. Journal: North American Actuarial Journal Pages: 48-58 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595859 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595859 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:48-58 Template-Type: ReDIF-Article 1.0 Author-Name: Donald Grubbs Author-X-Name-First: Donald Author-X-Name-Last: Grubbs Title: The Public Responsibility of Actuaries in American Pensions Abstract: This article traces the history of the public responsibility of actuaries concerning American pension plans. It includes both defined-benefit and defined-contribution plans for employees of both private and public employers. It does not include Social Security. Actuaries have provided innovative approaches to plan design, funding, funding instruments, accounting, and legal and regulatory requirements. Actuaries have made substantial contributions that have enabled pension plans, together with Social Security, to provide economic security for millions of workers and their dependents when employment ends. However, many Americans still lack assurance of a retirement income that is initially adequate, continues for life, and keeps pace with inflation. Thus, challenges will continue to face pension actuaries in the years ahead. Journal: North American Actuarial Journal Pages: 34-41 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595857 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595857 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:34-41 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Linda Heacox Author-X-Name-First: Linda Author-X-Name-Last: Heacox Title: Growth of the Public Responsibility of Actuaries in Life Insurance Abstract: The public responsibility of life insurance actuaries has changed from supervisory compliance with detailed state laws to certifying adherence to more general regulatory objectives complemented by actuarial standards of practice. Journal: North American Actuarial Journal Pages: 42-47 Issue: 4 Volume: 3 Year: 1999 X-DOI: 10.1080/10920277.1999.10595858 File-URL: http://hdl.handle.net/10.1080/10920277.1999.10595858 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:3:y:1999:i:4:p:42-47 Template-Type: ReDIF-Article 1.0 Author-Name: Mengyi Xu Author-X-Name-First: Mengyi Author-X-Name-Last: Xu Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: Ramona Meyricke Author-X-Name-First: Ramona Author-X-Name-Last: Meyricke Title: Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data Abstract: Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status. Journal: North American Actuarial Journal Pages: 197-219 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2018.1513369 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1513369 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:197-219 Template-Type: ReDIF-Article 1.0 Author-Name: Marc A. Ragin Author-X-Name-First: Marc A. Author-X-Name-Last: Ragin Author-Name: Jianren Xu Author-X-Name-First: Jianren Author-X-Name-Last: Xu Title: An Ex Post Assessment of Investor Response to Catastrophes Abstract: A large body of research has examined abnormal stock returns for insurance companies in the wake of major catastrophes. Most of these studies have investigated the ex ante factors that investors may consider when generating expectations of future profits, represented by postcatastrophe stock returns. We instead ask whether these expectations were ultimately correct by investigating the relationship between returns and the disaster’s effect on future earnings. We find that returns immediately following a disaster are not associated with future earnings. Approximately six days following a catastrophe, however, returns begin to show a significant positive relationship with future earnings. This relationship becomes stronger in subsequent days. We conclude that investors are unable to correctly predict a disaster’s net impact on profits immediately after a disaster because existing public information is insufficient or misunderstood. Only once insurers begin disclosing their estimated losses can investors make accurate predictions about a disaster’s effect on earnings. Our study shows that the investor expectations inferred in much of the existing literature are not predictive of future profits. Our findings are consistent with semistrong-form market efficiency in the wake of a major disaster. Journal: North American Actuarial Journal Pages: 250-275 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2018.1536885 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1536885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:250-275 Template-Type: ReDIF-Article 1.0 Author-Name: Michael M. Barth Author-X-Name-First: Michael M. Author-X-Name-Last: Barth Author-Name: Evan M. Eastman Author-X-Name-First: Evan M. Author-X-Name-Last: Eastman Author-Name: David L. Eckles Author-X-Name-First: David L. Author-X-Name-Last: Eckles Title: It’s About Time: An Examination of Loss Reserve Development Time Horizons Abstract: A rich body of academic research has addressed the question of earnings management in the property-casualty insurance industry via manipulation of loss reserve estimates. This study analyzes the variability of reserve estimates at different development horizons to determine whether the predominant practice of relying on five years of development is appropriate. We examine two common measures of reserve estimation error, calendar year development and accident year development, and compare and contrast the two approaches. We also consider the appropriateness of the common practice of aggregating lines of business. After examining reserve development patterns for each of the major lines of business, we conclude that the appropriate development horizon to adequately establish ultimate liability may be longer than the current maximum reported horizon of 10 years found in Schedule P for most lines of business, including the aggregate reserves. Although longer-term development horizons are necessary to establish insurers’ ultimate liability, relatively short-term development horizons may be more appropriate when attempting to identify deliberate manipulations or to assess solvency risk, where the short-term variations are the primary object of interest. Ultimately, this article investigates the degree to which methodology originally developed for estimating loss reserve errors is appropriate today, in particular, relative to current data availability. Journal: North American Actuarial Journal Pages: 143-168 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2018.1538804 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1538804 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:143-168 Template-Type: ReDIF-Article 1.0 Author-Name: Florian Klein Author-X-Name-First: Florian Author-X-Name-Last: Klein Author-Name: Hato Schmeiser Author-X-Name-First: Hato Author-X-Name-Last: Schmeiser Title: Heterogeneous Premiums for Homogeneous Risks? Asset Liability Management under Default Probability and Price-Demand Functions Abstract: We consider an asset liability model under an internal solvency constraint that includes default probability as well as price-demand functions and combine insights from empirical and theoretical research. Furthermore, as a result of policyholders’ heterogeneous willingness to pay, we introduce heterogeneous premiums to maximize the insurer’s overall net present value and compare the results with an optimal homogeneous premium. To determine a reservation price for the insurer, we use the Margrabe-Fischer option-pricing formula. Our numerical examples document that heterogeneous premiums for homogeneous risks improve the net present value when correct expectations underlie and are vulnerable against a cost shift but do not per se induce a decrease in the net present value. Moreover, we recognize that the optimal price setting under overall net present value maximization varies from the underwriting net present value maximization on the individual risk level. Hence, in practice, an overall asset liability management perspective should be in focus to reach the best results from the company’s point of view. Journal: North American Actuarial Journal Pages: 276-297 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2018.1538805 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1538805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:276-297 Template-Type: ReDIF-Article 1.0 Author-Name: Liqun Diao Author-X-Name-First: Liqun Author-X-Name-Last: Diao Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Title: Regression Tree Credibility Model Abstract: This article applies machine learning techniques to credibility theory and proposes a regression-tree-based algorithm to integrate covariate information into credibility premium prediction. The recursive binary algorithm partitions a collective of individual risks into mutually exclusive subcollectives and applies the classical Bühlmann-Straub credibility formula for the prediction of individual net premiums. The algorithm provides a flexible way to integrate covariate information into individual net premiums prediction. It is appealing for capturing nonlinear and/or interaction covariate effects. It automatically selects influential covariate variables for premium prediction and requires no additional ex ante variable selection procedure. The superiority in prediction accuracy of the proposed algorithm is demonstrated by extensive simulation studies. The proposed method is applied to the U.S. Medicare data for illustration purposes. Journal: North American Actuarial Journal Pages: 169-196 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2018.1554497 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1554497 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:169-196 Template-Type: ReDIF-Article 1.0 Author-Name: Giovanna Apicella Author-X-Name-First: Giovanna Author-X-Name-Last: Apicella Author-Name: Michel Dacorogna Author-X-Name-First: Michel Author-X-Name-Last: Dacorogna Author-Name: Emilia Di Lorenzo Author-X-Name-First: Emilia Author-X-Name-Last: Di Lorenzo Author-Name: Marilena Sibillo Author-X-Name-First: Marilena Author-X-Name-Last: Sibillo Title: Improving the Forecast of Longevity by Combining Models Abstract: Mortality is a dynamic process whose future evolution over time poses important challenges for life insurance, pension funds, public policy, and fiscal planning. In this paper, we propose two contributions: (1) a new dynamic corrective methodology of the predictive accuracy of the existing mortality projection models, by modeling a measure of their fitting errors as a Cox-Ingersoll-Ross process and; (2) various out-of-sample validation methods. Besides the usual static method, we develop a dynamic one allowing us to catch the change in behavior of the underlying data. For our numerical application, we choose the Cairns-Blake-Dowd (or M5) model. Using the Italian and French females mortality data and implementing the backtesting procedure, we empirically test the ex-post forecasting performance of the CBD model both for itself (CBD) and corrected by the CIR process (mCBD). We focus on age 65, but we show results for a wide range of ages, also much younger, and for cohort data. On the basis of average measures of forecasting errors and information criteria, we show that the mCBD model is parsimonious and provides better results in terms of predictive accuracy than the CBD model itself. Journal: North American Actuarial Journal Pages: 298-319 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2018.1556701 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1556701 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:298-319 Template-Type: ReDIF-Article 1.0 Author-Name: Maochao Xu Author-X-Name-First: Maochao Author-X-Name-Last: Xu Author-Name: Lei Hua Author-X-Name-First: Lei Author-X-Name-Last: Hua Title: Cybersecurity Insurance: Modeling and Pricing Abstract: Cybersecurity risk has attracted considerable attention in recent decades. However, the modeling of cybersecurity risk is still in its infancy, mainly because of its unique characteristics. In this study, we develop a framework for modeling and pricing cybersecurity risk. The proposed model consists of three components: the epidemic model, loss function, and premium strategy. We study the dynamic upper bounds for the infection probabilities based on both Markov and non-Markov models. A simulation approach is proposed to compute the premium for cybersecurity risk for practical use. The effects of different infection distributions and dependence among infection processes on the losses are also studied. Journal: North American Actuarial Journal Pages: 220-249 Issue: 2 Volume: 23 Year: 2019 Month: 4 X-DOI: 10.1080/10920277.2019.1566076 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1566076 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:2:p:220-249 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Authors' Reply: On Optimal Dividend Strategies in the Compound Poisson Model, discussion by Eric C. K. Cheung Journal: North American Actuarial Journal Pages: 161-162 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10707531 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10707531 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:161-162 Template-Type: ReDIF-Article 1.0 Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets Abstract: A model for pricing insurance and financial risks, based on recent developments in actuarial premium principles with elliptical distributions, is developed for application to incomplete markets and heavy-tailed distributions. The pricing model involves an application of a generalized variance premium principle from insurance pricing to the pricing of a portfolio of nontraded risks relative to a portfolio of traded risks. This pricing model for a portfolio of insurance or financial risks reflects preferences for features of the distributions other than mean and variance, including kurtosis. The model reduces to the Capital Asset Pricing Model for multinormal portfolios and to a form of the CAPM in the case where the traded and nontraded risks have the same elliptical distribution. Journal: North American Actuarial Journal Pages: 119-135 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597440 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597440 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:119-135 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: From Phelim Boyle, PhD, Wilfrid Laurier University and the University of Waterloo Journal: North American Actuarial Journal Pages: 13-13 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597431 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597431 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:13a-13a Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Dufresne Author-X-Name-First: Daniel Author-X-Name-Last: Dufresne Title: Stochastic Life Annuities Abstract: This paper gives analytic approximations for the distribution of a stochastic life annuity. It is assumed that returns follow a geometric Brownian motion. The distribution of the stochastic annuity may be used to answer questions such as “What is the probability that an amount F is sufficient to fund a pension with annual amount y to a pensioner aged x?” The main idea is to approximate the future lifetime distribution with a combination of exponentials, and then apply a known formula (due to Marc Yor) related to the integral of geometric Brownian motion. The approximations are very accurate in the cases studied. Journal: North American Actuarial Journal Pages: 136-157 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597441 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597441 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:136-157 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: From Hans Gerber, ASA, University of Lausanne Journal: North American Actuarial Journal Pages: 13-13 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597432 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597432 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:13-13 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Title: “On Optimal Dividend Strategies in the Compound Poisson Model”, by Elias S. W. Shiu and Hans U. Gerber, April 2006 Journal: North American Actuarial Journal Pages: 158-161 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597442 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:158-161 Template-Type: ReDIF-Article 1.0 Author-Name: Helmut Gründl Author-X-Name-First: Helmut Author-X-Name-Last: Gründl Author-Name: Hato Schmeiser Author-X-Name-First: Hato Author-X-Name-Last: Schmeiser Title: “Capital Allocation In Insurance: Economic Capital And The Allocation Of The Default Option Value,” By Michael Sherris And John van der Hoek, April 2006 Journal: North American Actuarial Journal Pages: 163-164 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597443 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597443 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:163-164 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: From John Beekman, ASA, Ball State University Journal: North American Actuarial Journal Pages: 11-13 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597430 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:11-13 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: James C. Hickman Journal: North American Actuarial Journal Pages: 1-11 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597429 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597429 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:1-11 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Panjer Author-X-Name-First: Harry Author-X-Name-Last: Panjer Title: Remembering Jim Hickman Journal: North American Actuarial Journal Pages: iii-iii Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597428 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597428 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Cristina Gutiérrez Author-X-Name-First: Cristina Author-X-Name-Last: Gutiérrez Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: Adult Polycystic Kidney Disease and Insurance Abstract: Adult Polycystic Kidney Disease (APKD) is a single-gene autosomal dominant genetic disorder leading to end-stage renal disease (ESRD, meaning kidney failure). It is associated with mutations in either of two genes, APKD1 and APKD2, and although diagnosis is still mostly by ultrasonography rather than DNA-based tests, this may change in the future. Recent studies have shown that the rates of onset of ESRD associated with APKD1 mutations are much greater than those associated with APKD2 mutations, a form of genetic heterogeneity that differs from, for example, familial breast cancer. In this paper we model the the impact of mutations in APKD1 or APKD2 on critical illness insurance, extending the work of Gutiérrez and Macdonald (2003), which was based on studies predating DNA-based tests. We then extend the model to life insurance and show that the financial impact is strongly dependent on the availability of treatment (dialysis and transplant), but that if it is available, extra premiums for life insurance are modest. We show that genetic heterogeneity introduces a novel problem, because carrying an APKD2 mutation is less risky than having a family history of APKD. Thus, in jurisdictions where family history may be used in underwriting but genetic tests may not, it may be illegal to use knowledge that benefits the applicant. Journal: North American Actuarial Journal Pages: 90-118 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597439 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597439 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:90-118 Template-Type: ReDIF-Article 1.0 Author-Name: Natalia Gavrilova Author-X-Name-First: Natalia Author-X-Name-Last: Gavrilova Author-Name: Leonid Gavrilov Author-X-Name-First: Leonid Author-X-Name-Last: Gavrilov Title: Search for Predictors of Exceptional Human Longevity Abstract: This paper explores new opportunities provided by the ongoing revolution in information technology, computer science, and Internet expansion for studies of exceptional human longevity. To this aim, the detailed family data for 991 alleged centenarians born between 1875 and 1899 in the United States were extracted from publicly available computerized family histories of 75 million individuals available at the Rootsweb site. To validate the age of the centenarians, these records were linked first to the Social Security Administration Death Master File records (for death date validation) and then to the records of the U.S. censuses for 1900, 1910, and 1920 (for birth date validation). The results of this cross-validation study demonstrated that computerized genealogies may serve as a useful starting point for developing a reliable family-linked scientific database on exceptional human longevity.The resulting database on centenarians with validated ages was used in the study of the predictors of exceptional human longevity, including familial factors and early-life living conditions. The comparison of households where children (future centenarians) were raised (using data obtained through linkage of genealogies to early U.S. censuses) with control households drawn from the Integrated Public Use Microdata Series for the 1900 U.S. census suggests that a farm background (farm ownership by parents in particular) and childhood residence in the Western region of the United States may be predictive for subsequent survival to age 100. These findings are consistent with the hypothesis that lower burden of sickness during childhood (expressed as lower child mortality in families of farm owners and families living in the West) may have far-reaching consequences for survival to extreme old ages.Analysis of familial factors suggests that there may be a link between exceptional longevity and a person’s birth order. It was found that first-born daughters are three times more likely to survive to age 100, compared to later-born daughters of higher birth orders (7+). First-born sons are twice more likely to become centenarians compared to sons having birth order between four and six. Further within-family comparison of centenarians with their siblings found that the protective effect of being first-born is driven mostly by the young maternal age at the person’s birth (being born to a mother younger than 25 years). Being born to a young mother is an important withinfamily predictor of human longevity, and even at age 75 it is still important to be born to young mother to survive to 100 years. Journal: North American Actuarial Journal Pages: 49-67 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597437 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597437 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:49-67 Template-Type: ReDIF-Article 1.0 Author-Name: Siu-Hang Li Author-X-Name-First: Siu-Hang Author-X-Name-Last: Li Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Title: The Lee-Carter Model for Forecasting Mortality, Revisited Abstract: Interrupting phenomena are commonly encountered in time-series data analysis with the study of mortality trends being no exception. Nevertheless, previous demographic forecasts have paid little attention to the existence of such phenomena. In this study we use mortality data from Canada and the United States to perform time-series outlier analysis on the key component of the Lee-Carter model: the mortality index. We begin by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical trends of the mortality index. We then try to match the identified outliers with important events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model reestimation. The empirical results indicate that the outlieradjusted model could achieve better fits and more efficient forecasts of variables such as the central rates of death and the life expectancies at birth. Finally, we conclude our study with possible extensions on the valuations of life annuities and the probabilistic distribution of the highest attained age, incorporating the effect of mortality improvement portrayed by the revised model. Journal: North American Actuarial Journal Pages: 68-89 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597438 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597438 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:68-89 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Capital Allocation In Insurance: Economic Capital And The Allocation Of The Default Option Value - Discussion by Helmut Gründl; Hato Schmeiser Journal: North American Actuarial Journal Pages: 164-165 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597444 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597444 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:164-165 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: From Robert Shapiro, FSA, The Shapiro Network Inc. Journal: North American Actuarial Journal Pages: 16-16 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597435 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597435 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:16-16 Template-Type: ReDIF-Article 1.0 Author-Name: Bonnie-Jeanne MacDonald Author-X-Name-First: Bonnie-Jeanne Author-X-Name-Last: MacDonald Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Title: The Impact of DC Pension Systems on Population Dynamics Abstract: This study investigates the risk inherent in defined contribution (DC) pension plans on an individual and aggregate basis, based on U.S. data. Our aim is to gain insight into the consequences of a DC pension scheme becoming the predominant pillar of retirement income for an entire society. Using the stochastic simulated output of a DC flexible age-of-retirement model, we first determine the optimal investment strategies. We then examine the demographic retirement dynamics of an entire population of DC pension plan participants.We observe that even for the most risk-averse plan members there is a high level of uncertainty in an individual’s age at retirement. At the aggregate population level, we find that this uncertainty does not get dampened to any great extent by a diversification effect. Instead, the central role played by the market in determining retirement dates results in significant variation in the dependency ratio (the ratio of retirees to workers) over time. In addition, an attempt to ameliorate the outcome by introducing additional realistic features in the DC population modeling did little to dampen this volatility, which suggests that countries dominated by DC schemes of this type may, over time, be exposed to significant risk in the size of its labor force. Journal: North American Actuarial Journal Pages: 17-48 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597436 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597436 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:17-48 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: From Robert V. Hogg, PhD, University of Iowa Journal: North American Actuarial Journal Pages: 13-14 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597433 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597433 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:13-14 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: From Warren Luckner, FSA, University of Nebraska-Lincoln Journal: North American Actuarial Journal Pages: 14-16 Issue: 1 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597434 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597434 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:1:p:14-16 Template-Type: ReDIF-Article 1.0 Author-Name: Jing Ai Author-X-Name-First: Jing Author-X-Name-Last: Ai Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Author-Name: Linda Golden Author-X-Name-First: Linda Author-X-Name-Last: Golden Title: Assessing Consumer Fraud Risk in Insurance Claims Abstract: We present an unsupervised learning method for classifying consumer insurance claims according to their suspiciousness of fraud versus nonfraud. The predictor variables contained within a claim file that are used in this analysis can be binary, ordinal categorical, or continuous variates. They are constructed such that the ordinal position of the response to the predictor variable bears a monotonic relationship with the fraud suspicion of the claim. Thus, although no individual variable is of itself assumed to be determinative of fraud, each of the individual variables gives a “hint” or indication as to the suspiciousness of fraud for the overall claim file. The presented method statistically concatenates the totality of these “hints” to make an overall assessment of the ranking of fraud risk for the claim files without using any a priori fraud-classified or -labeled subset of data. We first present a scoring method for the predictor variables that puts all the variables (whether binary “red flag indicators,” ordinal categorical variables with different categories of possible response values, or continuous variables) onto a common –1 to 1 scale for comparison and further use. This allows us to aggregate variables with disparate numbers of potential values. We next show how to concatenate the individual variables and obtain a measure of variable worth for fraud detection, and then how to obtain an overall holistic claim file suspicion value capable of being used to rank the claim files for determining which claims to pay and the order in which to investigate claims further for fraud. The proposed method provides three useful outputs not usually available with other unsupervised methods: (1) an ordinal measure of overall claim file fraud suspicion level, (2) a measure of the importance of each individual predictor variable in determining the overall suspicion levels of claims, and (3) a classification function capable of being applied to existing claims as well as new incoming claims. The overall claim file score is also available to be correlated with exogenous variables such as claimant demographics or highvolume physician or lawyer involvement. We illustrate that the incorporation of continuous variables in their continuous form helps classification and that the method has internal and external validity via empirical analysis of real data sets. A detailed application to automobile bodily injury fraud detection is presented. Journal: North American Actuarial Journal Pages: 438-458 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597568 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597568 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:438-458 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Kelly Author-X-Name-First: Mary Author-X-Name-Last: Kelly Author-Name: Sapna Isotupa Author-X-Name-First: Sapna Author-X-Name-Last: Isotupa Author-Name: Anne Kleffner Author-X-Name-First: Anne Author-X-Name-Last: Kleffner Title: The Impact of Adjuster Moral Hazard on Driving Records Abstract: In a first-party recovery scheme for automobile property damage, the first-party insurer compensates not-at-fault vehicular damage. In this scheme, adjusters may not have the incentive to assign liability when the driver is, in fact, at fault for the accident. This is due to adjusters not having to coordinate with a third-party adjuster, and, for insureds that carry collision coverage, the assignment of fault does not appreciably affect the compensation paid out. This in turn reduces the effectiveness of the experience-rating component of the insurance premium. Empirical evidence that supports the presence of incorrect fault assignment is provided. A stochastic model of experience rating analyzing the impact of incorrect fault assignment on driving record classes confirms that low-risk insureds pay more for insurance than if fault was correctly assigned. Journal: North American Actuarial Journal Pages: 425-437 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597567 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597567 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:425-437 Template-Type: ReDIF-Article 1.0 Author-Name: Kai Chen Author-X-Name-First: Kai Author-X-Name-Last: Chen Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: The DB Underpin Hybrid Pension Plan Abstract: In this paper the defined benefit underpin guarantee is valued as a financial option, within the traditional funding paradigms of actuarial science. Assuming fixed interest rates, and assuming that salaries can be treated as a tradable asset, we value the guarantee using fair value principles. Contribution rates are developed for the Entry Age Normal, Projected Unit Credit, and Traditional Unit Credit funding methods. In addition, for the accruals methods, we demonstrate the implied hedging strategy. The traditional unit credit offers the best method of these three, as it is consistent with the principles of financial economics, and the resulting contributions more naturally follow the cost of the emerging benefit, without creating expensive barriers to new hires. The method generates significant contribution volatility, and we demonstrate how this can be reduced with suitable benefit design and ongoing risk management. Journal: North American Actuarial Journal Pages: 407-424 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597566 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597566 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:407-424 Template-Type: ReDIF-Article 1.0 Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Author-Name: Yi Zhang Author-X-Name-First: Yi Author-X-Name-Last: Zhang Title: VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance Abstract: It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results. Journal: North American Actuarial Journal Pages: 459-482 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597569 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597569 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:459-482 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Yang Author-X-Name-First: Jun Author-X-Name-Last: Yang Title: “Valuation of Discrete Dynamic Fund Protection under Lévy Processes,” Hoi Ying Wong and Ka Wai Lam, April 2009 Journal: North American Actuarial Journal Pages: 520-524 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597573 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597573 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:520-524 Template-Type: ReDIF-Article 1.0 Author-Name: Kailiang Chen Author-X-Name-First: Kailiang Author-X-Name-Last: Chen Author-Name: Jia Liao Author-X-Name-First: Jia Author-X-Name-Last: Liao Author-Name: Xiaoyu Shang Author-X-Name-First: Xiaoyu Author-X-Name-Last: Shang Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Title: “A Quantitative Comparison of Stochastic Mortality Models Using Data from England and Wales and the United States,” Andrew J. G. Cairns, David Blake, Kevin Dowd, Guy D. Coughlan, David Epstein, Alen Ong, and Igor Balevich, Vol. 13, No. 1, 2009 Journal: North American Actuarial Journal Pages: 514-520 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597572 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597572 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:514-520 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Title: Analysis of a Generalized Penalty Function in a Semi-Markovian Risk Model Abstract: In this paper an extension of the semi-Markovian risk model studied by Albrecher and Boxma (2005) is considered by allowing for general interclaim times. In such a model, we follow the ideas of Cheung et al. (2010b) and consider a generalization of the Gerber-Shiu function by incorporating two more random variables in the traditional penalty function, namely, the minimum surplus level before ruin and the surplus level immediately after the second last claim prior to ruin. It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation. Detailed examples are also considered when either the interclaim times or the claim sizes are exponentially distributed. Finally, we also consider the case where the claim arrival process follows a Markovian arrival process. Probabilistic arguments are used to derive the discounted joint distribution of four random variables of interest in this risk model by capitalizing on an existing connection with a particular fluid flow process. Journal: North American Actuarial Journal Pages: 497-513 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597571 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597571 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:497-513 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Furman Author-X-Name-First: Edward Author-X-Name-Last: Furman Author-Name: Ričardas Zitikis Author-X-Name-First: Ričardas Author-X-Name-Last: Zitikis Title: Weighted Pricing Functionals With Applications to Insurance Abstract: We explore the role of weighted distributions in pricing insurance risks. In particular, we relate the distributions to actuarial and economic premium calculation principles and in this way provide a unifying methodology for constructing new principles and analyzing known ones. Journal: North American Actuarial Journal Pages: 483-496 Issue: 4 Volume: 13 Year: 2009 X-DOI: 10.1080/10920277.2009.10597570 File-URL: http://hdl.handle.net/10.1080/10920277.2009.10597570 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:13:y:2009:i:4:p:483-496 Template-Type: ReDIF-Article 1.0 Author-Name: Christopher Bone Author-X-Name-First: Christopher Author-X-Name-Last: Bone Author-Name: Olivia Mitchell Author-X-Name-First: Olivia Author-X-Name-Last: Mitchell Title: Authors’ Reply: Building Better Retirement Income Models - Discussion by Robert J. Myers; Anna Rappaport, January 1997 Journal: North American Actuarial Journal Pages: 11-12 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595581 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595581 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:11-12 Template-Type: ReDIF-Article 1.0 Author-Name: Cecil Nesbitt Author-X-Name-First: Cecil Author-X-Name-Last: Nesbitt Title: “Stochastic Models for Continuing Care Retirement Communities”, Bruce L. Jones, January 1997 Journal: North American Actuarial Journal Pages: 70-70 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595590 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595590 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:70-70 Template-Type: ReDIF-Article 1.0 Author-Name: Gregory Zebolsky Author-X-Name-First: Gregory Author-X-Name-Last: Zebolsky Title: “Stochastic Models for Continuing Care Retirement Communities”, Bruce L. Jones, January 1997 Journal: North American Actuarial Journal Pages: 70-72 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595591 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595591 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:70-72 Template-Type: ReDIF-Article 1.0 Author-Name: J. David Cummins Author-X-Name-First: J. Author-X-Name-Last: David Cummins Author-Name: Richard Phillips Author-X-Name-First: Richard Author-X-Name-Last: Phillips Author-Name: Stephen Smith Author-X-Name-First: Stephen Author-X-Name-Last: Smith Title: Corporate Hedging in the Insurance Industry Abstract: In this paper we investigate the extent to which insurance companies utilize financial derivatives contracts in the management of risks The data set we employ allows us to observe the universe of individual insurer transactions for a class of contracts, namely, those normally thought of as off-balance-sheet (OBS) We provide information on the number of insurers using various types of derivatives contracts and the volume of transactions in terms of notional amounts and the number of counterparties. Life insurers are most active in interest rate and foreign exchange derivatives, while property/casualty insurers tend to be active in trading equity option and foreign exchange contracts Using a multivariate probtt analysis, we explore the factors that potentially influence the existence of OBS activities. We also investigate questions relating to whether certain subsets of OBS transactions (for example, exchange traded) are related to such things as interest rate risk measures, organizational form and other characteristics that may discriminate between desired risk/return profiles across a cross-section of insurers. We find evidence consistent with the use of derivatives by insurers to hedge risks posed by guaranteed investment contracts (GICs), coilater-alized mortgage obligations (CMOs), and other sources of financial risk Journal: North American Actuarial Journal Pages: 13-40 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595582 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595582 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:13-40 Template-Type: ReDIF-Article 1.0 Author-Name: L. Lee Colquitt Author-X-Name-First: L. Author-X-Name-Last: Lee Colquitt Author-Name: Arlette Wilson Author-X-Name-First: Arlette Author-X-Name-Last: Wilson Title: “Corporate Hedging in the Insurance Industry: The Use of Financial Derivatives by U.S. Insurers”, J. David Cummins; Richard D. Phillips; Stephen D. Smith, January 1997 Journal: North American Actuarial Journal Pages: 40-44 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595583 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595583 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:40-44 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Venter Author-X-Name-First: Gary Author-X-Name-Last: Venter Author-Name: Morton Lane Author-X-Name-First: Morton Author-X-Name-Last: Lane Title: “Corporate Hedging in the Insurance Industry: The Use of Financial Derivatives by U.S. Insurers”, J. David Cummins; Richard D. Phillips; Stephen D. Smith, January 1997 Journal: North American Actuarial Journal Pages: 44-46 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595584 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595584 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:44-46 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Title: “Actuarial Issues in the Novels of Jane Austen”, Daniel D. Skwire, January 1997 Journal: North American Actuarial Journal Pages: 82-82 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595594 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595594 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:82-82 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Title: “Actuarial Issues in the Novels of Jane Austen”, Daniel D. Skwire, January 1997 Journal: North American Actuarial Journal Pages: 82-83 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595595 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595595 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:82-83 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: Author’s Reply: Stochastic Models for Continuing Care Retirement Communities - Discussion by Gray L. Brace; Ernest J. Moorhead; Niels H. Fischer; Cecil J. Nesbitt; Gregory T. Zebolsky, January 1997 Journal: North American Actuarial Journal Pages: 72-73 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595592 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595592 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:72-73 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Skwire Author-X-Name-First: Daniel Author-X-Name-Last: Skwire Title: Actuarial Issues in the Novels of Jane Austen Abstract: The novels of Jane Austen have enjoyed a resurgence of popularity recently, and many new readers have come to appreciate the relevance of her stories to modern times. This relevance should be particularly evident to actuaries, however, because the novels deal quite explicitly with the issues of wealth, inheritance, mortality, and life expectancy that confronted the nonworking classes of the early nineteenth century.This paper examines the six novels of Jane Austen from an actuarial perspective. It provides historical background on inheritances, clerical livings, and mortality, and it analyzes the way in which these issues are central to Austen’s novels. It uses a contemporary mortality table to assess the accuracy with which Austen’s characters estimate life expectancies and annuity calculations. It presents a close study of Sense and Sensibility, a novel in which a number of actuarial issues are central to the plot and are presented in great detail. Finally, it suggests that Austen’s own background and family life meant that actuarial issues were important in her life and therefore reflected in her novels.This paper offers a new argument for the relevance of great literature, and it offers actuaries a new perspective from which to explore and understand the history of their profession. Journal: North American Actuarial Journal Pages: 74-82 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595593 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595593 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:74-82 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rappaport Author-X-Name-First: Anna Author-X-Name-Last: Rappaport Title: “Building Better Retirement Income Models”, Christopher M. Bone; Olivia S. Mitchell, January 1997 Journal: North American Actuarial Journal Pages: 11-11 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595580 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595580 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:11-11 Template-Type: ReDIF-Article 1.0 Author-Name: Cecil Nesbitt Author-X-Name-First: Cecil Author-X-Name-Last: Nesbitt Title: “Statistical Independence and Fractional Age Assumptions”, Gordon E. Willmot, January 1997 Journal: North American Actuarial Journal Pages: 91-91 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595598 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595598 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:91-91 Template-Type: ReDIF-Article 1.0 Author-Name: Ernest Moorhead Author-X-Name-First: Ernest Author-X-Name-Last: Moorhead Author-Name: Niels Fischer Author-X-Name-First: Niels Author-X-Name-Last: Fischer Title: “Stochastic Models for Continuing Care Retirement Communities”, Bruce L. Jones, January 1997 Journal: North American Actuarial Journal Pages: 69-70 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595589 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595589 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:69-70 Template-Type: ReDIF-Article 1.0 Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: Author’s Reply: Statistical Independence and Fractional Age Assumptions - Discussion by Cecil Nesbitt; Elias S. W. Shiu; Serena Tiong, January 1997 Journal: North American Actuarial Journal Pages: 97-99 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595600 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595600 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:97-99 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Author-Name: Serena Tiong Author-X-Name-First: Serena Author-X-Name-Last: Tiong Title: “Statistical Independence and Fractional Age Assumptions”, Gordon E. Willmot, January 1997 Journal: North American Actuarial Journal Pages: 91-97 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595599 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595599 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:91-97 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Skwire Author-X-Name-First: Daniel Author-X-Name-Last: Skwire Title: Author’s Reply: Actuarial Issues in the Novels of Jane Austen - Discussion by Robert L. Brown; James C. Hickman, January 1997 Journal: North American Actuarial Journal Pages: 83-83 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595596 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595596 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:83-83 Template-Type: ReDIF-Article 1.0 Author-Name: Christopher Bone Author-X-Name-First: Christopher Author-X-Name-Last: Bone Author-Name: Olivia Mitchell Author-X-Name-First: Olivia Author-X-Name-Last: Mitchell Title: Building Better Retirement Income Models Abstract: U.S. policymakers interested in retirement issues are awakening to the fact that changes in our nation’s retirement income systems are absolutely essential in the years ahead. Predicting and understanding the effect of alternative policy choices require a concerted effort to build powerful retirement models. This paper assesses the state of the art in retirement income research and data and identifies important knowledge gaps that actuaries and economists can strive to fill in the near future. The paper also describes recent collaborative efforts of actuaries, economists, pension sponsors, and government policymakers that may be of interest to pension actuaries and others concerned with retirement issues. Journal: North American Actuarial Journal Pages: 1-10 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595578 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595578 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:1-10 Template-Type: ReDIF-Article 1.0 Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: Statistical Independence and Fractional Age Assumptions Abstract: This paper considers in some detail the issue of statistical independence of the curtate future lifetime and the fractional part of the future lifetime of a general status.Statistical independence is often employed in actuarial contexts, primarily because it leads to simple relationships between quantities of interest and statistical information that is of a discrete nature, such as a life table. The uniform distribution of deaths (UDD) assumption is the most commonly used because of its simplicity and intuitive appeal, but it can be somewhat restrictive. For example, all deaths or withdrawals may be assumed to be at a particular point in the year such as the middle; assumptions of this type are often made in a multiple decrement context. This paper attempts to unify these assumptions and extend their applicability in an actuarial context.The conditions for independence need to be stated carefully, and the last-survivor status is cited as an example in which failure to do so can lead to erroneous conclusions.The fractional independence (Fl) assumption is defined, and it is demonstrated that many of the formulas for life table functions that hold under the more restrictive UDD assumption are extended easily to the general Fl case. The simple relationship under UDD between insurances payable on other than an annual mode and those payable at the end of the year of death is extended to the Fl case as well. These results are then used to obtain results for annuities and reserves, again generalizing UDD relationships. It is then demonstrated that many contingent probabilities in the multiple life context are exactly the same under the Fl assumption as under the more restrictive UDD assumption. Finally, a very general result that holds in the multiple decrement context is shown to hold under the Fl assumption. Journal: North American Actuarial Journal Pages: 84-90 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595597 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595597 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:84-90 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Myers Author-X-Name-First: Robert Author-X-Name-Last: Myers Title: “Building Better Retirement Income Models”, Christopher M. Bone, Olivia S. Mitchell, January 1997 Journal: North American Actuarial Journal Pages: 10-11 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595579 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595579 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:10-11 Template-Type: ReDIF-Article 1.0 Author-Name: Joan Lamm-Tennant Author-X-Name-First: Joan Author-X-Name-Last: Lamm-Tennant Title: “Corporate Hedging in the Insurance Industry: The Use of Financial Derivatives by U.S. Insurers”, J. David Cummins; Richard D. Phillips; Stephen D. Smith, January 1997 Journal: North American Actuarial Journal Pages: 46-47 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595585 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595585 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:46-47 Template-Type: ReDIF-Article 1.0 Author-Name: J. David Cummins Author-X-Name-First: J. Author-X-Name-Last: David Cummins Author-Name: Richard Phillips Author-X-Name-First: Richard Author-X-Name-Last: Phillips Author-Name: Stephen Smith Author-X-Name-First: Stephen Author-X-Name-Last: Smith Title: Authors’ Reply: Corporate Hedging in the Insurance Industry: The Use of Financial Derivatives by U.S. Insurers - Discussion by L. Lee Colquitt; Arlette C. Wilson; Gray G. Venter; Morton Lane; Joan Lamm-Tennant, January 1997 Journal: North American Actuarial Journal Pages: 48-49 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595586 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595586 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:48-49 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: Stochastic Models for Continuing Care Retirement Communities Abstract: Continuing care retirement communities (CCRCs) offer housing and a variety of services, including long-term care. Typically, the cost of this long-term care is wholly or partially covered by entry and/or periodic fees. Thus, CCRCs provide a long-term-care insurance benefit. For this and other reasons, actuarial involvement in the financial management of CCRCs is desirable. To carry out actuarial analyses of CCRCs, appropriate models are required to describe the status of individual residents and the CCRC population.This paper presents models that assume that, at any time, a resident is in a given “state,” which is determined by the individual’s care requirements. The resident may make “transitions” between states at various times, and randomness is associated with both the transition times and the states entered. Actuarial calculations using such a model are discussed, and numerical illustrations are provided. A simple model is examined first; then generalizations are considered. The model for an individual resident can be embedded in a model for a CCRC population. This is explored with particular attention given to the “high-demand” situation in which potential residents are always waiting to enter the community. With this model, the goal is to analyze the future care requirements of the CCRC population. Journal: North American Actuarial Journal Pages: 50-68 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595587 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595587 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:50-68 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Brace Author-X-Name-First: Gary Author-X-Name-Last: Brace Title: “Stochastic Models for Continuing Care Retirement Communities”, Bruce L. Jones, January 1997 Journal: North American Actuarial Journal Pages: 69-69 Issue: 1 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595588 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595588 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:1:p:69-69 Template-Type: ReDIF-Article 1.0 Author-Name: Bob Beuerlein Author-X-Name-First: Bob Author-X-Name-Last: Beuerlein Title: Editorial Independence Journal: North American Actuarial Journal Pages: iii-iii Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597397 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597397 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:iii-iii Template-Type: ReDIF-Article 1.0 Author-Name: Bert Kestenbaum Author-X-Name-First: Bert Author-X-Name-Last: Kestenbaum Author-Name: B. Ferguson Author-X-Name-First: B. Author-X-Name-Last: Ferguson Title: The Number of Centenarians in the United States on January 1, 1990, 2000, AND 2010 Based on Improved Medicare Data Journal: North American Actuarial Journal Pages: 1-6 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597398 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597398 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:1-6 Template-Type: ReDIF-Article 1.0 Author-Name: C. Pinkham Author-X-Name-First: C. Author-X-Name-Last: Pinkham Author-Name: Marianne Cumming Author-X-Name-First: Marianne Author-X-Name-Last: Cumming Author-Name: Howard Minuk Author-X-Name-First: Howard Author-X-Name-Last: Minuk Title: The Metabolic Syndrome and All-Cause Mortality in an Insured Lives Population Abstract: Metabolic syndrome and its association with mortality have not been studied in insured lives populations. The Swiss Re Study evaluated metabolic syndrome prevalence and associated mortality from all causes and circulatory disease in a cohort of 35,470 predominantly healthy individuals, aged 18–83 years, who were issued life insurance policies between 1986 and 1997. Metabolic syndrome was defined using the National Cholesterol Education Program (NCEP) Expert Panel Adult Treatment Panel (ATP) III guidelines. The NCEP obesity criteria were modified with a prediction equation using body mass index, gender, and age substituted for waist circumference. Adjustments also were made for nonfasting triglyceride and blood glucose values. Risk ratios for policyholders identified with metabolic syndrome were 1.16 (P = .156) for mortality from all causes and 1.45 (P = .080) for mortality from circulatory disease compared with individuals without the syndrome. Risk was proportional to the number of components, or score, of the metabolic syndrome present. Risk ratios for metabolic syndrome score were 1.14 (P < .001) for mortality from all causes and 1.38 (P < .001) for mortality from circulatory disease compared with individuals without metabolic syndrome factors. In both all-cause and circulatory death models, relative risk was highest for the blood pressure risk factor. Based on a modified NCEP definition, increased mortality risk is associated with metabolic syndrome in an insured lives cohort and has life insurance mortality pricing implications. Journal: North American Actuarial Journal Pages: 7-16 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597399 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597399 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:7-16 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: “On Optimal Dividend Strategies in the Compound Poisson Model”, by Hans U. Gerber and Elias S. W. Shiu, April 2006 Journal: North American Actuarial Journal Pages: 78-79 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597408 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597408 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:78a-79a Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: On Optimal Dividend Strategies in the Compound Poisson Model - Discussion by Hansjörg Albrecher; Stefan Thonhauser; Bangwon Ko; Nathaniel Smith; Chuancun Yin; Xiaowen Zhou Journal: North American Actuarial Journal Pages: 84-84 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597409 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597409 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:84-84 Template-Type: ReDIF-Article 1.0 Author-Name: Bangwon Ko Author-X-Name-First: Bangwon Author-X-Name-Last: Ko Title: “On Optimal Dividend Strategies in the Compound Poisson Model”, by Hans U. Gerber and Elias S. W. Shiu, April 2006 Journal: North American Actuarial Journal Pages: 71-75 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597405 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597405 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:71-75 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Stefan Thonhauser Author-X-Name-First: Stefan Author-X-Name-Last: Thonhauser Title: “On Optimal Dividend Strategies in the Compound Poisson Model”, by Hans U. Gerber and Elias S. W. Shiu, April 2006 Journal: North American Actuarial Journal Pages: 68-71 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597404 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597404 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:68-71 Template-Type: ReDIF-Article 1.0 Author-Name: Chuancun Yin Author-X-Name-First: Chuancun Author-X-Name-Last: Yin Title: “On Optimal Dividend Strategies in the Compound Poisson Model”, by Hans U. Gerber and Elias S. W. Shiu, April 2006 Journal: North American Actuarial Journal Pages: 78-79 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597407 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597407 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:78-79 Template-Type: ReDIF-Article 1.0 Author-Name: Nathaniel Smith Author-X-Name-First: Nathaniel Author-X-Name-Last: Smith Title: “On Optimal Dividend Strategies in the Compound Poisson Model”, by Hans U. Gerber and Elias S. W. Shiu, April 2006 Journal: North American Actuarial Journal Pages: 76-78 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597406 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597406 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:76-78 Template-Type: ReDIF-Article 1.0 Author-Name: Beverly Orth Author-X-Name-First: Beverly Author-X-Name-Last: Orth Title: Managing Longevity Risk in U.S. Retirement Plans Through Mandatory Annuitization Abstract: Over the past 20 years, the United States has experienced a profound shift in the way that employment-based retirement benefits are delivered to workers. The traditional life annuity from a defined benefit (DB) plan has been largely replaced by lump sums from defined contribution (DC) plans. Along with investment risk, American workers are bearing a larger share of the longevity risk inherent in all retirement systems.As Americans benefit from longer lives, they are facing a harsh reality: will their retirement assets last long enough? Workers have embraced the flexibility offered by the widely available, and very popular, 401(k) plan. Often described as a do-it-yourself retirement program, these plans have allowed workers to accumulate significant levels of retirement savings. Employers like them too because they are less costly and easier to administer than traditional DB plans. Will this enthusiasm wane as baby boomers retire and face the daunting task of managing this pool of assets over retirements that can span 30 or 40 years or longer?Retirees have been reluctant to annuitize their assets for many reasons, and the annuity market in the United States is relatively small. The shift from DB to DC plans has left a majority of workers with only one form of annuitized benefit: Social Security. Yet life annuities offer the best method of managing longevity risk, both for the individual and for society.This paper suggests a possible framework for the mandatory annuitization of U.S. retirement savings, considers the experience of other countries, and analyzes the advantages and disadvantages of mandatory annuitization. If properly structured, it is possible that the benefits of an annuity mandate would outweigh the drawbacks. Journal: North American Actuarial Journal Pages: 32-44 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597401 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597401 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:32-44 Template-Type: ReDIF-Article 1.0 Author-Name: L. Colquitt Author-X-Name-First: L. Author-X-Name-Last: Colquitt Author-Name: Robert Hoyt Author-X-Name-First: Robert Author-X-Name-Last: Hoyt Author-Name: Kathleen McCullough Author-X-Name-First: Kathleen Author-X-Name-Last: McCullough Title: The Impact of Asbestos and Environmental Reserves Increases on Shareholder Wealth Abstract: Between 1992 and 2001 significant reserves increase announcements were made by several major property/liability insurers. These reserves increases were for the purpose of recognizing expected asbestos and environmental (A&E) liability. Although most analysts agree that U.S. insurers are underreserved for asbestos and environmental liability, how the market reacts to an insurer’s announcement of an increase in these reserves has not been analyzed. An insurer that is significantly underreserved is likely to be viewed by the market as lacking financial stability for the long term. However, when a company increases its reserves, there is a charge to income and a reduction in capital. If surplus is diminished sufficiently as a result of the increased reserving, regulatory attention and eroding shareholder and market confidence could result as well. By calculating the sample insurers’ cumulative abnormal returns surrounding the largest asbestos and environmental reserves increase announcements made between 1992 and 2001, the study estimates and documents the market’s reaction to these reserves increase announcements. We further explore the potential impact of additional asbestos and environmental liability exposure reporting requirements. Starting with 1995 statutory annual accounting statements, Footnote 24 required additional reporting by insurers of their asbestos and environmental liability exposure (1995 statements were publicly available by the end of the first quarter of 1996). When looking at reserves increase announcements prior to this additional reporting requirement, we find that most insurers announcing large increases in asbestos and environmental reserves prior to 1996 experience a significant reduction in stock price in the days surrounding their announcement. However, consistent with the notion that the additional accounting disclosure requirements after 1995 (Footnote 24) provide valuable information on insurers’ exposure, we find that the announcement of A&E reserves increases after 1995 had no statistically significant effect on the market value of announcing insurers. Journal: North American Actuarial Journal Pages: 17-31 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597400 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597400 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:17-31 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: On The Merger Of Two Companies Abstract: This paper examines the merger of two stock companies under the premise, due to Bruno de Finetti, that the companies pay out dividends to their shareholders in such a way so as to maximize the expectation of the discounted dividends until (possible) ruin or insolvency. The aggregate net income streams of the two companies are modeled by a bivariate Wiener process. Explicit results are presented. In particular, it is shown that if for each company the product of the valuation force of interest and the square of the coefficient of variation of its aggregate net income process is less than 6.87%, the merger of the two companies would result in a gain. Journal: North American Actuarial Journal Pages: 60-67 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597403 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597403 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:60-67 Template-Type: ReDIF-Article 1.0 Author-Name: Enrique de Alba Author-X-Name-First: Enrique Author-X-Name-Last: de Alba Title: Claims Reserving When There Are Negative Values in the Runoff Triangle Abstract: This paper is concerned with the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts. Typically these negative values will be the result of salvage recoveries, payments from third parties, total or partial cancellation of outstanding claims due to initial overestimation of the loss or to a possible favorable jury decision in favor of the insurer, rejection by the insurer, or just plain errors. Some of the traditional methods of claims reserving, such as the chain-ladder technique, may produce estimates of the reserves even when there are negative values. However, many methods can break down in the presence of enough (in number and/or size) negative incremental claims if certain constraints are not met. Historically the chain-ladder method has been used as a gold standard (benchmark) because of its generalized use and ease of application. A method that improves on the gold standard is one that can handle situations where there are many negative incremental claims and/or some of these are large. This paper presents a Bayesian model to consider negative incremental values, based on a three-parameter log-normal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. It is concluded that the method has a clear advantage over other existing methods. A Markov chain Monte Carlo simulation is applied using the package WinBUGS. Journal: North American Actuarial Journal Pages: 45-59 Issue: 3 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10597402 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10597402 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:3:p:45-59 Template-Type: ReDIF-Article 1.0 Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: X. Sheldon Lin Author-X-Name-First: X. Sheldon Author-X-Name-Last: Lin Title: Efficient Greek Calculation of Variable Annuity Portfolios for Dynamic Hedging: A Two-Level Metamodeling Approach Abstract: The financial risk associated with the guarantees embedded in variable annuities cannot be addressed adequately by traditional actuarial techniques. Dynamical hedging is used in practice to mitigate the financial risk arising from variable annuities. However, a major challenge of dynamical hedging is to calculate the dollar Deltas of a portfolio of variable annuities within a short time interval so that rebalancing can be done on a timely basis. In this article, we propose a two-level metamodeling approach to efficiently estimating the partial dollar Deltas of a portfolio of variable annuities under a multiasset framework. The first-level metamodel is used to estimate the partial dollar Deltas at some well-chosen market levels, and the second-level metamodel is used to estimate the partial dollar Deltas at the current market level based on the precalculated partial dollar Deltas. Our numerical results show that the proposed approach performs well in terms of accuracy and speed. Journal: North American Actuarial Journal Pages: 161-177 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2016.1245623 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1245623 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:161-177 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Tianxiang Shi Author-X-Name-First: Tianxiang Author-X-Name-Last: Shi Author-Name: Wei Wei Author-X-Name-First: Wei Author-X-Name-Last: Wei Title: Joint Insolvency Analysis of a Shared MAP Risk Process: A Capital Allocation Application Abstract: In recent years, multivariate insurance risk processes have received increasing attention in risk theory. First-passage-time problems in the context of these insurance risk processes are of primary interest for risk management purposes. In this article we study joint-ruin problems of two risk undertakers in a proportionally shared Markovian claim arrival process. Building on the existing work in the literature, joint-ruin–related quantities are thoroughly analyzed by capitalizing on existing results in certain univariate insurance surplus processes. Finally, an application is considered where the finite-time and infinite-time joint-ruin probabilities are used as risk measures to allocate risk capital among different business lines. The proposed joint-ruin allocation principle enables us to not only capture the risk dynamics over a given time horizon, but also overcome the “cross-subsidizing” effect of many existing allocation principles. Journal: North American Actuarial Journal Pages: 178-192 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2016.1246254 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1246254 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:178-192 Template-Type: ReDIF-Article 1.0 Author-Name: Ennio Badolati Author-X-Name-First: Ennio Author-X-Name-Last: Badolati Author-Name: Sandra Ciccone Author-X-Name-First: Sandra Author-X-Name-Last: Ciccone Title: On Cramér's First Contributions to Ruin Theory Abstract: In this article, we discuss some of the first contributions due to Harald Cramér to Collective Risk Theory. We examine the introduction and the use of a particular ruin function that nowadays has been lost even if, as we will see, it has many points in common with the severity of ruin. Journal: North American Actuarial Journal Pages: 193-203 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2016.1245624 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1245624 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:193-203 Template-Type: ReDIF-Article 1.0 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Author-Name: Tzuling Lin Author-X-Name-First: Tzuling Author-X-Name-Last: Lin Title: A Bühlmann Credibility Approach to Modeling Mortality Rates Abstract: In this article, we first propose a Bühlmann nonparametric credibility approach to forecasting mortality rates, and we then compare forecasting performances between the proposed Bühlmann approach and the Lee-Carter/Cairns-Blake-Dowd (CBD) models. Empirical results based on mortality data for both genders of Japan, the United Kingdom, and the United States with two age spans, a wide range of fitting year spans, and three forecasting periods show that the credibility approach contributes to much better forecasting performances measured by the mean absolute percentage error. Moreover, we give an informative credibility interpretation regarding the average decrements of an individual time trend for age x and a group time trend for all ages, and we discuss the effects of the slope and intercept of the linear functions for the forecasted mortality rates under the proposed Bühlmann nonparametric credibility approach and the Lee-Carter/CBD models. Finally, we also estimate the parameters of the Bühlmann credibility approach in a semiparametric framework, and we provide a stochastic version of forecasting mortality rates for the Bühlmann credibility approach. Journal: North American Actuarial Journal Pages: 204-227 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2016.1246253 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1246253 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:204-227 Template-Type: ReDIF-Article 1.0 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Author-Name: Ryan Martin Author-X-Name-First: Ryan Author-X-Name-Last: Martin Title: A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims Abstract: Accurate prediction of future claims is a fundamentally important problem in insurance. The Bayesian approach is natural in this context, as it provides a complete predictive distribution for future claims. The classical credibility theory provides a simple approximation to the mean of that predictive distribution as a point predictor, but this approach ignores other features of the predictive distribution, such as spread, that would be useful for decision making. In this article, we propose a Dirichlet process mixture of log-normals model and discuss the theoretical properties and computation of the corresponding predictive distribution. Numerical examples demonstrate the benefit of our model compared to some existing insurance loss models, and an R code implementation of the proposed method is also provided. Journal: North American Actuarial Journal Pages: 228-241 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2016.1247720 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1247720 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:228-241 Template-Type: ReDIF-Article 1.0 Author-Name: Ruilin Tian Author-X-Name-First: Ruilin Author-X-Name-Last: Tian Author-Name: Samuel H. Cox Author-X-Name-First: Samuel H. Author-X-Name-Last: Cox Author-Name: Luis F. Zuluaga Author-X-Name-First: Luis F. Author-X-Name-Last: Zuluaga Title: Moment Problem and Its Applications to Risk Assessment Abstract: This article discusses how to assess risk by computing the best upper and lower bounds on the expected value E[φ(X)], subject to the constraints E[Xi] = μi for i = 0, 1, 2, …, n. φ(x) can take the form of the indicator function ϕ(x)=I(-∞,K](x)$\phi (x)=\mathbb {I}_{(-\infty,K]}(x)$ in which the bounds on Pr(X≤K)$\Pr (X \le K)$ are calculated and the form φ(x) = (ϕ(x) − K)+ in which the bounds on financial payments are found. We solve the moment bounds on E[I(-∞,K](X)]$\mathrm{E}[\mathbb {I}_{(-\infty,K]}(X)]$ through three methods: the semidefinite programming method, the moment-matching method, and the linear approximation method. We show that for practical purposes, these methods provide numerically equivalent results. We explore the accuracy of bounds in terms of the number of moments considered. We investigate the usefulness of the moment method by comparing the moment bounds with the “point” estimate provided by the Johnson system of distributions. In addition, we propose a simpler formulation for the unimodal bounds on E[I(-∞,K](X)]$\mathrm{E}[\mathbb {I}_{(-\infty,K]}(X)]$ compared to the existing formulations in the literature. For those problems that could be solved both analytically and numerically given the first few moments, our comparisons between the numerical and analytical results call attention to the potential differences between these two methodologies. Our analysis indicates the numerical bounds could deviate from their corresponding analytical counterparts. The accuracy of numerical bounds is sensitive to the volatility of X. The more volatile the random variable X is, the looser the numerical bounds are, compared to their closed-form solutions. Journal: North American Actuarial Journal Pages: 242-266 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2017.1302805 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1302805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:242-266 Template-Type: ReDIF-Article 1.0 Author-Name: Axel Bücher Author-X-Name-First: Axel Author-X-Name-Last: Bücher Author-Name: Felix Irresberger Author-X-Name-First: Felix Author-X-Name-Last: Irresberger Author-Name: Gregor N. F. Weiss Author-X-Name-First: Gregor N. F. Author-X-Name-Last: Weiss Title: Testing Asymmetry in Dependence with Copula-Coskewness Abstract: A new measure of asymmetry in dependence is proposed that is based on taking the difference between the margin-free coskewness parameters of the underlying copula. The new measure and a related test are applied to both a hydrological and a financial market data sample, and we show that both samples exhibit systematic asymmetric dependence. Journal: North American Actuarial Journal Pages: 267-280 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2017.1282876 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1282876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:267-280 Template-Type: ReDIF-Article 1.0 Author-Name: Jungmin Choi Author-X-Name-First: Jungmin Author-X-Name-Last: Choi Title: Indifference Pricing of a GLWB Option in Variable Annuities Abstract: We investigate the valuation problem of variable annuities with guaranteed lifelong/lifetime withdrawal benefit (GLWB) options, which give the policyholder the right to withdraw a specified amount as long as he or she lives, regardless of the performance of the investment. We assume the static approach that the policyholder’s withdrawal rate is a constant throughout the life of the contract. We apply the principle of equivalent utility to find the indifference price for a variable annuity with a GLWB contract with an equity-indexed death benefit. Using an exponential utility function, Hamilton-Jacobi-Bellman (HJB) type partial differential equations (PDEs) are derived for the pricing functions. We first assume the mortality is deterministic, and the pricing PDE is solved numerically using a finite difference method. The effects of various parameters are investigated, including the age at inception of the policyholder, withdrawal rate, risk-free rate, and volatility of the underlying asset. We also consider a roll-up option and analyze the effect of delaying the start of the withdrawals. Another pricing PDE is derived with a stochastic mortality, when the force of mortality is modeled with a stochastic differential equation. A finite difference method is used again to solve the pricing PDE numerically, and the sensitivities of the GLWB contracts with respect to the withdrawal rate and the risk-free rate are explored. Journal: North American Actuarial Journal Pages: 281-296 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2017.1283237 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1283237 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:281-296 Template-Type: ReDIF-Article 1.0 Author-Name: Leon Chen Author-X-Name-First: Leon Author-X-Name-Last: Chen Author-Name: Steven W. Pottier Author-X-Name-First: Steven W. Author-X-Name-Last: Pottier Title: The Impact of a Rating Agency's Private Information and Disclosed Causes of Rating Downgrades on Insurer Stock Returns Abstract: Existing studies document that bond and insurer rating downgrades are associated with negative abnormal returns but generally do not consider the reasons for the downgrade disclosed or implied in the downgrade announcement. Using hand-collected press releases (downgrade announcements) of A.M. Best Company (Best) for a sample of publicly traded insurance firms during the period 1996–2012, we classify and analyze downgrades based on the disclosed causes of the downgrades and whether the rating agency has implied reliance upon unfavorable private information or opinion. We find that during the three-day event window (−1, +1), rating downgrades overall generate a statistically significant cumulative average abnormal return (CAAR) of negative 7.76%. A significantly more negative CAAR of negative 11.46% is found for “financial-prospects-deterioration” downgrades with the perceived presence of Best's private information or opinion. For downgrades without any indication of Best's private information or opinion, the CAAR is negative 3.35%, which is significantly different from zero but significantly less negative than the CAAR of downgrades where private information or opinion is indicated. Downgrades with reported causes other than deterioration of a firm's fundamental financial performance or condition, such as increases in financial leverage and increased business risk taking, produced statistically significant CAAR of negative 3.19% during the (−1, +1) three-day event window, which is also significantly less negative than the CAAR of downgrades where private information or opinion is indicated. Our results provide evidence that downgrades where private information or opinion is likely and downgrades due to a decline in fundamental financial profiles contain more value-relevant information than other types of downgrades. Journal: North American Actuarial Journal Pages: 297-304 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2017.1279061 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1279061 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:297-304 Template-Type: ReDIF-Article 1.0 Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Author-Name: Min-Ming Wen Author-X-Name-First: Min-Ming Author-X-Name-Last: Wen Title: An Efficiency-Based Approach to Determining Potential Cost Savings and Profit Targets for Health Insurers: The Case of Obamacare Health Insurance CO-OPs Abstract: This research analyzes the performance of the health insurance consumer-operated and -oriented plan (CO-OPs), examines their medical services and operating efficiency, proposes an efficiency-based goal-oriented approach for cost reductions, profit targets, premium changes, and government subsidies, and provides an important guide for improvement potentials for both the CO-OP health insurance model and other health insurers. The CO-OPs are not satisfactory in the medical services efficiency, and they are much less efficient compared with other insurers. Potential cost reductions are significant using various (conservative) efficiency goals. Most CO-OPs suffer underwriting losses, as do many other insurers; a few CO-OPs are much more operating efficient than other insurers, but all CO-OPs need significant improvement of financial performance relative to benchmark insurers. Incorporating potential cost reductions, many CO-OPs would barely require any “premium changes and government subsidies,” and they are even capable of paying back the federal loans. With both potential cost reductions and premium increases, more CO-OPs would not need any help from the government but survive on their own. This research informs public debates and all stakeholders (including management, consumers, regulators, policymakers) of improvement potentials to be considered for related decision making besides other factors including the political environment and government policies. Journal: North American Actuarial Journal Pages: 305-321 Issue: 2 Volume: 21 Year: 2017 Month: 4 X-DOI: 10.1080/10920277.2017.1282318 File-URL: http://hdl.handle.net/10.1080/10920277.2017.1282318 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:305-321 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Optimal Dividends: Analysis with Brownian Motion - Discussion by Olivier Deprez; Hansjörg Albrecher Journal: North American Actuarial Journal Pages: 113-115 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596143 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596143 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:113-115 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Title: “Optimal Dividends: Analysis with Brownian Motion,” Ana C. Cebrián, Hans U. Gerber and Elias S.W. Shiu, January 2004 Journal: North American Actuarial Journal Pages: 111-113 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596142 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596142 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:111-113 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Credit Standing and the Fair Value of Liabilities: A Critique - Discussion by M. W. Chambers Journal: North American Actuarial Journal Pages: 116-117 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596145 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596145 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:116-117 Template-Type: ReDIF-Article 1.0 Author-Name: M. W. Chambers Author-X-Name-First: M. W. Author-X-Name-Last: Chambers Title: “Credit Standing and the Fair Value of Liabilities: A Critique,” Philip E. Heckman, January 2004 Journal: North American Actuarial Journal Pages: 115-116 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596144 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596144 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:115-116 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Deprez Author-X-Name-First: Olivier Author-X-Name-Last: Deprez Title: “Optimal Dividends: Analysis with Brownian Motion,” Ana C. Cebrián, Hans U. Gerber and Elias S.W. Shiu, January 2004 Journal: North American Actuarial Journal Pages: 111-111 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596141 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596141 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:111-111 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Beirlant Author-X-Name-First: Jan Author-X-Name-Last: Beirlant Author-Name: Elisabeth Joossens Author-X-Name-First: Elisabeth Author-X-Name-Last: Joossens Author-Name: Johan Segers Author-X-Name-First: Johan Author-X-Name-Last: Segers Title: “Generalized Pareto Fit to the Society of Actuaries’ Large Claims Database,” Ana C. Cebrián, Michel Denuit, and Philippe Lambert, July 2003 Journal: North American Actuarial Journal Pages: 108-111 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596140 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596140 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:108-111 Template-Type: ReDIF-Article 1.0 Author-Name: Charles Cowling Author-X-Name-First: Charles Author-X-Name-Last: Cowling Author-Name: Jon Exley Author-X-Name-First: Jon Author-X-Name-Last: Exley Author-Name: Nick Hudson Author-X-Name-First: Nick Author-X-Name-Last: Hudson Author-Name: John Shuttleworth Author-X-Name-First: John Author-X-Name-Last: Shuttleworth Author-Name: Andrew Smith Author-X-Name-First: Andrew Author-X-Name-Last: Smith Author-Name: Ian Sykes Author-X-Name-First: Ian Author-X-Name-Last: Sykes Title: “Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans,” M. Iqbal Owadally and Steven Haberman, January 2004 Journal: North American Actuarial Journal Pages: 121-122 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596147 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596147 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:121-122 Template-Type: ReDIF-Article 1.0 Author-Name: Jeremy Gold Author-X-Name-First: Jeremy Author-X-Name-Last: Gold Title: “Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans,” M. Iqbal Owadally and Steven Haberman, January 2004 Journal: North American Actuarial Journal Pages: 117-120 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596146 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596146 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:117-120 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans - Discussion by Jeremy Gold; Charles Cowling; Jon Exley; Nick Hudson; John Shuttleworth; Andrew Smith; Ian Sykes; Cliff A. Speed; Tim J. Gordon Journal: North American Actuarial Journal Pages: 124-125 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596149 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596149 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:124-125 Template-Type: ReDIF-Article 1.0 Author-Name: Cliff Speed Author-X-Name-First: Cliff Author-X-Name-Last: Speed Author-Name: Tim Gordon Author-X-Name-First: Tim Author-X-Name-Last: Gordon Title: “Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans,” M. Iqbal Owadally and Steven Haberman, January 2004 Journal: North American Actuarial Journal Pages: 122-124 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596148 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596148 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:122-124 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Mildenhall Author-X-Name-First: Stephen Author-X-Name-Last: Mildenhall Title: A Note on the Myers and Read Capital Allocation Formula Abstract: The Myers and Read capital allocation formula is an important new actuarial result. This paper gives an overview of the Myers and Read result, explains its significance to actuaries, and provides a simple proof. Then it explains the assumption that the allocation formula makes on the underlying families of loss distributions as expected losses by line vary. It shows that this assumption does not hold when insurers grow by writing more risks from a discrete group of insureds—as is typically the case. Finally, it shows that this failure has a material impact on the predicted results in a realistically sized portfolio of property casualty risks which will severely limit the practical application of the Myers and Read allocation formula. Journal: North American Actuarial Journal Pages: 32-44 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596135 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596135 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:32-44 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Sutton Author-X-Name-First: Harry Author-X-Name-Last: Sutton Author-Name: Roger Feldman Author-X-Name-First: Roger Author-X-Name-Last: Feldman Author-Name: Bryan Dowd Author-X-Name-First: Bryan Author-X-Name-Last: Dowd Title: Disruption of a Managed Competition Environment by Low-Ball Premium Bids Abstract: This paper reviews the movement among multiple health plan options between 1994 and 1998 for Minnesota state employees whose work site was located in the Minneapolis/St. Paul metropolitan area. During this period the employer contribution was based on the lowest family premium bid from a qualified plan in the county of the employee’s work site. In 1995 the largest individual practice association model HMO in the state, Medica, reduced its state premium by 25%, becoming the lowest-priced option. This resulted in massive transfers of enrollees between plans. The point of this study was to estimate the risk changes that resulted from these movements between plan options. We obtained enrollment data by age and gender from Blue Cross Blue Shield of Minnesota (Blue Cross) and applied age/gender risk weight factors derived from actuarial rate tables to the Blue Cross cells. Annual changes in risk weights by 10-20% were common in a number of Blue Cross subpopulations, and in one case, by more than 50%.The Blue Cross POS plan experienced increases in risk and went into a death spiral, while a second Blue Cross plan with a more restrictive provider network started with low risk, but experienced increases in risk when the Medica plan was withdrawn. Similar demographic data were not available from other plans offered by the state and claim costs were confidential, so the results pertain only to Blue Cross risks. The question is raised as to whether managed competition can work without some means of adjusting premium rates to the expected cost level of the enrollees of a particular health plan. All carriers seemed reluctant to guarantee premium rates after the 1994-1998 experience, and the state soon became self-insured. Journal: North American Actuarial Journal Pages: 45-55 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596136 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596136 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:45-55 Template-Type: ReDIF-Article 1.0 Author-Name: Carlos Wong-Fupuy Author-X-Name-First: Carlos Author-X-Name-Last: Wong-Fupuy Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: Projecting Mortality Trends Abstract: The sustained reduction in mortality rates and its systematic underestimation has been attracting the significant interest of researchers in recent times because of its potential impact on population size and structure, social security systems, and (from an actuarial perspective) the life insurance and pensions industry worldwide. Despite the number of papers published in recent years, a comprehensive review has not yet been developed.This paper attempts to be the starting point for that review, highlighting the importance of recently published research—most of the references cited span the last 10 years—and covering the main methodologies that have been applied to the projection of mortality rates in the United Kingdom and the United States. A comparative review of techniques used in official population projections, actuarial applications, and the most influential scientific approaches is provided. In the course of the review an attempt is made to identify common themes and similarities in methods and results.In both official projections and actuarial applications there is some evidence of systematic overestimation of mortality rates. Models developed by academic researchers seem to reveal a trade-off between the plausibility of the projected age pattern and the ease of measuring the uncertainty involved. The Lee-Carter model is one approach that appears to solve this apparent dilemma.There is a broad consensus across the resulting projections: (1) an approximately log-linear relationship between mortality rates and time, (2) decreasing improvements according to age, and (3) an increasing trend in the relative rate of mortality change over age. In addition, evidence suggests that excessive reliance on expert opinion—present to some extent in all methods—has led to systematic underestimation of mortality improvements. Journal: North American Actuarial Journal Pages: 56-83 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596137 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596137 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:56-83 Template-Type: ReDIF-Article 1.0 Author-Name: Wenge Zhu Author-X-Name-First: Wenge Author-X-Name-Last: Zhu Title: Risk-Based Capital Factor Determination With Jump Risk Abstract: Two approaches exist to set the risk-based capital (RBC) factors: the traditional probability of ruin approach and the more recently developed expected policyholder deficit approach, the latter of which has been accepted as a basis for NAIC regulatory RBC formula. For both approaches, there are examples illustrating the advantages of one over the other. The goal of this paper is to present a discussion of this issue by modeling the evolution of insurance risk as a jump-diffusion process. It is more consistent with modern financial theory to consider the issue in an intertemporal general equilibrium framework. By comparing the two approaches as applied to the jump-diffusion model, we may help clarify the ambiguity arising from using the two approaches in different examples. Journal: North American Actuarial Journal Pages: 84-95 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596138 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596138 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:84-95 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Venter Author-X-Name-First: Gary Author-X-Name-Last: Venter Title: Capital Allocation Survey with Commentary Abstract: This paper discusses a number of methods of allocating capital to business units, for example, line of business, profit center, etc. The goals of capital allocation include testing the profitability of business units and determining which units could best be grown to add value to the firm. Methods of approaching these questions without allocating capital are included in the discussion. Journal: North American Actuarial Journal Pages: 96-107 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596139 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596139 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:96-107 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Uma Suresh Author-X-Name-First: Uma Author-X-Name-Last: Suresh Title: Further Analysis of Future Canadian Health Care Costs Abstract: The Canadian public health care delivery system continues to experience growing needs for increased funding. The total health care delivery system today costs Canadians $98 billion a year or about 9.7% of GDP. Of that total cost, 71% is paid by the government, which means the taxpayers. While that may pale in comparison to the costs in the United States, it does make the Canadian system one of the five most expensive health care delivery systems in the world.While today’s cost pressures are of major concern, of even more concern are the costs being projected by many participants in the current health care debate for the period when the baby boom makes higher demands on the Canadian health care delivery system.Traditional projection methods, however, do not differentiate as to the use of health care systems between the elderly who survive the year versus those who die. This paper first looks at the impact that this differentiation could have on projected costs. It then looks at the impact that the wide use of advance directives might have on future health care costs and some of the issues surrounding their use. Journal: North American Actuarial Journal Pages: 1-10 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596133 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596133 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:1-10 Template-Type: ReDIF-Article 1.0 Author-Name: Chi Liu Author-X-Name-First: Chi Author-X-Name-Last: Liu Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Optimal Investment for an Insurer to Minimize Its Probability of Ruin Abstract: This paper studies optimal investment strategies of an insurance company. We assume that the insurance company receives premiums at a constant rate, the total claims are modeled by a compound Poisson process, and the insurance company can invest in the money market and in a risky asset such as stocks. This model generalizes the model in Hipp and Plum (2000) by including a risk-free asset. The investment behavior is investigated numerically for various claim-size distributions. The optimal policy and the solution of the associated Hamilton-Jacobi-Bellman equation are then computed under each assumed distribution. Our results provide insights for managers of insurance companies on how to invest. We also investigate the effects of changes in various factors, such as stock volatility, on optimal investment strategies, and survival probability. The model is generalized to cases in which borrowing constraints or reinsurance are present. Journal: North American Actuarial Journal Pages: 11-31 Issue: 2 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596134 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596134 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:11-31 Template-Type: ReDIF-Article 1.0 Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Author-Name: Andreas Kleefeld Author-X-Name-First: Andreas Author-X-Name-Last: Kleefeld Title: Modeling Severity and Measuring Tail Risk of Norwegian Fire Claims Abstract: The probabilistic behavior of the claim severity variable plays a fundamental role in calculation of deductibles, layers, loss elimination ratios, effects of inflation, and other quantities arising in insurance. Among several alternatives for modeling severity, the parametric approach continues to maintain the leading position, which is primarily due to its parsimony and flexibility. In this article, several parametric families are employed to model severity of Norwegian fire claims for the years 1981 through 1992. The probability distributions we consider include generalized Pareto, lognormal-Pareto (two versions), Weibull-Pareto (two versions), and folded-t. Except for the generalized Pareto distribution, the other five models are fairly new proposals that recently appeared in the actuarial literature. We use the maximum likelihood procedure to fit the models and assess the quality of their fits using basic graphical tools (quantile-quantile plots), two goodness-of-fit statistics (Kolmogorov-Smirnov and Anderson-Darling), and two information criteria (AIC and BIC). In addition, we estimate the tail risk of “ground up” Norwegian fire claims using the value-at-risk and tail-conditional median measures. We monitor the tail risk levels over time, for the period 1981 to 1992, and analyze predictive performances of the six probability models. In particular, we compute the next-year probability for a few upper tail events using the fitted models and compare them with the actual probabilities. Journal: North American Actuarial Journal Pages: 1-16 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2015.1062784 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1062784 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:1-16 Template-Type: ReDIF-Article 1.0 Author-Name: Kristen S. Moore Author-X-Name-First: Kristen S. Author-X-Name-Last: Moore Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Minimizing the Probability of Lifetime Ruin When Shocks Might Occur: Perturbation Analysis Abstract: We determine the optimal investment strategy to minimize the probability of an individual’s lifetime ruin when the underlying model parameters are subject to a shock. Specifically, we consider two possibilities: (1) changes in the individual’s net consumption and mortality rate and (2) changes in the parameters of the financial market. We assume that these rates might change once at a random time. Changes in an individual’s net consumption and mortality rate occur when the individual experiences an accident or other unexpected life event, while changes in the financial market occur due to shifts in the economy or in the political climate. We apply perturbation analysis to approximate the probability of lifetime ruin and the corresponding optimal investment strategy for small changes in the model parameters and observe numerically that these approximations are reasonable ones, even when the changes are not small. Journal: North American Actuarial Journal Pages: 17-36 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2015.1061441 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1061441 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:17-36 Template-Type: ReDIF-Article 1.0 Author-Name: César Neves Author-X-Name-First: César Author-X-Name-Last: Neves Author-Name: Cristiano Fernandes Author-X-Name-First: Cristiano Author-X-Name-Last: Fernandes Author-Name: Álvaro Veiga Author-X-Name-First: Álvaro Author-X-Name-Last: Veiga Title: Forecasting Longevity Gains for a Population with Short Time Series Using a Structural SUTSE Model: An Application to Brazilian Annuity Plans Abstract: In this article, a multivariate structural time series model with common stochastic trends is proposed to forecast longevity gains of a population with a short time series of observed mortality rates, using the information of a related population for which longer mortality time series exist. The state space model proposed here makes use of the seemingly unrelated time series equation and applies the concepts of related series and common trends to construct a proper model to predict the future mortality rates of a population with little available information. This common trends approach works by assuming the two populations’ mortality rates are affected by common factors. Further, we show how this model can be used by insurers and pension funds to forecast mortality rates of policyholders and beneficiaries. We apply the proposed model to Brazilian annuity plans where life expectancies and their temporal evolution are predicted using the forecast longevity gains. Finally, to demonstrate how the model can be used in actuarial practice, the best estimate of the liabilities and the capital based on underwriting risk are estimated by means of Monte Carlo simulation. The idiosyncratic risk effect in the process of calculating an amount of underwriting capital is also illustrated using that simulation. Journal: North American Actuarial Journal Pages: 37-56 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2015.1061442 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1061442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:37-56 Template-Type: ReDIF-Article 1.0 Author-Name: Paola Sebastiani Author-X-Name-First: Paola Author-X-Name-Last: Sebastiani Author-Name: Stacy L. Andersen Author-X-Name-First: Stacy L. Author-X-Name-Last: Andersen Author-Name: Avery I. McIntosh Author-X-Name-First: Avery I. Author-X-Name-Last: McIntosh Author-Name: Lisa Nussbaum Author-X-Name-First: Lisa Author-X-Name-Last: Nussbaum Author-Name: Meredith D. Stevenson Author-X-Name-First: Meredith D. Author-X-Name-Last: Stevenson Author-Name: Leslie Pierce Author-X-Name-First: Leslie Author-X-Name-Last: Pierce Author-Name: Samantha Xia Author-X-Name-First: Samantha Author-X-Name-Last: Xia Author-Name: Kelly Salance Author-X-Name-First: Kelly Author-X-Name-Last: Salance Author-Name: Thomas T. Perls Author-X-Name-First: Thomas T. Author-X-Name-Last: Perls Title: Familial Risk for Exceptional Longevity Abstract: One of the most glaring deficiencies in the current assessment of mortality risk is the lack of information concerning the impact of familial longevity. In this article we update estimates of sibling relative risk of living to extreme ages using data from more than 1700 sibships, and we begin to examine the trend for heritability for different birth-year cohorts. We also build a network model that can be used to compute the increased chance for exceptional longevity of a subject, conditional on his or her family history of longevity. The network includes familial longevity from three generations and can be used to understand the effects of paternal and maternal longevity on an individual's chance to live to an extreme age. Journal: North American Actuarial Journal Pages: 57-64 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2015.1061946 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1061946 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:57-64 Template-Type: ReDIF-Article 1.0 Author-Name: I. Duncan Author-X-Name-First: I. Author-X-Name-Last: Duncan Author-Name: M. Loginov Author-X-Name-First: M. Author-X-Name-Last: Loginov Author-Name: M. Ludkovski Author-X-Name-First: M. Author-X-Name-Last: Ludkovski Title: Testing Alternative Regression Frameworks for Predictive Modeling of Health Care Costs Abstract: Predictive models of health care costs have become mainstream in much health care actuarial work. The Affordable Care Act requires the use of predictive modeling-based risk-adjuster models to transfer revenue between different health exchange participants. Although the predictive accuracy of these models has been investigated in a number of studies, the accuracy and use of models for applications other than risk adjustment have not been the subject of much investigation. We investigate predictive modeling of future health care costs using several statistical techniques. Our analysis was performed based on a dataset of 30,000 insureds containing claims information from two contiguous years. The dataset contains more than 100 covariates for each insured, including detailed breakdown of past costs and causes encoded via coexisting condition flags. We discuss statistical models for the relationship between next-year costs and medical and cost information to predict the mean and quantiles of future cost, ranking risks and identifying most predictive covariates. A comparison of multiple models is presented, including (in addition to the traditional linear regression model underlying risk adjusters) Lasso GLM, multivariate adaptive regression splines, random forests, decision trees, and boosted trees. A detailed performance analysis shows that the traditional regression approach does not perform well and that more accurate models are possible. Journal: North American Actuarial Journal Pages: 65-87 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2015.1110491 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1110491 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:65-87 Template-Type: ReDIF-Article 1.0 Author-Name: Xiao Wang Author-X-Name-First: Xiao Author-X-Name-Last: Wang Title: Discussion on “Capital Forbearance, Ex Ante Life Insurance Guaranty Schemes, and Interest Rate Uncertainty,” by Ya-Wen Hwang, Shih-Chieh Chang, and Yang-Che Wu, Volume 19(2) Journal: North American Actuarial Journal Pages: 88-93 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2016.1143731 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1143731 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:88-93 Template-Type: ReDIF-Article 1.0 Author-Name: Ya-Wen Hwang Author-X-Name-First: Ya-Wen Author-X-Name-Last: Hwang Author-Name: Shih-Chieh Chang Author-X-Name-First: Shih-Chieh Author-X-Name-Last: Chang Author-Name: Yang-Che Wu Author-X-Name-First: Yang-Che Author-X-Name-Last: Wu Title: Response to Xiao Wang on His Comments on Our Paper Entitled, “Capital Forbearance, Ex Ante Life Insurance Guaranty Schemes, and Interest Rate Uncertainty” Journal: North American Actuarial Journal Pages: 94-94 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2016.1154778 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1154778 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:94-94 Template-Type: ReDIF-Article 1.0 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Author-Name: Ryan Martin Author-X-Name-First: Ryan Author-X-Name-Last: Martin Title: Discussion on “Credibility Estimation of Distribution Functions with Applications to Experience Rating in General Insurance,” by Xiaoqiang Cai, Limin Wen, Xianyi Wu, and Xian Zhou, Volume 19(4) Journal: North American Actuarial Journal Pages: 95-98 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2016.1143751 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1143751 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:95-98 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoqiang Cai Author-X-Name-First: Xiaoqiang Author-X-Name-Last: Cai Author-Name: Limin Wen Author-X-Name-First: Limin Author-X-Name-Last: Wen Author-Name: Xianyi Wu Author-X-Name-First: Xianyi Author-X-Name-Last: Wu Author-Name: Xian Zhou Author-X-Name-First: Xian Author-X-Name-Last: Zhou Title: Response to Liang Hong and Ryan Martin on Their Comments on Our Paper Entitled, “Credibility Estimation of Distribution Functions with Applications to Experience Rating in General Insurance” Journal: North American Actuarial Journal Pages: 99-100 Issue: 1 Volume: 20 Year: 2016 Month: 1 X-DOI: 10.1080/10920277.2016.1159071 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1159071 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:99-100 Template-Type: ReDIF-Article 1.0 Author-Name: Brian Schott Author-X-Name-First: Brian Author-X-Name-Last: Schott Title: Norman Thomson. Journal: North American Actuarial Journal Pages: 92-93 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596096 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596096 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:92-93 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Brown Author-X-Name-First: Robert Author-X-Name-Last: Brown Author-Name: Joanne McDaid Author-X-Name-First: Joanne Author-X-Name-Last: McDaid Title: Factors Affecting Retirement Mortality Abstract: As many countries consider mandatory individual retirement accounts as their answer to a secure social security system, the question arises as to whether all workers can get true “market value” annuities when they retire. It is clear today that private-sector life annuities are priced assuming that the applicant is healthy—very healthy. Very little underwriting or risk classification now exists in the individual annuity marketplace. However, if a large percentage of the population were looking to annuitize their social security accounts upon retirement, there would be strong pressure for more risk classes in the annuity-pricing structure.Even without the advent of individual accounts for social security, the authors of this paper feel there may be real market opportunities for more risk classification in the individual annuity market and the offering of “impaired life annuities.” Given that this pressure does or might soon exist, this paper reviews 45 recent research papers that look at factors that affect mortality after retirement. In particular, factors that seem to be important in predicting retirement mortality include age, gender, race and ethnicity, education, income, occupation, marital status, religion, health behaviors, smoking, alcohol, and obesity. for each factor, this paper gives highlights relative to the named factor of the impact expected from that variable as described in the 45 reviewed research papers.The authors believe there is a wealth of information contained in the summaries that follow, and it is our sincere hope that this paper will cause an increased interest in a more broadly based risk classification structure for individual annuities.Summaries of the 45 papers can be found at www.soa.org/sections/farm/farm.html. Journal: North American Actuarial Journal Pages: 24-43 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596083 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596083 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:24-43 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Mark Goovaerts Author-X-Name-First: Mark Author-X-Name-Last: Goovaerts Author-Name: Rob Kaas Author-X-Name-First: Rob Author-X-Name-Last: Kaas Title: Economic Capital Allocation Derived from Risk Measures Abstract: We examine properties of risk measures that can be considered to be in line with some “best practice” rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk measure. As a consequence, conditions arise for comparison as well as for addition of risk measures. We demonstrate that imposing properties that are generally valid for risk measures, in all possible dependency structures, based on the difference of the risk and the solvency margin, though providing opportunities to derive nice mathematical results, violates best practice rules. We show that so-called coherent risk measures lead to problems. In particular we consider an exponential risk measure related to a discrete ruin model, depending on the initial surplus, the desired ruin probability, and the risk distribution. Journal: North American Actuarial Journal Pages: 44-56 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596084 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596084 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:44-56 Template-Type: ReDIF-Article 1.0 Author-Name: Eddy Van Den Borre Author-X-Name-First: Eddy Author-X-Name-Last: Van Den Borre Title: “Economic Capital Allocation Derived from Risk Measures”, Eddy Van den Borre, January 2003 Journal: North American Actuarial Journal Pages: 56-57 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596085 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596085 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:56-57 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Title: Boyle, Phelim P., and Boyle, Feidlim, 2001, Journal: North American Actuarial Journal Pages: 145-146 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596094 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596094 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:145-146 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: The Reviewing Process Journal: North American Actuarial Journal Pages: iii-iv Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596095 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596095 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Economic Capital Allocation Derived from Risk Measures - Discussion by Jan Dhaene; Mark J. Goovaerts; Rob Kaas Journal: North American Actuarial Journal Pages: 57-59 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596086 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596086 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:57-59 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Pricing Perpetual Fund Protection with Withdrawal Option Abstract: Consider an American option that provides the amountif it is exercised at time t, t ≥0. For simplicity of language, we interpret S1(t) and S2(t) as the prices of two stocks. The option payoff is guaranteed not to fall below the price of stock 1 and is indexed by the price of stock 2 in the sense that, if F(t) > S1(t), the instantaneous growth rate of F(t) is that of S2(t). We call this option the dynamic fund protection option. For the two stock prices, the bivariate Black-Scholes model with constant dividend-yield rates is assumed. In the case of a perpetual option, closed-form expressions for the optimal exercise strategy and the price of the option are given. Furthermore, this price is compared with the price of the perpetual maximum option, and it is shown that the optimal exercise of the maximum option occurs before that of the dynamic fund protection option.Two general concepts in the theory of option pricing are illustrated: the smooth pasting condition and the construction of the replicating portfolio. The general result can be applied to two special cases. One is where the guaranteed level S1(t) is a deterministic exponential or constant function. The other is where S2(t) is an exponential or constant function; in this case, known results concerning the pricing of Russian options are retrieved. Finally, we consider a generalization of the perpetual lookback put option that has payoff [F(t) − κS1(t)], if it is exercised at time t. This option can be priced with the same technique. Journal: North American Actuarial Journal Pages: 60-77 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596087 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596087 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:60-77 Template-Type: ReDIF-Article 1.0 Author-Name: Chi Chiu Chu Author-X-Name-First: Chi Chiu Author-X-Name-Last: Chu Author-Name: Yue Kuen Kwok Author-X-Name-First: Yue Kuen Author-X-Name-Last: Kwok Title: “Pricing Perpetual Fund Protection with Withdrawal Option”, Hans U. Gerber and Elias S.W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 77-81 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596088 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596088 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:77-81 Template-Type: ReDIF-Article 1.0 Author-Name: Jérôme Pansera Author-X-Name-First: Jérôme Author-X-Name-Last: Pansera Title: “Pricing Perpetual Fund Protection with Withdrawal Option”, Hans U. Gerber and Elias S.W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 82-87 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596089 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596089 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:82-87 Template-Type: ReDIF-Article 1.0 Author-Name: Howard Bolnick Author-X-Name-First: Howard Author-X-Name-Last: Bolnick Title: Designing a World-Class Health Care System Abstract: Public health systems are finding it increasingly difficult to fund all the health care that their citizens want and need. Fiscal constraint is causing many nations to reconsider the respective roles of their public programs and private health insurance. The author examines the potential for and performance of health systems around the world and the advantages and disadvantages of public and private health financing. This analysis leads to the development of a framework for improvements in today’s mix of health care financing and to high-level principles for a better-coordinated relationship between public and private programs. The role of health actuaries in moving toward more effective health systems is then explored. Journal: North American Actuarial Journal Pages: 1-23 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596082 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596082 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:1-23 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Pricing Perpetual Fund Protection with Withdrawal Option - Discussion by Chi Chiu Chu; Yue Kuen Kwok; Jérôme Pansera; Carisa K.W. Yu Journal: North American Actuarial Journal Pages: 90-92 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596091 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596091 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:90-92 Template-Type: ReDIF-Article 1.0 Author-Name: Carisa Yu Author-X-Name-First: Carisa Author-X-Name-Last: Yu Title: “Pricing Perpetual Fund Protection with Withdrawal Option”, Hans U. Gerber and Elias S.W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 87-90 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596090 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596090 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:87-90 Template-Type: ReDIF-Article 1.0 Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Author-Name: Udi Makov Author-X-Name-First: Udi Author-X-Name-Last: Makov Title: Contaminated Exponential Dispersion Loss Models Abstract: A new family of contaminated exponential dispersion loss models is defined and some of its properties are examined. These models offer a wider family of loss distributions, allowing the modeling of extreme claims. Their usefulness is illustrated with real data. Journal: North American Actuarial Journal Pages: 116-127 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596093 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596093 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:116-127 Template-Type: ReDIF-Article 1.0 Author-Name: Cristina Gutiérrez Author-X-Name-First: Cristina Author-X-Name-Last: Gutiérrez Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: Adult Polycystic Kidney Disease and Critical Illness Insurance Abstract: Adult polycystic kidney disease (APKD) is a single-gene autosomal dominant genetic disorder leading to end-stage renal disease (ESRD, meaning kidney failure). It is associated with mutations in at least two genes, APKD1 and APKD2, but diagnosis is mostly by ultrasonography. We propose a model for critical illness (CI) insurance and estimate rates of onset of ESRD from APKD using two studies. Other events leading to claims under CI policies are included in the model, which we use to study (a) extra premiums under CI policies if the presence of an APKD mutation is known, and (b) the possible costs arising from adverse selection if this information is unavailable to insurers. The extra premiums are typically very high, but because APKD is rare, the possible cost of adverse selection is low. However, APKD is just one of a significant number of single-gene disorders, and this benign conclusion cannot be assumed to apply to all genetic disorders taken together. Moreover, ignoring known genetic risks in underwriting sets a precedent that could have unintended consequences for the underwriting of nongenetic risks of similar magnitude. Journal: North American Actuarial Journal Pages: 93-115 Issue: 2 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596092 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596092 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:2:p:93-115 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoming Liu Author-X-Name-First: Xiaoming Author-X-Name-Last: Liu Title: Annuity Uncertainty with Stochastic Mortality and Interest Rates Abstract: Risk analysis in actuarial science has shifted its focus from diversifiable risk to systematic risk in the last 20 years or so. This article contributes further in this direction by proposing the concept of annuity rate to take account of systematic risk inherent in annuity products. The annuity rate is the conditional expectation of the annuity’s future payments, given the future paths of mortality and interest rates. We provide an empirical study to investigate the impact of the two systematic risk factors on the distribution of the annuity rate. In particular, we adopt the Lee-Carter and the Cairns-Blake-Dowd models for mortality risk, and the one-factor and two-factor CIR models for interest risk. Monte Carlo simulation is used to provide numerical illustrations of sensitivity analysis of the annuity rate and of risk assessment of a guaranteed annuity option. Journal: North American Actuarial Journal Pages: 136-152 Issue: 2 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.795481 File-URL: http://hdl.handle.net/10.1080/10920277.2013.795481 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:2:p:136-152 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Fier Author-X-Name-First: Stephen Author-X-Name-Last: Fier Author-Name: Andre Liebenberg Author-X-Name-First: Andre Author-X-Name-Last: Liebenberg Title: Life Insurance Lapse Behavior Abstract: Life insurance policy lapses are detrimental to issuing insurers when lapses substantially deviate from insurer expectations. The extant literature has proposed and tested, using macroeconomic data, several hypotheses regarding lapse determinants. While macroeconomic data are useful in providing a general test of lapse determinants, the use of aggregate data precludes an analysis of microeconomic factors that may drive the lapse decision. We develop and test a microeconomic model of voluntary life insurance lapse behavior and provide some of the first evidence regarding household factors related to life insurance lapses. Our findings support and extend the prior evidence regarding lapse determinants. Consistent with the emergency fund hypothesis we find that voluntary lapses are related to large income shocks, and consistent with the policy replacement hypothesis we find that the decision to lapse a life insurance policy is directly related to the purchase of a different life insurance policy. We also find that age is an important moderating factor in the lapse decision. Changes in income appear to more directly affect the decision to lapse for younger households, while they are generally unrelated to the lapse decision for older households. Journal: North American Actuarial Journal Pages: 153-167 Issue: 2 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.803438 File-URL: http://hdl.handle.net/10.1080/10920277.2013.803438 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:2:p:153-167 Template-Type: ReDIF-Article 1.0 Author-Name: Maria Martínez-Miranda Author-X-Name-First: Maria Author-X-Name-Last: Martínez-Miranda Author-Name: Jens Nielsen Author-X-Name-First: Jens Author-X-Name-Last: Nielsen Author-Name: Richard Verrall Author-X-Name-First: Richard Author-X-Name-Last: Verrall Title: Double Chain Ladder and Bornhuetter-Ferguson Abstract: In this article we propose a method close to Double Chain Ladder (DCL) introduced by Martínez-Miranda, Nielsen, and Verrall (2012a). The proposed method is motivated by the potential lack of stability of the DCL method (and of the classical Chain ladder method [CLM] itself). We consider the implicit estimation of the underwriting year inflation in the CLM method and the explicit estimation of it in DCL. This may represent a weak point for DCL and CLM because the underwriting year inflation might be estimated with significant uncertainty. A key feature of the new method is that the underwriting year inflation can be estimated from the less volatile incurred data and then transferred into the DCL model. We include an empirical illustration that illustrates the differences between the estimates of the IBNR and RBNS cash flows from DCL and the new method. We also apply bootstrap estimation to approximate the predictive distributions. Journal: North American Actuarial Journal Pages: 101-113 Issue: 2 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.793158 File-URL: http://hdl.handle.net/10.1080/10920277.2013.793158 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:2:p:101-113 Template-Type: ReDIF-Article 1.0 Author-Name: Yunfan Tang Author-X-Name-First: Yunfan Author-X-Name-Last: Tang Title: Polynomial Approximation to Option Prices under Regime Switching Abstract: In this article we obtain the option pricing results using a polynomial approximation. A continuous-time Markov chain–governed volatility and return underlie the stock price generating process. We give European and lookback option prices under various conditions as well as discuss the precision and efficiency of our approach compared to other methods. The approximation methods are applicable for arbitrary regime settings and prove to be fast and accurate with multiple regimes. Journal: North American Actuarial Journal Pages: 168-179 Issue: 2 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.813836 File-URL: http://hdl.handle.net/10.1080/10920277.2013.813836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:2:p:168-179 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Life Insurance Purchasing to Maximize Utility of Household Consumption Abstract: We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income. For insurance purchased via a single premium or premium payable continuously, we explicitly determine the optimal death benefit. We show that if the premium is determined to target a specific probability of loss per policy, then the rates of consumption are identical under single premium or continuously payable premium. Thus, not only is equivalence of consumption achieved for the households under the two premium schemes, it is also obtained for the insurance company in the sense of equivalence of loss probabilities. Journal: North American Actuarial Journal Pages: 114-135 Issue: 2 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.793159 File-URL: http://hdl.handle.net/10.1080/10920277.2013.793159 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:2:p:114-135 Template-Type: ReDIF-Article 1.0 Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Author-Name: Jae-Kyung Woo Author-X-Name-First: Jae-Kyung Author-X-Name-Last: Woo Title: On the Class of Erlang Mixtures with Risk Theoretic Applications Abstract: A wide variety of distributions are shown to be of mixed-Erlang type. Useful computational formulas result for many quantities of interest in a risk-theoretic context when the claim size distribution is an Erlang mixture. In particular, the aggregate claims distribution and related quantities such as stop-loss moments are discussed, as well as ruin-theoretic quantities including infinitetime ruin probabilities and the distribution of the deficit at ruin. A very useful application of the results is the computation of finite-time ruin probabilities, with numerical examples given. Finally, extensions of the results to more general gamma mixtures are briefly examined. Journal: North American Actuarial Journal Pages: 99-115 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597450 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:99-115 Template-Type: ReDIF-Article 1.0 Author-Name: Sarah Christiansen Author-X-Name-First: Sarah Author-X-Name-Last: Christiansen Title: “Managing Longevity Risk in the U.S. Retirement Plans through Mandatory Annuitization,” Beverly J. Orth, July 2006 Journal: North American Actuarial Journal Pages: 154-156 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597460 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597460 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:154-156 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Managing Longevity Risk in the U.S. Retirement Plans through Mandatory Annuitization - Discussion by Sarah L. M. Christiansen Journal: North American Actuarial Journal Pages: 156-156 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597461 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597461 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:156-156 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Stefan Thonhauser Author-X-Name-First: Stefan Author-X-Name-Last: Thonhauser Title: “On the Merger of Two Companies,” Hans Gerber and Elias S. W. Shiu, July 2006 Journal: North American Actuarial Journal Pages: 157-159 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597462 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597462 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:157-159 Template-Type: ReDIF-Article 1.0 Author-Name: Rong Wu Author-X-Name-First: Rong Author-X-Name-Last: Wu Author-Name: Yuhua Lu Author-X-Name-First: Yuhua Author-X-Name-Last: Lu Author-Name: Ying Fang Author-X-Name-First: Ying Author-X-Name-Last: Fang Title: On the Gerber-Shiu Discounted Penalty Function for the Ordinary Renewal Risk Model with Constant Interest Abstract: In this paper we study the Gerber-Shiu discounted penalty function for the ordinary renewal risk model modified by the constant interest on the surplus. Explicit answers are expressed by an infinite series, and a relational formula for some important joint density functions is derived. Applications of the results to the compound Poisson model are given. Finally, a lower bound and an upper bound for the ultimate ruin probability are derived. Journal: North American Actuarial Journal Pages: 119-134 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597453 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597453 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:119-134 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: On the Merger of Two Companies - Discussion by Hansjörg Albrecher; Stefan Thonhauser Journal: North American Actuarial Journal Pages: 159-159 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597463 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597463 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:159-159 Template-Type: ReDIF-Article 1.0 Author-Name: Bangwon Ko Author-X-Name-First: Bangwon Author-X-Name-Last: Ko Title: ”On the Gerber-Shiu Discounted Penalty Function for the Ordinary Renewal Risk Model with Constant Interest“, Rong Wu; Yuhua Lu and Ying Fang, April 2007 Journal: North American Actuarial Journal Pages: 134-135 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597454 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597454 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:134-135 Template-Type: ReDIF-Article 1.0 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Author-Name: Howard Waters Author-X-Name-First: Howard Author-X-Name-Last: Waters Title: “On the Class of Erlang Mixtures with Risk Theoretic Applications”, Gordon E. Willmot and Jae-Kyung Woo, April 2007 Journal: North American Actuarial Journal Pages: 115-117 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597451 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597451 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:115-117 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: On the Class of Erlang Mixtures with Risk Theoretic Applications - Discussion by David C. M. Dickson; Howard R. Waters Journal: North American Actuarial Journal Pages: 118-118 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597452 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597452 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:118-118 Template-Type: ReDIF-Article 1.0 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Title: Moments of the Dividend Payments and Related Problems in a Markov-Modulated Risk Model Abstract: In this paper we derive some results on the dividend payments prior to ruin in a Markovmodulated risk process in which the rate for the Poisson claim arrival process and the distribution of the claim sizes vary in time depending on the state of an underlying (external) Markov jump process {J(t); t ≥ 0}. The main feature of the model is the flexibility in modeling the arrival process in the sense that periods with very frequent arrivals and periods with very few arrivals may alternate, and that the states of {J(t); t ≥ 0} could describe, for example, epidemic types in health insurance or weather conditions in car insurance. A system of integro-differential equations with boundary conditions satisfied by the nth moment of the present value of the total dividends prior to ruin, given the initial environment state, is derived and solved. We show that the probabilities that the surplus process attains a dividend barrier from the initial surplus without first falling below zero and the Laplace transforms of the time that the surplus process first hits a barrier without ruin occurring can be expressed in terms of the solution of the above-mentioned system of integro-differential equations. In the two-state model, explicit results are obtained when both claim amounts are exponentially distributed. Journal: North American Actuarial Journal Pages: 65-76 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597448 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597448 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:65-76 Template-Type: ReDIF-Article 1.0 Author-Name: Bangwon Ko Author-X-Name-First: Bangwon Author-X-Name-Last: Ko Title: ”The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion“, Yi Lu and Cary Chi-Liang Tsai, April 2007 Journal: North American Actuarial Journal Pages: 149-150 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597457 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597457 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:149-150 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion - Discussion by Bangwon Ko Journal: North American Actuarial Journal Pages: 151-152 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597458 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597458 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:151-152 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Kornya Author-X-Name-First: Peter Author-X-Name-Last: Kornya Title: On Approximating the Individual Risk Model Abstract: Error bounds are developed for Kornya-Presman–type approximations to the individual risk model. In particular, error bounds are given for the compound Poisson approximation, with the Poisson parameter equal to the expected number of claims.The approximations considered are a modification by Hipp of an approximation originally developed by Kornya, as well as Kornya’s original approximation. The error bounds are similar in concept to Hipp’s original error bounds using concentration–functions, as refined by Čekanavičius, Roos, and others. Computation of the bounds, however, is considerably simplified. In particular, concentration function type bounds called width-norm bounds are calculated directly from the values of the approximation, avoiding completely the need for calculating a special auxiliary compound Poisson distribution. Two examples are given.Depending on the portfolio parameters, the width-norm error bounds may or may not be sharper than the Hipp-Roos error bounds. In any event, it is recommended that the simpler widthnorm calculation, possibly together with an increase in the order of the approximation, be considered in practical applications if the goal is to achieve a specified accuracy with the least amount of computation.For large portfolios, where the maximum claim on any one policy is relatively small compared to the expected aggregate claims, the width-norm error bounds compare quite favorably with error bounds developed by De Pril and by Dhaene. Journal: North American Actuarial Journal Pages: 77-98 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597449 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597449 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:77-98 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: On the Gerber-Shiu Discounted Penalty Function for the Ordinary Renewal Risk Model with Constant Interest - Discussion by Bangwon Ko Journal: North American Actuarial Journal Pages: 135-135 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597455 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597455 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:135-135 Template-Type: ReDIF-Article 1.0 Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Author-Name: Cary Tsai Author-X-Name-First: Cary Author-X-Name-Last: Tsai Title: The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion Abstract: A Markov-modulated risk process perturbed by diffusion is considered in this paper. In the model the frequencies and distributions of the claims and the variances of the Wiener process are influenced by an external Markovian environment process with a finite number of states. This model is motivated by the flexibility in modeling the claim arrival process, allowing that periods with very frequent arrivals and ones with very few arrivals may alternate. Given the initial surplus and the initial environment state, systems of integro-differential equations for the expected discounted penalty functions at ruin caused by a claim and oscillation are established, respectively; a generalized Lundberg’s equation is also obtained. In the two-state model, the expected discounted penalty functions at ruin due to a claim and oscillation are derived when both claim amount distributions are from the rational family. As an illustration, the explicit results are obtained for the ruin probability when claim sizes are exponentially distributed. A numerical example also is given for the case that two classes of claims are Erlang(2) distributed and of a mixture of two exponentials. Journal: North American Actuarial Journal Pages: 136-149 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597456 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597456 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:136-149 Template-Type: ReDIF-Article 1.0 Author-Name: Hélène Cossette Author-X-Name-First: Hélène Author-X-Name-Last: Cossette Author-Name: Antoine Delwarde Author-X-Name-First: Antoine Author-X-Name-Last: Delwarde Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Frédérick Guillot Author-X-Name-First: Frédérick Author-X-Name-Last: Guillot Author-Name: Étienne Marceau Author-X-Name-First: Étienne Author-X-Name-Last: Marceau Title: Pension Plan Valuation and Mortality Projection Abstract: It is now well documented that human mortality globally declined during the course of the twentieth century. These mortality improvements pose a challenge for pricing and reserving in life insurance and for the management of public pension regimes. Assuming a further continuation of the stable pace of mortality decline, a Poisson log-bilinear projection model is applied to population mortality data to forecast future death rates. Then a relational model embedded in a Poisson regression approach is used to merge a dynamic mortality table based on data of a large population (in this case the Canadian province of Quebec) to mortality data of a given pension plan (here the Régie des Rentes du Québec) to create another dynamic mortality table, which can be used to make any assessments on the total costs of the pension plan. We provide at the end numerical examples that illustrate the impact of mortality improvements on a pension plan. Journal: North American Actuarial Journal Pages: 1-34 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597445 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597445 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:1-34 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: “On the Expected Discounted Penalty Function for L´vy Risk Processes,” José Garrido and Manuel Morales, October 2006 Journal: North American Actuarial Journal Pages: 153-153 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597459 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597459 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:153-153 Template-Type: ReDIF-Article 1.0 Author-Name: Fabio Bellini Author-X-Name-First: Fabio Author-X-Name-Last: Bellini Author-Name: Camilla Caperdoni Author-X-Name-First: Camilla Author-X-Name-Last: Caperdoni Title: Coherent Distortion Risk Measures and Higher-Order Stochastic Dominances Abstract: We show that the only coherent distortion risk measure that is consistent with respect to 3-convex order and hence with stochastic dominance of order 3 is the expected value, thus generalizing previous results of Hurlimann and solving a problem posed by Yamai and Yoshiba. Journal: North American Actuarial Journal Pages: 35-42 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597446 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597446 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:35-42 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Jürgen Hartinger Author-X-Name-First: Jürgen Author-X-Name-Last: Hartinger Title: A Risk Model with Multilayer Dividend Strategy Abstract: In recent years various dividend payment strategies for the classical collective risk model have been studied in great detail. In this paper we consider both the dividend payment intensity and the premium intensity to be step functions depending on the current surplus level. Algorithmic schemes for the determination of explicit expressions for the Gerber-Shiu discounted penalty function and the expected discounted dividend payments are derived. This enables the analytical investigation of dividend payment strategies that, in addition to having a sufficiently large expected value of discounted dividend payments, also take the solvency of the portfolio into account. Since the number of layers is arbitrary, it also can be viewed as an approximation to a continuous surplus-dependent dividend payment strategy. A recursive approach with respect to the number of layers is developed that to a certain extent allows one to improve upon computational disadvantages of related calculation techniques that have been proposed for specific cases of this model in the literature. The tractability of the approach is illustrated numerically for a risk model with four layers and an exponential claim size distribution. Journal: North American Actuarial Journal Pages: 43-64 Issue: 2 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597447 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597447 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:43-64 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Johansen Author-X-Name-First: Robert Author-X-Name-Last: Johansen Title: Guest Editorial Journal: North American Actuarial Journal Pages: iii-iv Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596059 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596059 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: Yvonne Chueh Author-X-Name-First: Yvonne Author-X-Name-Last: Chueh Title: Efficient Stochastic Modeling for Large and Consolidated Insurance Business: Interest Rate Sampling Algorithms Abstract: One of the challenges of stochastic asset/liability modeling for large insurance businesses is the run time. Using a complete stochastic asset/liability model to analyze a large block of business is often too time consuming to be practical. In practice, the compromises made are reducing the number of runs or grouping assets into asset categories. This paper focuses on the strategies that enable efficient stochastic modeling for large and consolidated insurance business blocks. Efficient stochastic modeling can be achieved by applying effective interest rate sampling algorithms that are presented in this paper. The algorithms were tested on a simplified asset/liability model ASEM (Chueh 1999) as well as a commercial asset/liability model using assets and liabilities of the Aetna Insurance Company of America (AICA), a subsidiary of Aetna Financial Services. Another methodology using the New York 7 scenarios is proposed and could become an enhancement to the Model Regulation on cash flow testing, thus requiring all companies to do stochastic cash flow testing in a uniform, nononerous manner. Journal: North American Actuarial Journal Pages: 88-103 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596058 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596058 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:88-103 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Buettner Author-X-Name-First: Thomas Author-X-Name-Last: Buettner Title: Approaches and Experiences in Projecting Mortality Patterns for the Oldest-Old Abstract: In 1998 the United Nations Population Division extended the age format of its estimates and projections of population dynamics for all countries and areas of the world from 80 years and above to 100 years and above. The paper is based on experiences made during the implementation of relevant mortality projection methodologies and their application in two rounds of global population projections.The paper first briefly addresses the need for the explicit inclusion of very old population segments into the regular UN estimates and projections. It is argued that since population aging is an important issue for both developed and developing countries, the need for more information regarding the elderly, and the oldest-old in particular, is significant.The paper then documents the methods that have been evaluated and implemented, namely, the relational mortality standard proposed by Himes, Preston, and Condran, the Coale-Kisker extrapolation method for extending empirical age patterns of mortality to very high ages, and the Carter-Lee projection method for projecting model patterns of mortality to very high levels of life expectancy at birth. The methods are critically reviewed, and possible improvements to the methods are discussed.The paper concludes with a discussion of different views regarding the future evolution of mortality at older ages, their regional variability, and the necessity to improve the coverage and quality of data collected in this area. Journal: North American Actuarial Journal Pages: 14-29 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596053 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596053 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:14-29 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Bourbeau Author-X-Name-First: Robert Author-X-Name-Last: Bourbeau Author-Name: Bertrand Desjardins Author-X-Name-First: Bertrand Author-X-Name-Last: Desjardins Title: Dealing with Problems in Data Quality for the Measurement of Mortality at Advanced Ages in Canada Abstract: The level and age trajectory of mortality at advanced ages in Canada are not readily and exactly obtained, because of problems with the reliability of data on deaths and on population counts beyond a certain point in the official statistics. There are two ways to ensure nonetheless the termination of the life tables. One consists of finding ways to validate a sufficient number of unbiased high ages at death to produce an accurate measure with the extinct, or almost extinct, generation method. This paper presents the results of a systematic verification of ages at death and a preliminary estimation of centenarian mortality based on observations, which seems to lend credence to a leveling off of mortality rates at the highest ages for females.Another is to establish convincing evidence as to the pattern of survival at the very highest ages; mathematical techniques can then be used to generate the rates as an extension of mortality at ages 70 to 90 or 100. Historical data were used here to give an insight on what this pattern of survival could be. Contrary to what might have been expected, the progression of mortality remains pretty much exponential until the unavoidable erratic values corresponding to the few extreme observations are reached. This entails that whatever the nature of the selections that would produce a slowing down of the rate of increase of the rates at the highest ages, they did not express themselves conclusively a few centuries ago. Journal: North American Actuarial Journal Pages: 1-13 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596052 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596052 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:1-13 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Marie Robine Author-X-Name-First: Jean-Marie Author-X-Name-Last: Robine Author-Name: James Vaupel Author-X-Name-First: James Author-X-Name-Last: Vaupel Title: Emergence of Supercentenarians in Low-Mortality Countries Abstract: The exponential increase in the number of centenarians, which started just after World War II, is well documented in Europe and Japan. Much less is known about the population of extremely old persons reaching age 105—the semisupercentenarians—or age 110—the supercentenarians. The first cases of validated supercentenarians appeared in the 1960s, and their numbers have steadily increased since the mid-1980s. The current prevalence of known supercentenarians in low-mortality countries involved in the International Database on Longevity (IDL) is approximately 10 times higher than in the mid-1970s. In roughly 20 years, from 1980 to 2000, the maximum reported age at death, which was once assumed to indicate the maximum life span of the human species and seen as a stable characteristic of our species, has increased by about 10 years from 112 to 122 years. The annual probability of death at age 110 is about 50% and stays at that level through age 114. Our results strongly support the finding that mortality does not increase according to the Gompertz curve at the highest ages, and the results are consistent with a plateau between ages 110 and 115. The data after age 115 are so sparse that they are not analyzed here, but an earlier study suggested that mortality may fall after age 115. We intend to investigate this question in subsequent research. Journal: North American Actuarial Journal Pages: 54-63 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596057 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596057 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:54-63 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rappaport Author-X-Name-First: Anna Author-X-Name-Last: Rappaport Author-Name: Alan Parikh Author-X-Name-First: Alan Author-X-Name-Last: Parikh Title: Living to 100 and Beyond: Implications of Longer Life Spans Abstract: Life spans have increased remarkably in the last century. There is substantial disagreement and uncertainty among researchers today about the future course of mortality in the developed countries. Will we continue to live ever-longer lives, or is the human life span headed toward a biological upper limit? The answer to this question has important implications for the elderly, their spouses and children, businesses, and our society as a whole. Continued growth in life expectancy with good health would extend our ability to enjoy all the things we cherish.Simultaneously, this growth would increase our need to prepare carefully for some unexpected challenges. Among these challenges is a greater need by individuals to save for retirement and to prepare for the possibility of becoming dependent upon family members and others for one’s care. Businesses will enjoy access to experienced workers and expanding markets among the elderly, while they also will try to control the post employment costs that longer life spans will generate. Finally, governments will struggle to manage competing interests as the financial needs of the elderly are weighed against other societal obligations. Journal: North American Actuarial Journal Pages: 45-53 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596056 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596056 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:45-53 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Stallard Author-X-Name-First: Eric Author-X-Name-Last: Stallard Title: Underlying and Multiple Case Mortality Advanced Ages: United States 1980-1998 Abstract: This paper evaluates changes in cause-specific mortality for the general noninsured U.S. elderly population aged 65 years and older by sex and five-year age groups over the calendar years 1980, 1990, and 1998 for 14 leading causes of death coded according to the International Classification of Diseases (9th revision).The goals of the paper are substantive and methodological. Substantively, the goal is to assess the different contributions to the mortality decline made by diseases as underlying causes versus associated or contributing causes—as recorded in the multiple cause condition field of the death certificate. Methodologically, the goal is to introduce these data into actuarial practice and provide an initial set of tabulation methods that facilitate their use.The patterns of change over age and time of the 14 leading causes exhibited distinct characteristics in one or more of the tables presented, demonstrating unequivocally that the diseases are neither homogeneous nor independent. This suggests that standard models such as the multiple decrement life table model that assume independent competing risks may be invalid. However, the specification of realistic and accurate alternative models will be a major challenge because of the complexity of the morbid processes involved and the requirements for data linkages that are only beginning to be developed. Journal: North American Actuarial Journal Pages: 64-87 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.11073999 File-URL: http://hdl.handle.net/10.1080/10920277.2002.11073999 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:64-87 Template-Type: ReDIF-Article 1.0 Author-Name: Bertram Kestenbaum Author-X-Name-First: Bertram Author-X-Name-Last: Kestenbaum Author-Name: B. Reneé Ferguson Author-X-Name-First: B. Author-X-Name-Last: Reneé Ferguson Title: Mortality of the Extreme Aged in the United States in the 1990S, Based on Improved Medicare Data Abstract: The most extensive mortality experience of very old persons in North America is the experience reflected in the master records of Medicare enrollment. Furthermore, the data are of high quality; for example, the age in the record generally is not a mere allegation, but rather is supported by documentation. Indeed, this experience is used for the older ages in the construction of the decennial U.S. life tables.Even the best data, however, are not free of error, and the Medicare data contain errors of duplicate information, incorrect ages, and unreported deaths. These errors understandably are most serious at the oldest ages, when the true experience is least extensive. We have undertaken several initiatives at the microdata level to improve the quality of the information, and we report those initiatives and the mortality probabilities that were obtained in this paper.‡ Journal: North American Actuarial Journal Pages: 38-44 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596055 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596055 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:38-44 Template-Type: ReDIF-Article 1.0 Author-Name: Gene Held Author-X-Name-First: Gene Author-X-Name-Last: Held Title: Research Into the Aging Process: A Survey Abstract: We are in the midst of a revolution in biological knowledge. Although research into the aging process was begun long before the Human Genome Project, it has benefited greatly from the powerful tools and techniques spun off from that endeavor. Current research is providing knowledge about life processes that may offer the prospect of slowing the aging process. Dr. Francis Collins, Director of the National Human Genome Research Institute, has predicted that “By 2030, major genes responsible for the aging process in humans will likely have been identified, and clinical trials with drugs to retard the process may well be getting underway” (Collins 2000). A growing number of scientists recognize extension of the maximum life span as a possibility.The actuarial profession cannot lay claim to expertise in the area of mortality while ignoring scientific research into the causes of aging. This paper provides a brief overview of the subject and a bibliography for those interested in pursuing the matter further. It offers a brief historical perspective, a survey of current research, and a glimpse of future possibilities.† Journal: North American Actuarial Journal Pages: 30-37 Issue: 3 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596054 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596054 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:3:p:30-37 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: “Author’s Reply: A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving,” R. J. Verrall, July 2004 - Discussion by Katrien Antonio, Jan Beirlant, Tom Hoedemakers, and David P. M. Scollnik Journal: North American Actuarial Journal Pages: 149-149 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596218 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596218 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:149-149 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Title: “A Framework For Long-Term Actuarial Projections of Health Care Costs: The Importance of Population Aging and Other Factors,” Howard J. Bolnick, October 2004 Journal: North American Actuarial Journal Pages: 150-151 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596219 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596219 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:150-151 Template-Type: ReDIF-Article 1.0 Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Author-Name: Jan Beirlant Author-X-Name-First: Jan Author-X-Name-Last: Beirlant Author-Name: Tom Hoedemakers Author-X-Name-First: Tom Author-X-Name-Last: Hoedemakers Title: “A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving,” R. J. Verrall, July 2004 Journal: North American Actuarial Journal Pages: 130-142 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596216 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596216 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:130-142 Template-Type: ReDIF-Article 1.0 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: “A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving,” R. J. Verrall, July 2004 Journal: North American Actuarial Journal Pages: 143-145 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596217 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596217 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:143-145 Template-Type: ReDIF-Article 1.0 Author-Name: S. David Promislow Author-X-Name-First: S. Author-X-Name-Last: David Promislow Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift Abstract: We extend the work of Browne (1995) and Schmidli (2001), in which they minimize the probability of ruin of an insurer facing a claim process modeled by a Brownian motion with drift. We consider two controls to minimize the probability of ruin: (1) investing in a risky asset and (2) purchasing quota-share reinsurance. We obtain an analytic expression for the minimum probability of ruin and the corresponding optimal controls, and we demonstrate our results with numerical examples. Journal: North American Actuarial Journal Pages: 110-128 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596214 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596214 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:110-128 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Title: Dettweiler, Egbery, 2004, , EAGLE-Lecture, Leipzig: edition am Gutenbergplatz Leipzig Journal: North American Actuarial Journal Pages: 152-152 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596220 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596220 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:152-152 Template-Type: ReDIF-Article 1.0 Author-Name: Kam-Chuen Yuen Author-X-Name-First: Kam-Chuen Author-X-Name-Last: Yuen Author-Name: Guojing Wang Author-X-Name-First: Guojing Author-X-Name-Last: Wang Title: Some Ruin Problems for a Risk Process with Stochastic Interest Abstract: As investment plays an increasingly important role in the insurance business, ruin analysis in the presence of stochastic interest (or stochastic return on investments) has become a key issue in modern risk theory, and the related results should be of interest to actuaries. Although the study of insurance risk models with stochastic interest has attracted a fair amount of attention in recent years, many significant ruin problems associated with these models remain to be investigated. In this paper we consider a risk process with stochastic interest in which the basic risk process is the classical risk process and the stochastic interest process (or the stochastic return-on-investmentgenerating process) is a compound Poisson process with positive drift. Within this framework, we first derive an integro-differential equation for the Gerber-Shiu expected discounted penalty function, and then obtain an exact solution to the equation. We also obtain closed-form expressions for the expected discounted penalty function in some special cases. Finally, we examine a lower bound for the ruin probability of the risk process. Journal: North American Actuarial Journal Pages: 129-142 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596215 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596215 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:129-142 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Author-Name: Eddy Van den Borre Author-X-Name-First: Eddy Author-X-Name-Last: Van den Borre Author-Name: Roger Laeven Author-X-Name-First: Roger Author-X-Name-Last: Laeven Title: Managing Economic and Virtual Economic Capital Within Financial Conglomerates Abstract: In this paper we show how the optimal amount of economic capital can be derived such that it minimizes the economic cost of risk-bearing. The economic cost of risk-bearing takes into account the cost of the economic capital as well as the exposure to residual risk. In addition to the absolute problem of determining the amount of economic capital, we also consider the relative problem of how to establish the allocation of economic capital among subsidiaries. Because subsidiaries are juridical entities, they will also consider the absolute problem of economic capital allocation themselves. In an equilibrium situation, the relative allocation derived by the conglomerate and the absolute allocation derived by the subsidiaries coincide. We show that the diversification benefit that is typically obtained in a conglomerate construction creates a virtual economic capital for subsidiaries within the conglomerate. We show further that the approach we propose to solve the absolute problem of economic capital allocation also can be applied to the problem of optimal portfolio selection, extending the well-known Markowitz approach and providing a tool for management by economic capital. Journal: North American Actuarial Journal Pages: 77-89 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596212 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596212 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:77-89 Template-Type: ReDIF-Article 1.0 Author-Name: Donald Mango Author-X-Name-First: Donald Author-X-Name-Last: Mango Title: Risk Management Research Imperatives Journal: North American Actuarial Journal Pages: iii-v Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596221 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596221 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:iii-v Template-Type: ReDIF-Article 1.0 Author-Name: Ioannis Ntzoufras Author-X-Name-First: Ioannis Author-X-Name-Last: Ntzoufras Author-Name: Athanassios Katsis Author-X-Name-First: Athanassios Author-X-Name-Last: Katsis Author-Name: Dimitris Karlis Author-X-Name-First: Dimitris Author-X-Name-Last: Karlis Title: Bayesian Assessment of the Distribution of Insurance Claim Counts Using Reversible Jump MCMC Abstract: The aim of this paper is to construct Bayesian model comparison tests between discrete distributions used for claim count modeling in the actuarial field. We use advanced computational techniques to estimate the posterior model odds among different distributions for claim counts. We construct flexible reversible jump Markov Chain Monte Carlo algorithms and implement them in various illustrated examples. Journal: North American Actuarial Journal Pages: 90-108 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596213 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596213 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:90-108 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Petertil Author-X-Name-First: Jeffrey Author-X-Name-Last: Petertil Title: Aging Curves for Health Care Costs in Retirement Abstract: This paper explores the relative significance of aging as a determinant of financial cost of health care beyond age fifty, with particular attention to the effect for ages 65 and over. The paper presents concepts of aging factors and aging curves, which define relative values between ages for utilization or cost of health care services. General conclusions are drawn from Medicare data that utilization and cost differ by age, but that aging factors vary across services and may be less significant at the very old ages. The author then turns to the question of measuring the significance of an aging curve assumption and what accuracy is lost in the simpler alternative of a single value across an age range. The practical effects of relative value aging curves are examined through hypothetical examples of increasing complexity in a retiree health valuation. A method to measure the impact is put forth. Three important variables are discussed in some detail. A survey to ascertain aging curve findings and preferences of health actuaries is introduced and discussed, with one representative curve presented. This curve is then measured to understand its impact vis-à-vis other curves.It may be important to note this is not a study deriving a recommended aging curve. Rather, it is an exploration of the significance of an assumption that has not received much public actuarial scrutiny. A conclusion places the paper-s findings in a context of a dynamic health care economy in an aging society. Journal: North American Actuarial Journal Pages: 22-49 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596210 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596210 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:22-49 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Yongzeng Lai Author-X-Name-First: Yongzeng Author-X-Name-Last: Lai Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: Pricing Options Using Lattice Rules Abstract: There are many examples of option contracts in which the payoff depends on several stochastic variables. These options often can be priced by the valuation of multidimensional integrals. Quasi–Monte Carlo methods are an effective numerical tool for this task. We show that, when the dimensions of the problem are small (say, less than 10), a special type of quasi–Monte Carlo known as the lattice rule method is very efficient. We provide an overview of lattice rules, and we show how to implement this method and demonstrate its efficiency relative to standard Monte Carlo and classical quasi–Monte Carlo. To maximize the efficiency gains, we show how to exploit the regularity of the integrand through a periodization technique. We demonstrate the superior efficiency of the method both in the estimation of prices as well as in the estimation of partial derivatives of these prices (the so-called Greeks). In particular this approach provides good estimates of the second derivative (the gamma) of the price in contrast to traditional Monte Carlo methods, which normally yield poor estimates. Although this method is not new, it appears that the advantages of lattice rules in the context of insurance and finance applications have not been fully appreciated in the literature. Journal: North American Actuarial Journal Pages: 50-76 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596211 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596211 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:50-76 Template-Type: ReDIF-Article 1.0 Author-Name: Jeremy Gold Author-X-Name-First: Jeremy Author-X-Name-Last: Gold Title: Accounting/Actuarial Bias Enables Equity Investment By Defined Benefit Pension Plans Abstract: Although pension finance theory says most defined benefit pension plans sponsored by publicly traded corporations should invest entirely in fixed income, 60% of assets are invested in equities. The existing theory makes a strong—but often unstated—assumption of transparency, implying that investors view the pension plan as a financial subsidiary of the operating parent and value it as a market portfolio. I explain the equity choice made by managers as a reaction to how investors perceive the opaque standard pension accounting model. Investors view the plan in operating terms and value it based on reported earnings.Defined benefit pension plans- earnings (expenses) are computed using actuarial methods and economic assumptions that anticipate expected equity returns and strongly dampen the volatility of actual equity returns. Thus, corporations whose plans invest in equities overstate the financial value of their earnings and understate the volatility of such earnings.Under the transparent model, managers who invest in equities may be confronted by arbitrage arguments that show equity investment injures shareholders. Under the opaque model, these arbitrage arguments are not available and managers who invest in equities enjoy premium returns to risk while those who invest in fixed income instruments are punished by higher costs without visible risk reduction. Journal: North American Actuarial Journal Pages: 1-21 Issue: 3 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596209 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596209 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:1-21 Template-Type: ReDIF-Article 1.0 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Title: Remarks on the Mossin Theorem Abstract: We establish several new results regarding the Mossin Theorem under both nonrandom initial wealth and random initial wealth. For the nonrandom initial wealth case, we show that the Mossin Theorem holds for any constrained class of insurance contracts whose maximum coverage provides full coverage of the potential loss. This result not only settles an open conjecture, but also provides a unified treatment for extant varieties of the Mossin Theorem. For the random initial wealth case, we give a thorough study of the upper-limit insurance. In particular, we show that (1) for a fair premium, the Generalized Mossin Theorem for coinsurance does not hold for upper-limit insurance, and (2) for an unfair premium, partial insurance will always be optimal, regardless of the risk preference of the individual and the dependence structure between the random loss and the random initial wealth. Journal: North American Actuarial Journal Pages: 1-10 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1477605 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1477605 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:1-10 Template-Type: ReDIF-Article 1.0 Author-Name: Guangyuan Gao Author-X-Name-First: Guangyuan Author-X-Name-Last: Gao Author-Name: Shengwang Meng Author-X-Name-First: Shengwang Author-X-Name-Last: Meng Author-Name: Yanlin Shi Author-X-Name-First: Yanlin Author-X-Name-Last: Shi Title: Stochastic Payments per Claim Incurred Abstract: We propose a Bayesian model to quantify the uncertainty associated with the payments per claim incurred (PPCI) algorithm. Based on the PPCI algorithm, two submodels are proposed for the number of reported claims run-off triangle and the PPCI run-off triangle, respectively. The model for the claims amount is then derived from the two submodels under the assumption of independence between the number of incurred claims and the PPCI. The joint likelihood of the number of reported claims and claims amount is derived. The posterior distribution of parameters is estimated via the Hamiltonian Monte Carlo (HMC) sampling approach. The Bayesian estimator, the process variance, the estimation variance, and the predictive distribution of unpaid claims are also studied. The proposed model and the HMC inference engine are applied to to an empirical claims dataset of the WorkSafe Victoria to estimate the unpaid claims of the doctor benefit. The Bayesian modeling procedure is further refined by including a preliminary generalized linear model analysis. The results are compared with those in a PwC report. An alternative model is compared with the proposed model based on various information criteria. Journal: North American Actuarial Journal Pages: 11-26 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1480390 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1480390 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:11-26 Template-Type: ReDIF-Article 1.0 Author-Name: Michelle Li Author-X-Name-First: Michelle Author-X-Name-Last: Li Author-Name: Donald Richards Author-X-Name-First: Donald Author-X-Name-Last: Richards Title: Statistical Implications of the Revenue Transfer Methodology in the Affordable Care Act Abstract: The Affordable Care Act (ACA) includes a permanent revenue transfer methodology that provides financial incentives to health insurance plans that have higher than average actuarial risk. In this article, we derive some statistical implications of the revenue transfer methodology in the ACA. We treat as random variables the revenue transfers between individual insurance plans in a given marketplace, where each plan’s revenue transfer amount is measured as a percentage of the plan’s total premium. We analyze the means and variances of those random variables and deduce from the zero-sum nature of the revenue transfers that there is no limit to the magnitude of revenue transfer payments relative to plans’ total premiums. Using data provided by the American Academy of Actuaries and by the Centers for Medicare & Medicaid Services, we obtain an explanation for empirical phenomena that revenue transfers were more variable and can be substantially greater for insurance plans with smaller market shares. We show that it is often the case that an insurer that has decreasing market share will also have increased volatility in its revenue transfers. Journal: North American Actuarial Journal Pages: 27-32 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1486718 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1486718 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:27-32 Template-Type: ReDIF-Article 1.0 Author-Name: Jose Blanchet Author-X-Name-First: Jose Author-X-Name-Last: Blanchet Author-Name: Henry Lam Author-X-Name-First: Henry Author-X-Name-Last: Lam Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Author-Name: Zhongyi Yuan Author-X-Name-First: Zhongyi Author-X-Name-Last: Yuan Title: Robust Actuarial Risk Analysis Abstract: This article investigates techniques for the assessment of model error in the context of insurance risk analysis. The methodology is based on finding robust estimates for actuarial quantities of interest, which are obtained by solving optimization problems over the unknown probabilistic models, with constraints capturing potential nonparametric misspecification of the true model. We demonstrate the solution techniques and the interpretations of these optimization problems, and illustrate several examples, including calculating loss probabilities and conditional value-at-risk. Journal: North American Actuarial Journal Pages: 33-63 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1504686 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1504686 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:33-63 Template-Type: ReDIF-Article 1.0 Author-Name: Palma Daawin Author-X-Name-First: Palma Author-X-Name-Last: Daawin Author-Name: Seonjin Kim Author-X-Name-First: Seonjin Author-X-Name-Last: Kim Author-Name: Tatjana Miljkovic Author-X-Name-First: Tatjana Author-X-Name-Last: Miljkovic Title: Predictive Modeling of Obesity Prevalence for the U.S. Population Abstract: Modeling obesity prevalence is an important part of the evaluation of mortality risk. A large volume of literature exists in the area of modeling mortality rates, but very few models have been developed for modeling obesity prevalence. In this study we propose a new stochastic approach for modeling obesity prevalence that accounts for both period and cohort effects as well as the curvilinear effects of age. Our model has good predictive power as we utilize multivariate ARIMA models for forecasting future obesity rates. The proposed methodology is illustrated on the U.S. population, aged 23–90, during the period 1988–2012. Forecasts are validated on actual data for the period 2013–2015 and it is suggested that the proposed model performs better than existing models. Journal: North American Actuarial Journal Pages: 64-81 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1506348 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1506348 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:64-81 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph H. T. Kim Author-X-Name-First: Joseph H. T. Author-X-Name-Last: Kim Author-Name: Jiwook Jang Author-X-Name-First: Jiwook Author-X-Name-Last: Jang Author-Name: Chaehyun Pyun Author-X-Name-First: Chaehyun Author-X-Name-Last: Pyun Title: Capital Allocation for a Sum of Dependent Compound Mixed Poisson Variables: A Recursive Algorithm Approach Abstract: The sum of independent compound Poisson random variables is a widely used stochastic model in many economic applications, including non-life insurance, credit and operational risk management, and environmental sciences. In this article we generalize this model by introducing dependence among Poisson frequency variables through a latent random variable in a linear fashion, which can be translated as a common underlying risk factors affecting the frequencies of individual compound Poisson variables. Despite its natural interpretation, this generalization leads to a highly complicated model with no closed-form distribution function. For this dependent compound mixed Poisson sum with an arbitrary severity distribution, we obtain the Laplace transform and further develop a new recursive algorithm to efficiently compute the probability mass function, extending the well-known Panjer recursion. Furthermore, based on this recursion, we derive another recursive scheme to determine the capital allocation associated with the Conditional Tail Expectation, a popular risk management exercise. A numerical example is presented for the illustration of our findings. Journal: North American Actuarial Journal Pages: 82-97 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1506705 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1506705 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:82-97 Template-Type: ReDIF-Article 1.0 Author-Name: Min Ji Author-X-Name-First: Min Author-X-Name-Last: Ji Author-Name: Rui Zhou Author-X-Name-First: Rui Author-X-Name-Last: Zhou Title: A General Semi-Markov Model for Coupled Lifetimes Abstract: Joint-life annuities with a high last survivor benefit play an important role in the optimal annuity portfolio for a retired couple. The dependence between coupled lifetimes is crucial for valuing joint-life annuities. Existing bivariate modeling of coupled lifetimes is based on outdated data with limited observation periods and does not take into account mortality improvement. In this article, we propose a transparent and dynamic framework for modeling coupled lifetime dependence caused by both marital status and common mortality improvement factors. Dependence due to marital status is captured by a semi-Markov joint life model. Dependence due to common mortality improvement, which represents the correlation between mortality improvement patterns of coupled lives, is incorporated by a two-population mortality improvement model. The proposed model is applied to pricing the longevity risk in last survivor annuities sold in the United States and the United Kingdom. Journal: North American Actuarial Journal Pages: 98-119 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1513370 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1513370 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:98-119 Template-Type: ReDIF-Article 1.0 Author-Name: Lin He Author-X-Name-First: Lin Author-X-Name-Last: He Author-Name: Zongxia Liang Author-X-Name-First: Zongxia Author-X-Name-Last: Liang Author-Name: Yang Liu Author-X-Name-First: Yang Author-X-Name-Last: Liu Author-Name: Ming Ma Author-X-Name-First: Ming Author-X-Name-Last: Ma Title: Optimal Control of DC Pension Plan Management under Two Incentive Schemes Abstract: Since the late 1990s, a performance fee arrangement has been approved as a managerial incentive in direction contribution (DC) pension plan management to motivate managers. However, the fact that managers may take undue risk for the larger performance fees and thus reduce members’ utility has been a subject of debate. As such, this study investigates the optimal risk-taking policies of DC pension fund managers under both the single management fee scheme and a mixed scheme with a lower management fee, as well as an additional performance fee. The analytical solutions are derived by using the duality method and concavification techniques in a singular optimization problem. The results show the complex risk-taking structures of fund managers and recognize the win-win situation of implementing performance-based incentives in DC pension plan management. Under the setting of geometric Brownian motion asset price dynamics and constant relative risk aversion utility, the optimal risk investment proportion shows a peak-valley pattern under the mixed scheme. Further, the manager gambles for gain when fund wealth is low and time to maturity is short. As opposed to the existing literature, this study found that the risk-taking policy is more conservative when fund wealth is relatively large. Furthermore, the utilities of the manager and members could both be improved by appropriately choosing the performance fee rate. Journal: North American Actuarial Journal Pages: 120-141 Issue: 1 Volume: 23 Year: 2019 Month: 1 X-DOI: 10.1080/10920277.2018.1513371 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1513371 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:23:y:2019:i:1:p:120-141 Template-Type: ReDIF-Article 1.0 Author-Name: Stuart Klugman Author-X-Name-First: Stuart Author-X-Name-Last: Klugman Title: “Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results”, Edward L. Robbins; Samuel H. Cox; Richard D. Phillips, April 1997 Journal: North American Actuarial Journal Pages: 100-100 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595616 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595616 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:100-100 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Ang Author-X-Name-First: Andrew Author-X-Name-Last: Ang Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Interest Rate Risk Management Abstract: This paper surveys the main concepts and techniques of recent developments in the modeling of the term structure of interest rates that are used in the risk management and valuation of interest-rate-dependent cash flows. These developments extend the concepts of immunization and matching to a stochastic interest rate environment. Such cash flows include the cash flows on assets such as bonds and mortgage-backed securities as well as those for annuity products, life insurance products with interest-rate-sensitive withdrawals, accrued liabilities for defined-benefit pension funds, and property and casualty liability cash flows. Journal: North American Actuarial Journal Pages: 1-26 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595601 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595601 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:1-26 Template-Type: ReDIF-Article 1.0 Author-Name: Allan Brender Author-X-Name-First: Allan Author-X-Name-Last: Brender Title: “Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results”, Edward L. Robbins; Samuel H. Cox; Richard D. Phillips, April 1997 Journal: North American Actuarial Journal Pages: 98-99 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595615 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595615 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:98-99 Template-Type: ReDIF-Article 1.0 Author-Name: David Creswell Author-X-Name-First: David Author-X-Name-Last: Creswell Title: “Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results”, Edward L. Robbins; Samuel H. Cox; Richard D. Phillips, April 1997 Journal: North American Actuarial Journal Pages: 102-103 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595618 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595618 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:102-103 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: Methods for the Analysis of CCRC Data Abstract: This paper presents an approach to analyzing continuing care retirement community (CCRC) data and demonstrates the methodology by using data from a CCRC. It is assumed that residents make "transitions" among a number of "states" that represent the levels of care required by residents. There is randomness associated with both the transition times and the states entered at these times. The model is conveniently characterized in terms of “transition intensity functions,” which represent the instantaneous rates of transition between pairs of states. Statistical methods for estimating these functions are discussed, and estimates are obtained from the data-set. A simulation approach for determining probabilities and other interesting quantities based on the estimated intensity functions is also described and illustrated. Journal: North American Actuarial Journal Pages: 40-54 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595603 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595603 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:40-54 Template-Type: ReDIF-Article 1.0 Author-Name: Alastair Longley-Cook Author-X-Name-First: Alastair Author-X-Name-Last: Longley-Cook Title: “Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results”, Edward L. Robbins; Samuel H. Cox; Richard D. Phillips, April 1997 Journal: North American Actuarial Journal Pages: 100-102 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595617 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595617 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:100-102 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Xiaodong Lin Author-X-Name-First: Xiaodong Author-X-Name-Last: Lin Title: Optimal Portfolio Selection with Transaction Costs Abstract: This paper examines the lifetime portfolio-selection problem in the presence of transaction costs. Using a discrete time approach, we develop analytical expressions for the investor's indirect utility function and also for the boundaries of the no-transactions region. The economy consists of a single risky asset and a riskless asset. Transactions in the risky asset incur proportional transaction costs. The investor has a power utility function and is assumed to maximize expected utility of end-of-period wealth. We illustrate the solution procedure in the case in which the returns on the risky asset follow a multiplicative binomial process. Our paper both complements and extends the recent work by Gennotte and Jung (1994), which used numerical approximations to tackle this problem. Journal: North American Actuarial Journal Pages: 27-39 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595602 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595602 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:27-39 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Robbins Author-X-Name-First: Edward Author-X-Name-Last: Robbins Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Author-Name: Richard Phillips Author-X-Name-First: Richard Author-X-Name-Last: Phillips Title: Author’s Reply: Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results - Discussion by Allan Brender; Stuart A. Klugman; Alastair G. Longley-Cook; David L. Creswell Journal: North American Actuarial Journal Pages: 103-104 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595619 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595619 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:103-104 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Bühlmann Author-X-Name-First: Hans Author-X-Name-Last: Bühlmann Title: Collective Risk Theory for Assets Journal: North American Actuarial Journal Pages: 104-104 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595620 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595620 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:104-104 Template-Type: ReDIF-Article 1.0 Author-Name: Emilia Di Lorenzo Author-X-Name-First: Emilia Author-X-Name-Last: Di Lorenzo Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 74-75 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595608 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:74-75 Template-Type: ReDIF-Article 1.0 Author-Name: Leda Minkova Author-X-Name-First: Leda Author-X-Name-Last: Minkova Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 75-75 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595609 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595609 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:75-75 Template-Type: ReDIF-Article 1.0 Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 75-76 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595610 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595610 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:75-76 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Parker Author-X-Name-First: Gary Author-X-Name-Last: Parker Title: Stochastic Analysis of the Interaction Between Investment and Insurance Risks Abstract: A portfolio of different insurance policies, such as temporary, endowment, and whole life, is studied in a stochastic mortality and interest environment. The first two moments of the present value of the benefits of the portfolio are derived. The riskiness of the portfolio as measured by the variance of the present value of the benefits can be divided into an insurance risk and an investment risk in two different ways. One way leads to a more natural interpretation of the two risk components. A simple portfolio is used to illustrate the results. Journal: North American Actuarial Journal Pages: 55-71 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595604 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595604 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:55-71 Template-Type: ReDIF-Article 1.0 Author-Name: Svein-Arne Persson Author-X-Name-First: Svein-Arne Author-X-Name-Last: Persson Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 76-79 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595611 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595611 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:76-79 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 71-72 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595605 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595605 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:71-72 Template-Type: ReDIF-Article 1.0 Author-Name: Wojciech Szatzschneider Author-X-Name-First: Wojciech Author-X-Name-Last: Szatzschneider Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 79-80 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595612 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595612 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:79-80 Template-Type: ReDIF-Article 1.0 Author-Name: Griselda Deelstra Author-X-Name-First: Griselda Author-X-Name-Last: Deelstra Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 72-73 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595606 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595606 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:72-73 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Parker Author-X-Name-First: Gary Author-X-Name-Last: Parker Title: Author’s Reply: Stochastic Analysis of the Interaction Between Investment and Insurance Risks - Discussion by John A. Beekman; Griselda Deelstra; Andrew J.G. Cairns; Emilia Di Lorenzo; Leda Minkova; Ragnar Norberg; Svein-Arne Persson; Wojciech Szatzschneider Journal: North American Actuarial Journal Pages: 80-84 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595613 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595613 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:80-84 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Robbins Author-X-Name-First: Edward Author-X-Name-Last: Robbins Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Author-Name: Richard Phillips Author-X-Name-First: Richard Author-X-Name-Last: Phillips Title: Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results Abstract: This paper offers practical guidance to actuaries who are seeking ways to evaluate and manage the output from the stochastic cash-flow-testing process. A commonly expressed opinion about the stochastic approach is that almost all the results are successes, whereas the adverse scenarios are arguably the ones of major interest. This paper responds to the following question: “Given that I have run a large number of stochastic cash-flow-testing scenarios resulting in only a very small number of scenarios landing in the adverse area, or “ruin tail,” how can I use the results of the entire set of observations to better estimate the area under the ruin tail?We begin the paper with a discussion of the types of variables that could be investigated by using the output from typical simulation models. The choice of variable worth examining appears flexible and could include the accumulated surplus at the end of the time horizon of the scenario, the present value of the accumulated surplus discounted to the beginning of the time horizon, or the lowest risk-based capital (RBC) multiple realized during the time horizon. We use the present value of accumulated surplus in this study.Once the variable of choice has been decided, we illustrate various methods from risk theory that could be used to investigate the variable of choice. All the methods we discuss are tools readily available to the actuary, originally developed as part of traditional risk theory. To illustrate these methods, we use output from a simulation model valuing a portfolio of single-premium deferred annuities under various stochastic interest rate scenarios. We review each technique and then illustrate how to adapt them for a specific purpose. In particular, we discuss parametric model selection for standard families based on maximum likelihood estimation (MLE), mixtures of standard models, Esscher approximations, and the normal power method. Our work shows that parametric models selected via MLE have several advantages over the classical methods such as Esscher and normal power. Parametric models fit the entire distribution, whereas the classical methods give only point estimates. Also, the statistical theory of MLE estimation is well-understood and, for example, allows the actuary to calculate such useful statistics as confidence intervals. Simple mixtures of familiar two-parameter models are also discussed because they are easy to fit using moment estimators. Their main drawback, however, is that the large number of parameters to be estimated can make them difficult to work with. The classical methods are shown to be harder to use and do not give better results than fitting the parametric models.We also address the issue of sample size. Journal: North American Actuarial Journal Pages: 85-98 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595614 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595614 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:85-98 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Title: “Stochastic Analysis of the Interaction Between Investment and Insurance Risks”, Gary Parker, April 1997 Journal: North American Actuarial Journal Pages: 73-74 Issue: 2 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595607 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:2:p:73-74 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Emms Author-X-Name-First: Paul Author-X-Name-Last: Emms Title: Equilibrium Pricing of General Insurance Policies Abstract: A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants. Journal: North American Actuarial Journal Pages: 323-349 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590645 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590645 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:323-349 Template-Type: ReDIF-Article 1.0 Author-Name: Li Zhu Author-X-Name-First: Li Author-X-Name-Last: Zhu Author-Name: Haijun Li Author-X-Name-First: Haijun Author-X-Name-Last: Li Title: Asymptotic Analysis of Multivariate Tail Conditional Expectations Abstract: Tail conditional expectations refer to the expected values of random variables conditioning on some tail events and are closely related to various coherent risk measures. In the univariate case, the tail conditional expectation is asymptotically proportional to Value-at-Risk, a popular risk mea-sure. The focus of this paper is on asymptotic relations between the multivariate tail conditional expectation and Value-at-Risk for heavy-tailed scale mixtures of multivariate distributions. Explicit tail estimates of multivariate tail conditional expectations are obtained using the method of regular variation. Examples involving multivariate Pareto and elliptical distributions, as well as application to risk allocation, are also discussed. Journal: North American Actuarial Journal Pages: 350-363 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590646 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590646 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:350-363 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Kelly Author-X-Name-First: Mary Author-X-Name-Last: Kelly Author-Name: Anne Kleffner Author-X-Name-First: Anne Author-X-Name-Last: Kleffner Author-Name: Si Li Author-X-Name-First: Si Author-X-Name-Last: Li Title: Loss Reserves and the Employment Status of the Appointed Actuary Abstract: Property/casualty (P/C) insurers are required to establish loss reserves for unpaid losses at the time that the loss has occurred or is reasonably expected to have occurred. We examine factors that may impact the accurate setting of loss reserves. These include the level of rate regulation faced by the insurer and the incentives to underestimate or overestimate reserves to improve financial ratios or improve solvency scores, to reduce earnings, to defer taxes, or to smooth earnings volatility in order to meet shareholder expectations. The employment status of the Appointed Actuary, that is, whether the Appointed Actuary is an employee of the firm or a consultant, may also impact reserve accuracy. Using a variety of regression models with data from 1995 to 2010, we examine the impact of these factors on the accuracy of reserves posted by Canadian P/C insurers. Our results provide no evidence of systematic differences in the magnitude or direction of loss reserve errors between insurers that use company actuaries versus those that use consultant actuaries. However, we find that for both consultant and company actuaries positive reserve errors are associated with increases in global stock market returns and decreases in unanticipated inflation. The insurance market cycle impacts reserve errors for company actuaries and not consultant actuaries. As well, our results indicate that as the proportion of short-tailed business increases in a company, consultant actuaries are more likely to over-reserve. Similar to many previous studies using U.S. data, we do not find strong evidence regarding insurers’ incentives to deliberately overstate or understate reserves: Loss reserves are relatively unbiased estimates of the true losses paid. Thus these findings should be welcome news to the actuarial profession in Canada and to the prudential regulator: The Appointed Actuary, regardless of employment status, provides objective and unbiased estimates of insurers’ largest liability. Journal: North American Actuarial Journal Pages: 285-305 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590643 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590643 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:285-305 Template-Type: ReDIF-Article 1.0 Author-Name: Cassandra Cole Author-X-Name-First: Cassandra Author-X-Name-Last: Cole Author-Name: Kevin Eastman Author-X-Name-First: Kevin Author-X-Name-Last: Eastman Author-Name: Patrick Maroney Author-X-Name-First: Patrick Author-X-Name-Last: Maroney Author-Name: Kathleen McCullough Author-X-Name-First: Kathleen Author-X-Name-Last: McCullough Author-Name: David Macpherson Author-X-Name-First: David Author-X-Name-Last: Macpherson Title: The Impact of No-Fault Legislation on Automobile Insurance Abstract: Since its inception, the effectiveness of no-fault legislation has been highly debated. Although some research suggests that no-fault laws are effective in reducing costs, other evidence suggests that the current no-fault systems may not meet the original objectives. This study provides a detailed assessment of the relation of no-fault laws and automobile insurance losses for the period 1994 to 2007. By examining total automobile insurance losses along with liability and personal injury protection losses, we are able to determine if and how specific provisions of the laws are related to claims costs. We find a negative relation between the presence of a no-fault law and total losses, which suggests that no-fault systems are associated with lower losses than the traditional tort system. In addition, an examination of no-fault-only states suggests that specific provisions of no-fault laws, such as thresholds and limitations on benefits, have some effect on losses. With the sunset of Colorado’s no-fault legislation in 2003, the recent passage of Personal Injury Protection Reform in Florida, and proposed federal choice legislation, the overall impact of no-fault as well as the specific components of the laws are of heightened importance to consumers, insurers, and lawmakers. Journal: North American Actuarial Journal Pages: 306-322 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590644 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590644 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:306-322 Template-Type: ReDIF-Article 1.0 Author-Name: Mario Wϋthrich Author-X-Name-First: Mario Author-X-Name-Last: Wϋthrich Title: “A Bayesian Log-Normal Model for Multivariate Loss Reserving”, Peng Shi, Sanjib Basu, and Glenn G. Meyers, March 2012 Journal: North American Actuarial Journal Pages: 398-401 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590649 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590649 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:398-401 Template-Type: ReDIF-Article 1.0 Author-Name: A. Debón Author-X-Name-First: A. Author-X-Name-Last: Debón Author-Name: F. Martínez-Ruiz Author-X-Name-First: F. Author-X-Name-Last: Martínez-Ruiz Author-Name: F. Montes Author-X-Name-First: F. Author-X-Name-Last: Montes Title: Temporal Evolution of Mortality Indicators Abstract: In Spain, as in other developed countries, significant changes in mortality patterns have occurred during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, although the robustness of this indicator prevents these changes from being of the same order as those for the probability of death. If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study. These indicators are applied to Spanish mortality data for the period 1981–2008, for the age range 0–99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely, the Lee-Carter model. Confidence intervals for these predictions can be calculated using the methodology that Lee and Carter apply in their original article for expected lifetime confidence intervals, but they take into account only the error in the prediction of the mortality index obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, permitting the combination of all sources of uncertainty. Journal: North American Actuarial Journal Pages: 364-377 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590647 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590647 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:364-377 Template-Type: ReDIF-Article 1.0 Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Author-Name: Zhongyi Yuan Author-X-Name-First: Zhongyi Author-X-Name-Last: Yuan Title: A Hybrid Estimate for the Finite-Time Ruin Probability in a Bivariate Autoregressive Risk Model with Application to Portfolio Optimization Abstract: Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another auto regressive process, independent of the former one. We derive an asymptotic formula for the finite-time ruin probability and propose a hybrid method, combining simulation with asymptotics, to compute this ruin probability more efficiently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the ruin probability. Journal: North American Actuarial Journal Pages: 378-397 Issue: 3 Volume: 16 Year: 2012 X-DOI: 10.1080/10920277.2012.10590648 File-URL: http://hdl.handle.net/10.1080/10920277.2012.10590648 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:378-397 Template-Type: ReDIF-Article 1.0 Author-Name: Ruodu Wang Author-X-Name-First: Ruodu Author-X-Name-Last: Wang Author-Name: Liang Peng Author-X-Name-First: Liang Author-X-Name-Last: Peng Title: Jackknife Empirical Likelihood Intervals for Spearman’s Rho Abstract: In connection with copulas, rank correlation such as Kendall’s tau and Spearman’s rho has been employed in risk management for summarizing dependence between two variables and estimating parameters in bivariate copulas and elliptical models. In this paper a jackknife empirical likelihood method is proposed to construct confidence intervals for Spearman’s rho without estimating the asymptotic variance. A simulation study confirms the advantages of the proposed method. Journal: North American Actuarial Journal Pages: 475-486 Issue: 4 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597633 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:4:p:475-486 Template-Type: ReDIF-Article 1.0 Author-Name: Hong-Jen Lin Author-X-Name-First: Hong-Jen Author-X-Name-Last: Lin Author-Name: Min-Ming Wen Author-X-Name-First: Min-Ming Author-X-Name-Last: Wen Author-Name: Charles Yang Author-X-Name-First: Charles Author-X-Name-Last: Yang Title: Effects of Risk Management on Cost Efficiency and Cost Function of the U.S. Property and Liability Insurers Abstract: This paper adopts the one-step stochastic frontier approach to investigate the impact of risk management tools of derivatives and reinsurance on cost efficiency of U.S. property-liability insurance companies. The stochastic frontier approach considers both the mean and variance of cost efficiency. The sample includes both stock and mutual insurers. Among the findings, the cost function of the entire sample carries the concavity feature, and insurers tend to use financial derivatives for firm value creation. The results also show that for the entire sample the use of derivatives enhances the mean of cost efficiency but accompanied with larger efficiency volatility. Nevertheless, the utilization of financial derivatives mitigates efficiency volatility for mutual insurers. This research provides important insights for the practice of risk management in the property-liability insurance industry. Journal: North American Actuarial Journal Pages: 487-498 Issue: 4 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597634 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597634 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:4:p:487-498 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Kim Author-X-Name-First: Joseph Author-X-Name-Last: Kim Title: Capital Allocation Using the Bootstrap Abstract: This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart. Journal: North American Actuarial Journal Pages: 499-516 Issue: 4 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597635 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597635 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:4:p:499-516 Template-Type: ReDIF-Article 1.0 Author-Name: Massimo Costabile Author-X-Name-First: Massimo Author-X-Name-Last: Costabile Author-Name: Ivar Massabò Author-X-Name-First: Ivar Author-X-Name-Last: Massabò Author-Name: Emilio Russo Author-X-Name-First: Emilio Author-X-Name-Last: Russo Title: Fair Valuation of Equity-Linked Policies under Insurer Default Risk Abstract: We consider the problem of computing the fair value of equity-linked policies with an interestrate guarantee when the insurer is subject to credit risk. The framework is developed based on modern financial theory using the no-arbitrage principle. In this context, an equity-linked policy is considered as a vulnerable contingent claim that expires before maturity if the firm asset value reaches a prespecified default threshold depending on the firm’s liabilities. We derive a closedform formula in a continuous-time environment to compute the fair value of the contract. We also develop a discrete-time model that allows us to address fair evaluation when the policy embeds a surrender option. Journal: North American Actuarial Journal Pages: 517-534 Issue: 4 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597636 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597636 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:4:p:517-534 Template-Type: ReDIF-Article 1.0 Author-Name: Greg Taylor Author-X-Name-First: Greg Author-X-Name-Last: Taylor Title: A Statistical Basis for Claims Experience Monitoring Abstract: By claims experience monitoring is meant the systematic comparison of the forecasts from a claims model with claims experience as it emerges subsequently. In the event that the stochastic properties of the forecasts are known, the comparison can be represented as a collection of probabilistic statements. This is stochastic monitoring. This paper defines this process rigorously in terms of statistical hypothesis testing. If the model is a regression model (which is the case for most stochastic claims models), then the natural form of hypothesis test is a number of likelihood ratio tests, one for each parameter in the valuation model. Such testing is shown to be very easily implemented by means of generalized linear modeling software. This tests the formal structure of the claims model and is referred to as microtesting. There may be other quantities (e.g., amount of claim payments in a defined interval) that require testing for practical reasons. This sort of testing is referred to as macrotesting, and its formulation is also discussed. Journal: North American Actuarial Journal Pages: 535-552 Issue: 4 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597637 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597637 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:4:p:535-552 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Cowell Author-X-Name-First: Michael Author-X-Name-Last: Cowell Title: “Human Survival at Older Ages and the Implications for Longevity Bond Pricing,” Leslie Mayhew and David Smith, June, 2011 Journal: North American Actuarial Journal Pages: 553-558 Issue: 4 Volume: 15 Year: 2011 X-DOI: 10.1080/10920277.2011.10597638 File-URL: http://hdl.handle.net/10.1080/10920277.2011.10597638 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:15:y:2011:i:4:p:553-558 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equivalent Utility Abstract: The author applies the principle of equivalent utility to price and reserve equity-indexed life insurance. Young and Zariphopoulou (2002a, b) extended this principle to price insurance products in a dynamic framework. However, in those papers, the insurance risks were independent of the risky asset in the financial market. By contrast, the death benefit for equity-indexed life insurance is a function of a risky asset; therefore, this paper further extends the principle of equivalent utility. In a second extension, the author applies the principle of equivalent utility to calculate reserves, as introduced by Gerber (1976). In a related paper, Moore and Young (2002) price equity-indexed pure endowments, the building blocks of equity-indexed life annuities. Journal: North American Actuarial Journal Pages: 68-86 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596078 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596078 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:68-86 Template-Type: ReDIF-Article 1.0 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Author-Name: John A. Mereu Author-X-Name-First: John A. Author-X-Name-Last: Mereu Title: “Comparison of Future Lifetime Distribution and Its Approximations,” Esther Frostig, April 2002 Journal: North American Actuarial Journal Pages: 87-87 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596079 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596079 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:87a-87a Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Pricing Lookback Options and Dynamic Guarantees Abstract: Pricing exotic options or guarantees in equity-indexed annuities can be problematic. The authors present closed-form formulas for pricing lookback options and dynamic guarantees that facilitate the hedging and reserving for such products. The principal tool used is a closed-form expression for B(u, T), the Laplace-Stieltjes transform of the expected excess of the running maximum of a Wiener process above a positive constant u in a finite time interval of length T. If the aggregate net income of a company is modeled with a Wiener process, then the excess of the running maximum above u can be interpreted as aggregate dividend payments, and the quantity B(u, T) is the expectation of the discounted value of the dividend payments up to time T. The formula for B(u, T) is used to price European lookback options (call and put, fixed and floating strike). It is also used to price dynamic fund protection, which is a guarantee on an investment fund: The number of units of the investment fund is increased whenever necessary, so that their total value does not fall below a guaranteed level. The guaranteed level can be stochastic, such as that given by a stock index. Some well-known results for the first passage time of the Wiener process are explained in the appendix. Journal: North American Actuarial Journal Pages: 48-66 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596076 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596076 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:48-66 Template-Type: ReDIF-Article 1.0 Author-Name: Griselda Deelstra Author-X-Name-First: Griselda Author-X-Name-Last: Deelstra Title: “Pricing Lookback Options and Dynamic Guarantees”, Hans U. Gerber and Elias S.W. Shiu, January 2003 Journal: North American Actuarial Journal Pages: 66-67 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596077 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596077 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:66-67 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Title: Multivariate Credibility for Aggregate Loss Models Abstract: Credibility is a form of insurance pricing that is widely used, particularly in North America. It is a special type of experience rating that employs a weighted average of claims experience and a previously established price to determine a new price for each risk class under consideration. This article extends traditional credibility formulas in two aspects. The new procedures are called “multivariate credibility” because both aspects make use of additional sources of data when compared to traditional formulas.Specifically, the first portion of the paper considers data from both the claims number and claims amount processes. Assuming an aggregate loss model for total claims, optimal insurance pricing formulas are derived. The insurance prices turn out to be an intuitively appealing weighted average of the overall mean claim, the claims number experience, and the claims amount experience. The second portion of the paper considers data from claims number and amount processes from multiple lines of business. By using covariances among lines of business (that are conditional on the unobserved heterogeneity), this article shows how to derive more efficient insurance prices.Accounting for covariance among different random quantities (securities) is standard practice in the investment industry. It is more difficult in an insurance context because of the heterogeneity associated with different risk classes. Nonetheless, ignoring this covariance has important ramifications, both theoretically and practically. For an illustrative sample of Massachusetts automobile claims, we show that the relative differences in accounting for and ignoring the covariance range from −3.9% to 14.5% for a selected bundle of insurance coverages. Journal: North American Actuarial Journal Pages: 13-37 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596074 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596074 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:13-37 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Bartholomew Leung Author-X-Name-First: Bartholomew Author-X-Name-Last: Leung Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Indicator Function and Hattendorff Theorem Abstract: This paper presents an integration-by-parts proof of the Hattendorff theorem in the general fully continuous insurance model. The proof motivates a derivation of the theorem in the general fully discrete insurance model. Increments of a martingale over disjoint time intervals are uncorrelated random variables; the paper explains that the Hattendorff theorem can be viewed as an application of this result. A notable feature of the paper is the extensive use of the indicator function. Journal: North American Actuarial Journal Pages: 38-47 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596075 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596075 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:38-47 Template-Type: ReDIF-Article 1.0 Author-Name: Yebin Cheng Author-X-Name-First: Yebin Author-X-Name-Last: Cheng Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Title: Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process Abstract: This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends to infinity. Also, we show the joint probability density function of the surplus before ruin and the deficit at ruin. Journal: North American Actuarial Journal Pages: 1-12 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596073 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596073 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:1-12 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Briys, Eric, and de Varenne, François, Journal: North American Actuarial Journal Pages: 88-89 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596081 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596081 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:88-89 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Comparison of Future Lifetime Distribution and Its Approximations - Discussion by Bruce L. Jones and John A. Mereu Journal: North American Actuarial Journal Pages: 87-87 Issue: 1 Volume: 7 Year: 2003 X-DOI: 10.1080/10920277.2003.10596080 File-URL: http://hdl.handle.net/10.1080/10920277.2003.10596080 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:87-87 Template-Type: ReDIF-Article 1.0 Author-Name: M. Iqbal Owadally Author-X-Name-First: M. Iqbal Author-X-Name-Last: Owadally Author-Name: Haberman Steven Author-X-Name-First: Haberman Author-X-Name-Last: Steven Title: Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans Abstract: The authors consider efficient methods of amortizing actuarial gains and losses in defined-benefit pension plans. In the context of a simple model where asset gains and losses emerge as a consequence of random (independent and identically distributed) rates of investment return, it has been shown that direct amortization of such gains and losses leads to more variable funding levels and contribution rates, compared with an indirect and proportional form of amortization that “spreads” the gains and losses. Stochastic simulations are performed and they indicate that spreading remains more efficient than amortization with simple AR(1) and MA(1) rates of return. Similar results are obtained when a more comprehensive actuarial stochastic investment model (which includes economic wage inflation) is simulated. Proportional spreading is rationalized as the contribution control that optimizes mean square deviations in the contributions and fund levels when the funding process is Markovian and the fund is invested in two assets (a random risky and a risk-free asset). Efficient spreading and amortization periods are suggested for the United States, the United Kingdom, and Canada. Journal: North American Actuarial Journal Pages: 21-36 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596126 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596126 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:21-36 Template-Type: ReDIF-Article 1.0 Author-Name: Greg Taylor Author-X-Name-First: Greg Author-X-Name-Last: Taylor Title: Risk and Discounted Loss Reserves Abstract: The author places the discounting of loss reserves for investment income within a financial economics context. This enables the evaluation of a loss reserve containing a security margin, such as to produce p% confidence in adequacy, taking account of both asset and liability risks. This loss reserve is expressed as a multiple of the economic value of the liabilities. If the security margin is defined as the difference between these two quantities, it is found to increase (decrease) withincreasing asset risk for high (low) values of p. Finally, the author provides a numerical example. Journal: North American Actuarial Journal Pages: 37-44 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596127 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596127 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:37-44 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: Optimal Dividends Abstract: In the absence of dividends, the surplus of a company is modeled by a Wiener process (or Brownian motion) with positive drift. Now dividends are paid according to a barrier strategy: Whenever the (modified) surplus attains the level b, the “overflow” is paid as dividends to shareholders. An explicit expression for the moment-generating function of the time of ruin is given. Let D denote the sum of the discounted dividends until ruin. Explicit expressions for the expectation and the moment-generating function of D are given; furthermore, the limiting distribution of D is determined when the variance parameter of the surplus process tends toward infinity. It is shown that the sum of the (undiscounted) dividends until ruin is a compound geometric random variable with exponentially distributed summands.The optimal level b* is the value of b for which the expectation of D is maximal. It is shown that b* is an increasing function of the variance parameter; as the variance parameter tends toward infinity, b* tends toward the ratio of the drift parameter and the valuation force of interest, which can be interpreted as the present value of a perpetuity. The leverage ratio is the expectation of D divided by the initial surplus invested; it is observed that this leverage ratio is a decreasing function of the initial surplus. For b = b*, the expectation of D, considered as a function of the initial surplus, has the properties of a risk-averse utility function, as long as the initial surplus is less than b*. The expected utility of D is calculated for quadratic and exponential utility functions. In the appendix, the original discrete model of De Finetti (1957) is explained and a probabilistic identity is derived. Journal: North American Actuarial Journal Pages: 1-20 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596125 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596125 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Derrig Author-X-Name-First: Richard Author-X-Name-Last: Derrig Author-Name: Elisha Orr Author-X-Name-First: Elisha Author-X-Name-Last: Orr Title: Equity Risk Premium Abstract: The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about −1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered. Journal: North American Actuarial Journal Pages: 45-69 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596128 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596128 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:45-69 Template-Type: ReDIF-Article 1.0 Author-Name: Philip Heckman Author-X-Name-First: Philip Author-X-Name-Last: Heckman Title: Credit Standing and the Fair Value of Liabilities Abstract: The author reviews the positions of major accounting and actuarial bodies on the issue of whether the holder’s own credit standing should be reflected in the fair value of its liabilities, identifying certain anomalies, both in the current GAAP treatment of debt and in the FASB approach to the fair valuation of liabilities. He also examines the treatment in financial theory of risk capital in the case of unsecured debt. An alternative approach is proposed, stressing the need for an objective valuation standard based solely on contractual terms and ambient economic conditions, and yielding readily interpretable public information. Finally, he reviews the probable consequences if, as seems likely, the FASB approach prevails, or, as seems unlikely, the views advocated here prevail. Journal: North American Actuarial Journal Pages: 70-85 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596129 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596129 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:70-85 Template-Type: ReDIF-Article 1.0 Author-Name: Werner Hürlimann Author-X-Name-First: Werner Author-X-Name-Last: Hürlimann Title: Distortion Risk Measures and Economic Capital Abstract: To provide incentive for active risk management, it is argued that a sound coherent distortion risk measure should preserve some higher degree stop-loss orders, at least the degree-three convex order. Such risk measures are called tail-preserving risk measures. It is shown that, under some common axioms and other plausible conditions, a tail-preserving coherent distortion risk measure identifies necessarily with the Wang right-tail measure or the expected value measure. This main result is applied to derive an optimal economic capital formula. Journal: North American Actuarial Journal Pages: 86-95 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596130 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596130 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:86-95 Template-Type: ReDIF-Article 1.0 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: “Pricing Perpetual Fund Protection with Withdrawal Option,” Hans U. Gerber and Elias S. W. Shiu, April 2003 Journal: North American Actuarial Journal Pages: 96-97 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596131 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596131 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:96-97 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Pricing Perpetual Fund Protection with Withdrawal Option - Discussion by Virginia R. Young Journal: North American Actuarial Journal Pages: 97-99 Issue: 1 Volume: 8 Year: 2004 X-DOI: 10.1080/10920277.2004.10596132 File-URL: http://hdl.handle.net/10.1080/10920277.2004.10596132 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:97-99 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas E. Getzen Author-X-Name-First: Thomas E. Author-X-Name-Last: Getzen Title: Accuracy of Long-Range Actuarial Projections of Health Care Costs Abstract: The Office of the Actuary, mandated to provide projections of future medical spending for use by the U.S. Medicare and Medicaid programs, publishes forecasts that have been widely used by private firms and government budget officials as a baseline for expected long-run premium trends and to estimate liabilities for retiree health benefits. Although these projections have been made publicly available since 1986, they have not yet been subject to systematic evaluation by an external reviewer. This article develops a method for assessment of both short- and long-run accuracy and applies it to the 17 sets of projections made public over the last 25 years. The more recent set of projections (1998–2010) incorporating lagged macroeconomic effects appear to be more accurate than the older (1986–1995) projections that relied more heavily on demographic cost of illness trends. The average annualized error of the forecasts is approximately 0.5–1% per year, whether assessed over a span of one, two, or 10 years. Projecting “excess” growth in health spending (the rise in the share of wages or GDP) tends to be more accurate than forecasting nominal or real spending per capita. Journal: North American Actuarial Journal Pages: 101-113 Issue: 2 Volume: 20 Year: 2016 Month: 4 X-DOI: 10.1080/10920277.2015.1110490 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1110490 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:101-113 Template-Type: ReDIF-Article 1.0 Author-Name: Peng Shi Author-X-Name-First: Peng Author-X-Name-Last: Shi Author-Name: Brian M. Hartman Author-X-Name-First: Brian M. Author-X-Name-Last: Hartman Title: Credibility in Loss Reserving Abstract: This article proposes using credibility theory in the context of stochastic claims reserving. We consider the situation where an insurer has access to the claims experience of its peer competitors and has the potential to improve prediction of outstanding liabilities by incorporating information from other insurers. Based on the framework of Bayesian linear models, we show that the development factor in the classical chain-ladder setting has a credibility expression: a weighted average of the prior mean and the best estimate from the data. In the empirical analysis, we examine loss triangles for the line of commercial auto insurance from a portfolio of insurers in the United States. We employ hierarchical model for the specification of prior and show that prediction could be improved through borrowing strength among insurers based on a hold-out sample validation. Journal: North American Actuarial Journal Pages: 114-132 Issue: 2 Volume: 20 Year: 2016 Month: 4 X-DOI: 10.1080/10920277.2015.1109456 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1109456 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:114-132 Template-Type: ReDIF-Article 1.0 Author-Name: Fei Su Author-X-Name-First: Fei Author-X-Name-Last: Su Author-Name: Kung-Sik Chan Author-X-Name-First: Kung-Sik Author-X-Name-Last: Chan Title: Option Pricing with Threshold Diffusion Processes Abstract: The threshold diffusion (TD) model assumes a piecewise linear drift term and piecewise smooth diffusion term, which can capture many nonlinear features and volatility clustering often observed in financial time series data. We solve the problem of option pricing with a TD asset pricing process by deriving the minimum entropy martingale measure, which is the risk-neutral measure closest to the underlying TD probability measure in terms of Kullback-Leibler divergence, given the historical regime-switching pattern. The proposed valuation model is illustrated with a numerical example. Journal: North American Actuarial Journal Pages: 133-141 Issue: 2 Volume: 20 Year: 2016 Month: 4 X-DOI: 10.1080/10920277.2015.1106953 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1106953 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:133-141 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander Maegebier Author-X-Name-First: Alexander Author-X-Name-Last: Maegebier Author-Name: Nadine Gatzert Author-X-Name-First: Nadine Author-X-Name-Last: Gatzert Title: The Impact of Disability Insurance on a Portfolio of Life Insurances Abstract: The aim of this article is to study the impact of disability insurance on an insurer's risk situation for a portfolio that also consists of annuity and term life contracts. We provide a model framework using discrete time nonhomogeneous bivariate Markov renewal processes and in a simulation study focus on diversification benefits as well as potential natural hedging effects (risk-minimizing or risk-immunizing portfolio compositions) that may arise within the portfolio because of the different types of biometric risks. Our analyses emphasize that disability insurances are a less efficient tool to hedge shocks to mortality and that their high sensitivity toward shocks to disability risks cannot be easily counterbalanced by other life insurance products. However, the addition of disability insurance can still considerably lower the overall company risk. Journal: North American Actuarial Journal Pages: 142-159 Issue: 2 Volume: 20 Year: 2016 Month: 4 X-DOI: 10.1080/10920277.2015.1109457 File-URL: http://hdl.handle.net/10.1080/10920277.2015.1109457 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:142-159 Template-Type: ReDIF-Article 1.0 Author-Name: Nathan R. Lally Author-X-Name-First: Nathan R. Author-X-Name-Last: Lally Author-Name: Brian M. Hartman Author-X-Name-First: Brian M. Author-X-Name-Last: Hartman Title: Predictive Modeling in Long-Term Care Insurance Abstract: The accurate prediction of long-term care insurance (LTCI) mortality, lapse, and claim rates is essential when making informed pricing and risk management decisions. Unfortunately, academic literature on the subject is sparse and industry practice is limited by software and time constraints. In this article, we review current LTCI industry modeling methodology, which is typically Poisson regression with covariate banding/modification and stepwise variable selection. We test the claim that covariate banding improves predictive accuracy, examine the potential downfalls of stepwise selection, and contend that the assumptions required for Poisson regression are not appropriate for LTCI data. We propose several alternative models specifically tailored toward count responses with an excess of zeros and overdispersion. Using data from a large LTCI provider, we evaluate the predictive capacity of random forests and generalized linear and additive models with zero-inflated Poisson, negative binomial, and Tweedie errors. These alternatives are compared to previously developed Poisson regression models.Our study confirms that variable modification is unnecessary at best and automatic stepwise model selection is dangerous. After demonstrating severe overprediction of LTCI mortality and lapse rates under the Poisson assumption, we show that a Tweedie GLM enables much more accurate predictions. Our Tweedie regression models improve average predictive accuracy (measured by several prediction error statistics) over Poisson regression models by as much as four times for mortality rates and 17 times for lapse rates. Journal: North American Actuarial Journal Pages: 160-183 Issue: 2 Volume: 20 Year: 2016 Month: 4 X-DOI: 10.1080/10920277.2016.1176933 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1176933 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:160-183 Template-Type: ReDIF-Article 1.0 Author-Name: Anas Abdallah Author-X-Name-First: Anas Author-X-Name-Last: Abdallah Author-Name: Jean-Philippe Boucher Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Boucher Author-Name: Hélène Cossette Author-X-Name-First: Hélène Author-X-Name-Last: Cossette Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Title: Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis Abstract: The correlation among multiple lines of business plays a critical role in aggregating claims and thus determining loss reserves for an insurance portfolio. We show that the Sarmanov family of bivariate distributions is a convenient choice to capture the dependencies introduced by various sources, including the common calendar year, accident year, and development period effects. The density of the bivariate Sarmanov distributions with different marginals can be expressed as a linear combination of products of independent marginal densities. This pseudo-conjugate property greatly reduces the complexity of posterior computations. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer. Journal: North American Actuarial Journal Pages: 184-200 Issue: 2 Volume: 20 Year: 2016 Month: 4 X-DOI: 10.1080/10920277.2016.1161525 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1161525 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:184-200 Template-Type: ReDIF-Article 1.0 Author-Name: Yichun Chi Author-X-Name-First: Yichun Author-X-Name-Last: Chi Author-Name: Ming Zhou Author-X-Name-First: Ming Author-X-Name-Last: Zhou Title: Optimal Reinsurance Design: A Mean-Variance Approach Abstract: In this article, we study an optimal reinsurance model from the perspective of an insurer who has a general mean-variance preference. In order to reduce ex post moral hazard, we assume that both parties in a reinsurance contract are obligated to pay more for a larger realization of loss. We further assume that the reinsurance premium is calculated only based on the mean and variance of the indemnity. This class of premium principles is quite general in the sense that it includes many widely used premium principles such as expected value, mean value, variance, and standard deviation principles. Moreover, to protect the insurer's profit, a lower bound is imposed on its expected return. We show that any admissible reinsurance policy is dominated by a change-loss reinsurance or a dual change-loss reinsurance, depending upon the coefficient of variation of the ceded loss. Further, the change-loss reinsurance is shown to be optimal if the premium loading increases in the actuarial value of the coverage; while it becomes decreasing, the optimal reinsurance policy is in the form of dual change loss. As a result, the quota-share reinsurance is always optimal for any variance-related reinsurance premium principle. Finally, some numerical examples are applied to illustrate the applicability of the theoretical results. Journal: North American Actuarial Journal Pages: 1-14 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1192478 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1192478 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:1-14 Template-Type: ReDIF-Article 1.0 Author-Name: Mario Ghossoub Author-X-Name-First: Mario Author-X-Name-Last: Ghossoub Title: Arrow's Theorem of the Deductible with Heterogeneous Beliefs Abstract: In Arrow's classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification for an insurance buyer—or decision maker (DM)—is a deductible contract when the insurer is a risk-neutral Expected-Utility (EU) maximizer and when the DM is a risk-averse EU maximizer. In Arrow's framework, however, both parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. This article reexamines Arrow's problem in a setting where the DM and the insurer have different subjective beliefs. Under a requirement of compatibility between the insurer's and the DM's subjective beliefs, we show the existence and monotonicity of optimal indemnity schedules for the DM. The belief compatibility condition is shown to be a weakening of the assumption of a monotone likelihood ratio. In the latter case, we show that the optimal indemnity schedule is a variable deductible schedule, with a state-contingent deductible that depends on the state of the world only through the likelihood ratio. Arrow's classical result is then obtained as a special case. Journal: North American Actuarial Journal Pages: 15-35 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1192477 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1192477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:15-35 Template-Type: ReDIF-Article 1.0 Author-Name: Tatiana Belkina Author-X-Name-First: Tatiana Author-X-Name-Last: Belkina Author-Name: Shangzhen Luo Author-X-Name-First: Shangzhen Author-X-Name-Last: Luo Title: Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process Abstract: We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk-free asset and a Black-Scholes risky asset. The optimization objective is to minimize the probability of ruin. We show by new operators that the minimal ruin probability function is a classical solution to the corresponding HJB equation. Asymptotic behaviors of the optimal investment control policy and the minimal ruin probability function are studied for low surplus levels with a general claim size distribution. Some new asymptotic results for large surplus levels in the case with exponential claim distributions are obtained. We consider two cases of investment control: unconstrained investment and investment with a limited amount. Journal: North American Actuarial Journal Pages: 36-62 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1246252 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1246252 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:36-62 Template-Type: ReDIF-Article 1.0 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Zhenyu Cui Author-X-Name-First: Zhenyu Author-X-Name-Last: Cui Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Title: Impact of Flexible Periodic Premiums on Variable Annuity Guarantees Abstract: In this article, we study the fair fee of a flexible premium variable annuity (FPVA), in which the policyholder can choose to pay periodic premiums during the accumulation phase instead of a single initial premium. We are able to express fair fees using a fast and accurate approximation based on bounds on the price of the FPVA. We identify scenarios that are particularly costly for the insurer. Our study could help insurers estimate the magnitude of typical underpricing when offering flexible-premium variable annuities with the same fee as the corresponding single-premium variable annuity. Journal: North American Actuarial Journal Pages: 63-86 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1209119 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1209119 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:63-86 Template-Type: ReDIF-Article 1.0 Author-Name: Yan Zhang Author-X-Name-First: Yan Author-X-Name-Last: Zhang Author-Name: Yonghong Wu Author-X-Name-First: Yonghong Author-X-Name-Last: Wu Author-Name: Shuang Li Author-X-Name-First: Shuang Author-X-Name-Last: Li Author-Name: Benchawan Wiwatanapataphee Author-X-Name-First: Benchawan Author-X-Name-Last: Wiwatanapataphee Title: Mean-Variance Asset Liability Management with State-Dependent Risk Aversion Abstract: This article investigates the asset liability management problem with state-dependent risk aversion under the mean-variance criterion. The investor allocates the wealth among multiple assets including a risk-free asset and multiple risky assets governed by a system of geometric Brownian motion stochastic differential equations, and the investor faces the risk of paying uncontrollable random liabilities. The state-dependent risk aversion is taken into account in our model, linking the risk aversion to the current wealth held by the investor. An extended Hamilton-Jacobi-Bellman system is established for the optimization of asset liability management, and by solving the extended Hamilton-Jacobi-Bellman system, the analytical closed-form expressions for the time-inconsistent optimal investment strategies and the optimal value function are derived. Finally, numerical examples are presented to illustrate our results. Journal: North American Actuarial Journal Pages: 87-106 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1247719 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1247719 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:87-106 Template-Type: ReDIF-Article 1.0 Author-Name: Adrian O’Hagan Author-X-Name-First: Adrian Author-X-Name-Last: O’Hagan Author-Name: Colm Ferrari Author-X-Name-First: Colm Author-X-Name-Last: Ferrari Title: Model-Based and Nonparametric Approaches to Clustering for Data Compression in Actuarial Applications Abstract: Clustering is used by actuaries in a data compression process to make massive or nested stochastic simulations practical to run. A large data set of assets or liabilities is partitioned into a user-defined number of clusters, each of which is compressed to a single representative policy. The representative policies can then simulate the behavior of the entire portfolio over a large range of stochastic scenarios. Such processes are becoming increasingly important in understanding product behavior and assessing reserving requirements in a big-data environment. This article proposes a variety of clustering techniques that can be used for this purpose. Initialization methods for performing clustering compression are also compared, including principal components, factor analysis, and segmentation. A variety of methods for choosing a cluster's representative policy is considered. A real data set comprising variable annuity policies, provided by Milliman, is used to test the proposed methods. It is found that the compressed data sets produced by the new methods, namely, model-based clustering, Ward's minimum variance hierarchical clustering, and k-medoids clustering, can replicate the behavior of the uncompressed (seriatim) data more accurately than those obtained by the existing Milliman method. This is verified within sample by examining location variable totals of the representative policies versus the uncompressed data at the five levels of compression of interest. More crucially it is also verified out of sample by comparing the distributions of the present values of several variables after 20 years across 1000 simulated scenarios based on the compressed and seriatim data, using Kolmogorov-Smirnov goodness-of-fit tests and weighted sums of squared differences. Journal: North American Actuarial Journal Pages: 107-146 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1234398 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1234398 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:107-146 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Hua Author-X-Name-First: Lei Author-X-Name-Last: Hua Author-Name: Michelle Xia Author-X-Name-First: Michelle Author-X-Name-Last: Xia Author-Name: Sanjib Basu Author-X-Name-First: Sanjib Author-X-Name-Last: Basu Title: Factor Copula Approaches for Assessing Spatially Dependent High-Dimensional Risks Abstract: In this article, we propose an innovative approach for modeling spatial dependence among losses from various geographical locations. The proposed model converts the challenging task of modeling complex spatial dependence structures into a relatively easier task of estimating a continuous function, of which the arguments can be the coordinates of the locations. The approach is based on factor copula models, which can capture various linear and nonlinear dependence. We use radial basis functions as the kernel smoother for estimating the key function that models all the spatial dependence structures. A case study on a thunderstorm wind loss dataset demonstrates the analysis and the usefulness of the proposed approach. Extensions to spatiotemporal models and to models for discrete data are briefly introduced, with an example given for modeling loss frequency with excess zeros. Journal: North American Actuarial Journal Pages: 147-160 Issue: 1 Volume: 21 Year: 2017 Month: 1 X-DOI: 10.1080/10920277.2016.1246251 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1246251 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:147-160 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Stuart Klugman Author-X-Name-First: Stuart Author-X-Name-Last: Klugman Title: Case Studies Add Unique Perspective Journal: North American Actuarial Journal Pages: iii-iv Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596025 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596025 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: Fabrizio Cacciafesta Author-X-Name-First: Fabrizio Author-X-Name-Last: Cacciafesta Title: “Financial and Demographic Risk of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications,” M. G. Bruno, E. Camerini, and A. Tomassetti, October 2000 Journal: North American Actuarial Journal Pages: 112-114 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596022 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596022 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:112-114 Template-Type: ReDIF-Article 1.0 Author-Name: Jill Schield Author-X-Name-First: Jill Author-X-Name-Last: Schield Author-Name: James Murphy Author-X-Name-First: James Author-X-Name-Last: Murphy Author-Name: Howard Bolnick Author-X-Name-First: Howard Author-X-Name-Last: Bolnick Title: Evaluating Managed Care Effectiveness Abstract: Offered to almost everyone who receives employment-based health care benefits, managed care has become the predominant framework for health care plan design. Plan options that emphasize managed care have been added to Medicare and Medicaid programs, making managed care the primary model for health financing and delivery in many parts of the United States. This analysis provides an overview of the functional components of the managed care system. It discusses the market forces underlying the U.S. system for health care financing and delivery and suggests how market forces impact the health care industry. The analysis focuses on societal goals for health care delivery and on managed care’s effectiveness in enabling achievement of those goals.This paper develops and uses a descriptive model to summarize the complex interplay among the many stakeholders, or participants, in the health care system. The paper does not propose a quantitative approach to measuring effectiveness; rather, it sets up a model upon which assessments can be made or an index can be developed. The model provides a framework for looking at the many relationships among stakeholders. The discussion also highlights current issues in managed care, particularly the barriers that impede collaboration among stakeholders. Journal: North American Actuarial Journal Pages: 95-111 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596021 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596021 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:95-111 Template-Type: ReDIF-Article 1.0 Author-Name: Leonie Tickle Author-X-Name-First: Leonie Author-X-Name-Last: Tickle Title: “Why Men Die Younger: Causes of Mortality Differences By Sex,” Barbara Blatt Kalben, October 2000 Journal: North American Actuarial Journal Pages: 116-116 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596024 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596024 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:116-116 Template-Type: ReDIF-Article 1.0 Author-Name: Jess Mast Author-X-Name-First: Jess Author-X-Name-Last: Mast Title: “Why Men Die Younger: Causes of Mortality Differences By Sex,” Barbara Blatt Kalben, October 2000 Journal: North American Actuarial Journal Pages: 114-116 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596023 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596023 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:114-116 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Mark Browne Author-X-Name-First: Mark Author-X-Name-Last: Browne Title: The Impact of the Inpatient Prospective Payment System and Diagnosis-Related Groups Abstract: The outpatient prospective payment system for the Medicare program became effective Aug. 1, 2000, as mandated by the Balanced Budget Act of 1997. This outpatient program complements Medicare’s inpatient prospective payment system, which was introduced in 1983. A survey of the literature over the past 20 years is undertaken to review the effects of the inpatient prospective payment system and diagnosis-related groups (DRGs) on inpatient hospital utilization, expenditures, and outcomes. The level of the DRG payment has been questioned, as well as the process of adjusting the payment levels from one year to the next. In addition, past research has speculated that the DRG classification may not be sensitive to severity and is subject to coding ambiguities. These conclusions can be used as input to future research on the new outpatient program, as well as updating research on the inpatient program. Journal: North American Actuarial Journal Pages: 84-94 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596020 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596020 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:84-94 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Author-Name: Yu Luo Author-X-Name-First: Yu Author-X-Name-Last: Luo Title: Case Studies Using Panel Data Models Abstract: In this paper, we examine case studies from three different areas of insurance practice: health care, workers’ compensation, and group term life. These different case studies illustrate how the broad class of panel data models can be applied to different functional areas and to data that have different features. Panel data, also known as longitudinal data, models are regression-type models that have been developed extensively in the biological and economic sciences. The data features that we discuss include heteroscedasticity, random and fixed effect covariates, outliers, serial correlation, and limited dependent variable bias. We demonstrate the process of identifying these features using graphical and numerical diagnostic tools from standard statistical software.Our motivation for examining these cases comes from credibility rate making, a technique for pricing certain types of health care, property and casualty, workers’ compensation, and group life coverages. It has been a part of actuarial practice since Mowbray’s (1914) fundamental contribution. In earlier work, we showed how many types of credibility models could be expressed as special cases of panel data models. This paper exploits this link by using tools developed in connection with panel data models for credibility rate-making purposes. In particular, special routines written for credibility rate-making purposes are not required. Journal: North American Actuarial Journal Pages: 24-42 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596010 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596010 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:24-42 Template-Type: ReDIF-Article 1.0 Author-Name: Udi Makov Author-X-Name-First: Udi Author-X-Name-Last: Makov Title: Principal Applications of Bayesian Methods in Actuarial Science Abstract: Bayesian ideas were introduced into actuarial science in the late 1960s in the form of empirical credibility methods for premium setting. The advance of the Bayesian methodology was slow due to its subjective nature and to the computational difficulties associated with the full Bayesian analysis. This paper offers a brief survey of Bayesian solutions to some actuarial problems and discusses the current state of research. Journal: North American Actuarial Journal Pages: 53-57 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596011 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:53-57 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 57-60 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596012 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596012 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:57-60 Template-Type: ReDIF-Article 1.0 Author-Name: M. Mendoza Author-X-Name-First: M. Author-X-Name-Last: Mendoza Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 60-62 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596013 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:60-62 Template-Type: ReDIF-Article 1.0 Author-Name: Francisco Vázquez-Polo Author-X-Name-First: Francisco Author-X-Name-Last: Vázquez-Polo Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 62-67 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596014 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596014 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:62-67 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Donald Jones Author-X-Name-First: Donald Author-X-Name-Last: Jones Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 67-69 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596015 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596015 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:67-69 Template-Type: ReDIF-Article 1.0 Author-Name: Enrique de Alba Author-X-Name-First: Enrique Author-X-Name-Last: de Alba Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 69-72 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596016 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596016 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:69-72 Template-Type: ReDIF-Article 1.0 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 72-72 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596017 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596017 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:72-72 Template-Type: ReDIF-Article 1.0 Author-Name: John Beekman Author-X-Name-First: John Author-X-Name-Last: Beekman Author-Name: Eli Donkar Author-X-Name-First: Eli Author-X-Name-Last: Donkar Title: The Relationship Between the Supplemental Security Income and the Old-Age, Survivors, and Disability Insurance Programs During the 1990s Abstract: The purpose of this paper is to discuss the relationships between the Supplemental Security Income (SSI) program and the Old-Age, Survivors, and Disability Insurance (OASDI) programs during the 1990s. The focus is on the persons concurrently receiving benefits from both programs, but analyzed from the alternative perspectives of the SSI and OASDI programs separately. Longitudinal sample data drawn from Social Security Administration administrative records are used to perform the analysis. Fourteen tables and eight figures present the data stratified in various ways by gender, age, and program involvement. An analysis of observed trends is presented, along with some suggestions for needed future research. Journal: North American Actuarial Journal Pages: 1-23 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596009 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:1-23 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Author’s Reply: Principal Applications of Bayesian Methods in Actuarial Science: A Perspective - Discussion by Marjorie A. Rosenberg; M. Mendoza; Francisco José VáZquez-Polo; James C. Hickman; Donald A. Jones; Enrique de Alba; David P. M. Scollnik Journal: North American Actuarial Journal Pages: 72-73 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596018 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596018 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:72-73 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Title: A Statistical Method for Monitoring a Change in the Rate of Nonacceptable Inpatient Claims Abstract: This paper is an extension of earlier work (Rosenberg 1998; Rosenberg, Andrews, and Lenk 1999; Rosenberg and Griffith 2000) that introduced a statistical control model to supplement current efforts inexpensively to help reduce unnecessary expenditures. The application of the study was to predict the rate of nonacceptable inpatient claims (NACs). In that work, a statistical model was proposed to link information obtained through an expensive audit with inexpensive information that is readily available to estimate the probability that a claim is a NAC. The premise was that a statistical system can be developed to supplement the expensive audit for additional control between audits.Estimates of the NAC rate obtained from the statistical model are used as input in a statistical monitor to assess whether the NAC rate had changed over time. The statistical monitor is the subject of this paper. The idea is that subgroups of claims can be analyzed inexpensively with the statistical monitor to determine whether any current intervention is required prior to the time of the next scheduled audit, or whether adjustments are needed in the determination of claims to be sampled for the audit. In this study, the estimate for the NAC rate at t0 is compared against the estimate of the NAC rate at some later time t1. A decision rule is proposed to assess whether a change in the NAC rate has occurred for that subgroup. The methodology is also applicable to other health care measurements. Journal: North American Actuarial Journal Pages: 74-83 Issue: 4 Volume: 5 Year: 2001 X-DOI: 10.1080/10920277.2001.10596019 File-URL: http://hdl.handle.net/10.1080/10920277.2001.10596019 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:5:y:2001:i:4:p:74-83 Template-Type: ReDIF-Article 1.0 Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Richard MacMinn Author-X-Name-First: Richard Author-X-Name-Last: MacMinn Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Longevity Risk and Capital Markets: The 2012–2013 Update Journal: North American Actuarial Journal Pages: 1-13 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2014.883233 File-URL: http://hdl.handle.net/10.1080/10920277.2014.883233 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:1-13 Template-Type: ReDIF-Article 1.0 Author-Name: Andrés Villegas Author-X-Name-First: Andrés Author-X-Name-Last: Villegas Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England Abstract: In any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area, or socioeconomic variables (e.g., occupation, level of education, or income). These differentials, and in particular those related to socioeconomic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modeling and forecasting of socioeconomic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modeling of the mortality in socioeconomic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyze the impact of socioeconomic differences in mortality on the valuation of annuities. Journal: North American Actuarial Journal Pages: 168-193 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.866034 File-URL: http://hdl.handle.net/10.1080/10920277.2013.866034 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:168-193 Template-Type: ReDIF-Article 1.0 Author-Name: Emilio Bisetti Author-X-Name-First: Emilio Author-X-Name-Last: Bisetti Author-Name: Carlo Favero Author-X-Name-First: Carlo Author-X-Name-Last: Favero Title: Measuring the Impact of Longevity Risk on Pension Systems: The Case of Italy Abstract: This article estimates the impact of longevity risk on pension systems by combining the prediction based on a Lee-Carter mortality model with the projected pension payments for different cohorts of retirees. We measure longevity risk by the difference between the upper bound of the total old-age pension expense and its mean estimate. This difference is as high as 4% of annual GDP over the period 2040–2050. The impact of longevity risk is sizeably reduced, but not fully eliminated, by the introduction of indexation of retirement age to expected life at retirement. Our evidence speaks in favor of a market for longevity risk and calls for a closer scrutiny of the potential redistributive effects of longevity risk. Journal: North American Actuarial Journal Pages: 87-103 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.852463 File-URL: http://hdl.handle.net/10.1080/10920277.2013.852463 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:87-103 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Hunt Author-X-Name-First: Andrew Author-X-Name-Last: Hunt Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: A General Procedure for Constructing Mortality Models Abstract: Recently a large number of new mortality models have been proposed to analyze historic mortality rates and project them into the future. Many of these suffer from being over-parametrized or have terms added in an ad hoc manner that cannot be justified in terms of demographic significance. In addition, poor specification of a model can lead to period effects in the data being wrongly attributed to cohort effects, which results in the model making implausible projections. We present a general procedure for constructing mortality models using a combination of a toolkit of functions and expert judgment. By following the general procedure, it is possible to identify sequentially every significant demographic feature in the data and give it a parametric structural form. We demonstrate using U.K. mortality data that the general procedure produces a relatively parsimonious model that nevertheless has a good fit to the data. Journal: North American Actuarial Journal Pages: 116-138 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.852963 File-URL: http://hdl.handle.net/10.1080/10920277.2013.852963 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:116-138 Template-Type: ReDIF-Article 1.0 Author-Name: Shuo-Li Chuang Author-X-Name-First: Shuo-Li Author-X-Name-Last: Chuang Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Title: Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform Abstract: The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk–related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association. Journal: North American Actuarial Journal Pages: 22-37 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.873708 File-URL: http://hdl.handle.net/10.1080/10920277.2013.873708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:22-37 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Alai Author-X-Name-First: Daniel Author-X-Name-Last: Alai Author-Name: Hua Chen Author-X-Name-First: Hua Author-X-Name-Last: Chen Author-Name: Daniel Cho Author-X-Name-First: Daniel Author-X-Name-Last: Cho Author-Name: Katja Hanewald Author-X-Name-First: Katja Author-X-Name-Last: Hanewald Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions Abstract: Equity release products are sorely needed in an aging population with high levels of home ownership. There has been a growing literature analyzing risk components and capital adequacy of reverse mortgages in recent years. However, little research has been done on the risk analysis of other equity release products, such as home reversion contracts. This is partly due to the dominance of reverse mortgage products in equity release markets worldwide. In this article we compare cash flows and risk profiles from the provider's perspective for reverse mortgage and home reversion contracts. An at-home/in long-term care split termination model is employed to calculate termination rates, and a vector autoregressive (VAR) model is used to depict the joint dynamics of economic variables including interest rates, house prices, and rental yields. We derive stochastic discount factors from the no arbitrage condition and price the no negative equity guarantee in reverse mortgages and the lease for life agreement in the home reversion plan accordingly. We compare expected payoffs and assess riskiness of these two equity release products via commonly used risk measures: Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Journal: North American Actuarial Journal Pages: 217-241 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2014.882252 File-URL: http://hdl.handle.net/10.1080/10920277.2014.882252 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:217-241 Template-Type: ReDIF-Article 1.0 Author-Name: Atsuyuki Kogure Author-X-Name-First: Atsuyuki Author-X-Name-Last: Kogure Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Author-Name: Shinichi Kamiya Author-X-Name-First: Shinichi Author-X-Name-Last: Kamiya Title: A Bayesian Multivariate Risk-Neutral Method for Pricing Reverse Mortgages Abstract: In this article, we propose a Bayesian multivariate framework to price reverse mortgages that involve several risks in both insurance and financial sectors (e.g., mortality rates, interest rates, and house prices). Our method is a multivariate extension of the Bayesian risk-neutral method developed by Kogure and Kurachi. We apply the proposed method to Japanese data to examine the possibility for a successful introduction of reverse mortgages into Japan. The results suggest a promising future for this new market. Journal: North American Actuarial Journal Pages: 242-257 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.872983 File-URL: http://hdl.handle.net/10.1080/10920277.2013.872983 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:242-257 Template-Type: ReDIF-Article 1.0 Author-Name: Nan Zhu Author-X-Name-First: Nan Author-X-Name-Last: Zhu Author-Name: Daniel Bauer Author-X-Name-First: Daniel Author-X-Name-Last: Bauer Title: A Cautionary Note on Natural Hedging of Longevity Risk Abstract: In this article, we examine the so-called natural hedging approach for life insurers to internally manage their longevity risk exposure by adjusting their insurance portfolio. In particular, unlike the existing literature, we also consider a nonparametric mortality forecasting model that avoids the assumption that all mortality rates are driven by the same factor(s).Our primary finding is that higher order variations in mortality rates may considerably affect the performance of natural hedging. More precisely, although results based on a parametric single factor model—in line with the existing literature—imply that almost all longevity risk can be hedged, results are far less encouraging for the nonparametric mortality model. Our finding is supported by robustness tests based on alternative mortality models. Journal: North American Actuarial Journal Pages: 104-115 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.876911 File-URL: http://hdl.handle.net/10.1080/10920277.2013.876911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:104-115 Template-Type: ReDIF-Article 1.0 Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Tom Boardman Author-X-Name-First: Tom Author-X-Name-Last: Boardman Author-Name: Andrew Cairns Author-X-Name-First: Andrew Author-X-Name-Last: Cairns Title: Sharing Longevity Risk: Why Governments Should Issue Longevity Bonds Abstract: Government-issued longevity bonds would allow longevity risk to be shared efficiently and fairly between generations. In exchange for paying a longevity risk premium, the current generation of retirees can look to future generations to hedge their systematic longevity risk. Longevity bonds will lead to a more secure pension savings market, together with a more efficient annuity market. By issuing longevity bonds, governments can aid the establishment of reliable longevity indices and key price points on the longevity risk term structure and help the emerging capital market in longevity-linked instruments to build on this term structure with liquid longevity derivatives. Journal: North American Actuarial Journal Pages: 258-277 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2014.883229 File-URL: http://hdl.handle.net/10.1080/10920277.2014.883229 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:258-277 Template-Type: ReDIF-Article 1.0 Author-Name: Enrico Biffis Author-X-Name-First: Enrico Author-X-Name-Last: Biffis Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: Keeping Some Skin in the Game: How to Start a Capital Market in Longevity Risk Transfers Abstract: The recent activity in pension buyouts and bespoke longevity swaps suggests that a significant process of aggregation of longevity exposures is under way, led by major insurers, investment banks, and buyout firms with the support of leading reinsurers. As regulatory capital charges and limited reinsurance capacity constrain the scope for market growth, there is now an opportunity for institutions that are pooling longevity exposures to issue securities that appeal to capital market investors, thereby broadening the sharing of longevity risk and increasing market capacity. For this to happen, longevity exposures need to be suitably pooled and tranched to maximize diversification benefits offered to investors and to address asymmetric information issues. We argue that a natural way for longevity risk to be transferred is through suitably designed principal-at-risk bonds. Journal: North American Actuarial Journal Pages: 14-21 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.872552 File-URL: http://hdl.handle.net/10.1080/10920277.2013.872552 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:14-21 Template-Type: ReDIF-Article 1.0 Author-Name: Yijia Lin Author-X-Name-First: Yijia Author-X-Name-Last: Lin Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Author-Name: Ruilin Tian Author-X-Name-First: Ruilin Author-X-Name-Last: Tian Author-Name: Jifeng Yu Author-X-Name-First: Jifeng Author-X-Name-Last: Yu Title: Downside Risk Management of a Defined Benefit Plan Considering Longevity Basis Risk Abstract: To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies. Journal: North American Actuarial Journal Pages: 68-86 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.852064 File-URL: http://hdl.handle.net/10.1080/10920277.2013.852064 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:68-86 Template-Type: ReDIF-Article 1.0 Author-Name: Helena Aro Author-X-Name-First: Helena Author-X-Name-Last: Aro Title: Systematic and Nonsystematic Mortality Risk in Pension Portfolios Abstract: We study the effects of nonsystematic and systematic mortality risks on the required initial capital in a pension plan, in the presence of financial risks. We discover that for a pension plan with few members the impact of pooling on the required capital per person is strong, but nonsystematic risk diminishes rapidly as the number of members increases. Systematic mortality risk, on the other hand, is a significant source of risk in a pension portfolio. Journal: North American Actuarial Journal Pages: 59-67 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.861340 File-URL: http://hdl.handle.net/10.1080/10920277.2013.861340 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:59-67 Template-Type: ReDIF-Article 1.0 Author-Name: Les Mayhew Author-X-Name-First: Les Author-X-Name-Last: Mayhew Author-Name: David Smith Author-X-Name-First: David Author-X-Name-Last: Smith Title: Gender Convergence in Human Survival and the Postponement of Death Abstract: It has been a long-accepted demographic maxim that females outlive males. Using data for England and Wales, we show that life expectancy at age 30 is converging, and continuation of this long-term trend suggests life expectancy could reach parity in 2030, resulting in considerable economic and social ramifications. The degree of parity in life expectancy is examined by comparing the historical record in four countries that show that convergence is not a new phenomenon. Contributory factors are considered including changes in male smoking habits and male employment patterns. A model is presented that considers gender differences in longevity using novel methods for analyzing life tables. It determines the ages from which death is being postponed, to the ages at which people now die, the relative speed at which these changes are taking place between genders, and how the changes observed are affecting survival prospects at different ages up to 2030. It finds that as life expectancy continues to rise there is accompanying convergence in modal age of death of between 92 and 93 years. Journal: North American Actuarial Journal Pages: 194-216 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.863140 File-URL: http://hdl.handle.net/10.1080/10920277.2013.863140 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:194-216 Template-Type: ReDIF-Article 1.0 Author-Name: Valeria D’Amato Author-X-Name-First: Valeria Author-X-Name-Last: D’Amato Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Gabriella Piscopo Author-X-Name-First: Gabriella Author-X-Name-Last: Piscopo Author-Name: Maria Russolillo Author-X-Name-First: Maria Author-X-Name-Last: Russolillo Author-Name: Lorenzo Trapani Author-X-Name-First: Lorenzo Author-X-Name-Last: Trapani Title: Detecting Common Longevity Trends by a Multiple Population Approach Abstract: Recently the interest in the development of country and longevity risk models has been growing. The investigation of long-run equilibrium relationships could provide valuable information about the factors driving changes in mortality, in particular across ages and across countries. In order to investigate cross-country common longevity trends, tools to quantify, compare, and model the strength of dependence become essential. On one hand, it is necessary to take into account either the dependence for adjacent age groups or the dependence structure across time in a single population setting—a sort of intradependence structure. On the other hand, the dependence across multiple populations, which we describe as interdependence, can be explored for capturing common long-run relationships between countries. The objective of our work is to produce longevity projections by taking into account the presence of various forms of cross-sectional and temporal dependencies in the error processes of multiple populations, considering mortality data from different countries. The algorithm that we propose combines model-based predictions in the Lee-Carter (LC) framework with a bootstrap procedure for dependent data, and so both the historical parametric structure and the intragroup error correlation structure are preserved. We introduce a model which applies a sieve bootstrap to the residuals of the LC model and is able to reproduce, in the sampling, the dependence structure of the data under consideration. In the current article, the algorithm that we build is applied to a pool of populations by using ideas from panel data; we refer to this new algorithm as the Multiple Lee-Carter Panel Sieve (MLCPS). We are interested in estimating the relationship between populations of similar socioeconomic conditions. The empirical results show that the MLCPS approach works well in the presence of dependence. Journal: North American Actuarial Journal Pages: 139-149 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.875884 File-URL: http://hdl.handle.net/10.1080/10920277.2013.875884 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:139-149 Template-Type: ReDIF-Article 1.0 Author-Name: Rui Zhou Author-X-Name-First: Rui Author-X-Name-Last: Zhou Author-Name: Yujiao Wang Author-X-Name-First: Yujiao Author-X-Name-Last: Wang Author-Name: Kai Kaufhold Author-X-Name-First: Kai Author-X-Name-Last: Kaufhold Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Title: Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II Abstract: Recently Cairns et al. introduced a general framework for modeling the dynamics of mortality rates of two related populations simultaneously. Their method ensures that the resulting forecasts do not diverge over the long run by modeling the difference in the stochastic factors between the two populations with a mean-reverting autoregressive process. In this article, we investigate how the modeling of the stochastic factors may be improved by using a vector error correction model. This extension is highly intuitive, allowing us to visualize the cross-correlations and the long-term equilibrium relation between the two populations. Another key benefit is that this extension does not require the user to assume which one of the two populations is dominant. This benefit is important because, as we demonstrate, it is not always easy to identify the dominant population, even if one population is much larger than the other. We illustrate our proposed extension with data from a pair of populations and apply it to the calculation of Solvency II risk capital. Journal: North American Actuarial Journal Pages: 150-167 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.872553 File-URL: http://hdl.handle.net/10.1080/10920277.2013.872553 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:150-167 Template-Type: ReDIF-Article 1.0 Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Title: The CBD Mortality Indexes: Modeling and Applications Abstract: Most extrapolative stochastic mortality models are constructed in a similar manner. Specifically, when they are fitted to historical data, one or more series of time-varying parameters are identified. By extrapolating these parameters to the future, we can obtain a forecast of death probabilities and consequently cash flows arising from life contingent liabilities. In this article, we first argue that, among various time-varying model parameters, those encompassed in the Cairns-Blake-Dowd (CBD) model (also known as Model M5) are most suitably used as indexes to indicate levels of longevity risk at different time points. We then investigate how these indexes can be jointly modeled with a more general class of multivariate time-series models, instead of a simple random walk that takes no account of cross-correlations. Finally, we study the joint prediction region for the mortality indexes. Such a region, as we demonstrate, can serve as a graphical longevity risk metric, allowing practitioners to compare the longevity risk exposures of different portfolios readily. Journal: North American Actuarial Journal Pages: 38-58 Issue: 1 Volume: 18 Year: 2014 X-DOI: 10.1080/10920277.2013.854161 File-URL: http://hdl.handle.net/10.1080/10920277.2013.854161 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:38-58 Template-Type: ReDIF-Article 1.0 Author-Name: William Panning Author-X-Name-First: William Author-X-Name-Last: Panning Title: Managing the Invisible: Identifying Value-Maximizing Combinations of Risk and Capital Abstract: This article demonstrates the linkage—often asserted but seldom described—between Enterprise Risk Management (ERM) and maximizing a firm's value. I show that knowing a firm's aggregate risk exposure (via ERM), when combined with a valuation model like the one presented here, can enable the firm's managers to identify and choose value-maximizing combinations of risk and capital. Using value maximization as the criterion for choosing a firm's capital structure is quite distinct from rules of thumb that CFOs often use for such decisions. The valuation model shows that increasing an insurer's surplus from an initially low level typically increases the present value of future cash flows that take into account the probability of impairment from extreme losses. In contrast to traditional literature on the risk of ruin, impairment here is taken to mean a loss of creditworthiness such that the firm's business model is no longer sustainable, whether or not the firm is solvent. However, beyond a certain optimal level relative to a firm's risk, further increases in surplus actually reduce a firm's value added measured in this fashion. Sensitivity analyses presented here show how these conclusions are affected by changes in the values of crucial variables. In particular, the article shows how managers can use this model to identify specific actions that their firm can take to increase its value added, and it emphasizes the practical importance of making a firm's value both visible and manageable. Journal: North American Actuarial Journal Pages: 13-28 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.775011 File-URL: http://hdl.handle.net/10.1080/10920277.2013.775011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:13-28 Template-Type: ReDIF-Article 1.0 Author-Name: Colin Ramsay Author-X-Name-First: Colin Author-X-Name-Last: Ramsay Author-Name: Luis Arcila Author-X-Name-First: Luis Author-X-Name-Last: Arcila Title: Pricing Funeral (Burial) Insurance in a Microinsurance World with Emphasis on Africa Abstract: Funeral (burial) insurance is one of the most common microinsurance policies sold in Africa. Funeral insurance is important because it pays for the cost of funeral arrangements, thus forming an important part of protection for low-income workers. We develop a model of a microinsurance market in an African context where funeral insurance policies are sold to low-income households through a burial society, which contracts with a risk-neutral profit-maximizing monopolistic insurer to supply funeral insurance policies. We assume the burial society is sufficiently large that it has bargaining power and can negotiate on behalf of its members. The burial society requires that the insurer offer separate policies that are affordable to both low-risk and high-risk individuals and waiting periods cannot exceed m months. Applicants for insurance are identical except for their mortality, which is known to the insurer except for a single parameter called the frailty parameter. As death benefits and premiums are low, the insurer cannot afford to use a costly but effective underwriting technology to provide accurate information on each applicant's future mortality. To mitigate the effect of adverse selection, the insurer uses a simple low-cost practical underwriting strategy that requires all applicants to complete a questionnaire on their personal/family medical history, certify their “good health,” and confirm that they are gainfully employed. The insurer also includes a waiting period before policyholders are eligible for death benefits. As there is no established actuarial theory that suggests how the optimum waiting period should be determined, the objective of this article is to establish a sound basis for determining both the premium and the waiting period for these policies. To this end we develop a discounted expected utility model of consumption by members of a burial society and use this model to determine the optimal premiums and waiting periods subject to solvency, lapse, and participation constraints. Journal: North American Actuarial Journal Pages: 63-81 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.774592 File-URL: http://hdl.handle.net/10.1080/10920277.2013.774592 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:63-81 Template-Type: ReDIF-Article 1.0 Author-Name: Charles Yang Author-X-Name-First: Charles Author-X-Name-Last: Yang Title: The Impact of the Interest Rate on Insurance/Financials Industries: The Analysis of the Stock Market's Reactions to Federal Funds Rate Changes Abstract: Taking an event-study approach, this article examines the impact of the interest rate on the insurance industry and its subindustries in contrast with other financials industries through the analysis of the stock market's reactions to federal funds rate changes. In addition to calculating the stock market's reaction on event days, this article analyzes market over- or underreaction by examining the stock market's responses on the following days. Furthermore, the stock market's reaction on days preceding event days is explored to test pre-announcement effects. This article also investigates asymmetries in responses of insurance and financials stock markets to certain characteristics of federal rate changes. This research provides important insights to investors, regulators and policymakers, and the management of insurance and financials companies in understanding the link between monetary policy and asset prices and the policy transmission mechanism particularly related to insurance and financials industries. Journal: North American Actuarial Journal Pages: 29-40 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.773243 File-URL: http://hdl.handle.net/10.1080/10920277.2013.773243 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:29-40 Template-Type: ReDIF-Article 1.0 Author-Name: Christian Genest Author-X-Name-First: Christian Author-X-Name-Last: Genest Author-Name: Alberto Carabarín-Aguirre Author-X-Name-First: Alberto Author-X-Name-Last: Carabarín-Aguirre Title: A Digital Picture of the Actuarial Research Community Abstract: The evolution of publication patterns in actuarial research is described through a survey of the contents of four peer-reviewed journals identified in several studies as the most influential in the field, including the North American Actuarial Journal. The research output of countries and institutions is compared over the 30-year period 1982–2011 on the basis of the number of articles and pages published, adjusted for journal page size. While simple counts such as these are only a cursory measure of productivity, and certainly not a measure of quality, they lead to rankings that broadly reflect the level of activity in actuarial research worldwide. Countries and institutions that are most active in the field are easily identified from these rankings. Such information is valuable to governmental funding agencies and administrators in academia or industry responsible for the quantitative assessment of research performance. Young researchers and prospective graduate students may also find it useful to acquaint themselves with the breadth of the actuarial research community. Journal: North American Actuarial Journal Pages: 3-12 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.779917 File-URL: http://hdl.handle.net/10.1080/10920277.2013.779917 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:3-12 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Editorial Journal: North American Actuarial Journal Pages: 1-2 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.792219 File-URL: http://hdl.handle.net/10.1080/10920277.2013.792219 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:1-2 Template-Type: ReDIF-Article 1.0 Author-Name: Philip Booth Author-X-Name-First: Philip Author-X-Name-Last: Booth Title: State Pension Reform in a Public Choice Framework Abstract: Social security systems for old age have been explicitly studied in a public choice framework for more than 30 years. They illustrate extremely well the problems of allocating economic resources through a system of voting. Despite actuarial interest in state pension systems and despite the actuarial calculations that are needed to understand long-term public choice trends, there is almost no reference to public choice economics in the actuarial pensions literature. It can be argued that pension systems currently provide some of the most significant threats to the long-term budget positions of developed countries, a point that was made in the Nobel Laureate lecture of Professor James Buchanan over 24 years ago. In this article, we look at the costs and benefits that will be faced by different groups of voters as a result of state pension reform in the United Kingdom. The results of this analysis suggest that a majority of the electorate will have a strong financial interest in opposing state pension reform except where reform involves raising retirement ages. These results are in accordance not just with theoretical work but with other empirical work and practical observations. Journal: North American Actuarial Journal Pages: 82-97 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.774194 File-URL: http://hdl.handle.net/10.1080/10920277.2013.774194 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:82-97 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Title: Pricing and Hedging Variable Annuity Guarantees with Multiasset Stochastic Investment Models Abstract: Variable annuities are often sold with guarantees to protect investors from downside investment risk. The majority of variable annuity guarantees are written on more than one asset, but in practice, single-asset (univariate) stochastic investment models are mostly used for pricing and hedging these guarantees. This practical shortcut may lead to problems such as basis risk. In this article, we contribute a multivariate framework for pricing and hedging variable annuity guarantees. We explain how to transform multivariate stochastic investment models into their risk-neutral counterparts, which can then be used for pricing purposes. We also demonstrate how dynamic hedging can be implemented in a multivariate framework and how the potential hedging error can be quantified by stochastic simulations. Journal: North American Actuarial Journal Pages: 41-62 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.773240 File-URL: http://hdl.handle.net/10.1080/10920277.2013.773240 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:41-62 Template-Type: ReDIF-Article 1.0 Author-Name: S. Vanduffel Author-X-Name-First: S. Author-X-Name-Last: Vanduffel Author-Name: Jing Yao Author-X-Name-First: Jing Author-X-Name-Last: Yao Title: Discussion on “Asymptotic Analysis of Multivariate Tail Conditional Expectations,” by Li Zhu and Haijun Li, Volume 16(3) Journal: North American Actuarial Journal Pages: 98-100 Issue: 1 Volume: 17 Year: 2013 X-DOI: 10.1080/10920277.2013.781409 File-URL: http://hdl.handle.net/10.1080/10920277.2013.781409 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:17:y:2013:i:1:p:98-100 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Friend Author-X-Name-First: Edward Author-X-Name-Last: Friend Title: “The Shift to Defined Contribution Pension Plans: Why Did It Not Happen in Canada?” Robert L. Brown and Jianxun Liu, July 2001 Journal: North American Actuarial Journal Pages: 125-125 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596048 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596048 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:125-125 Template-Type: ReDIF-Article 1.0 Author-Name: Heath Windcliff Author-X-Name-First: Heath Author-X-Name-Last: Windcliff Author-Name: Martin Le Roux Author-X-Name-First: Martin Author-X-Name-Last: Le Roux Author-Name: Peter Forsyth Author-X-Name-First: Peter Author-X-Name-Last: Forsyth Author-Name: Kenneth Vetzal Author-X-Name-First: Kenneth Author-X-Name-Last: Vetzal Title: Understanding the Behavior and Hedging of Segregated Funds Offering the Reset Feature Abstract: Segregated funds have become an extremely popular Canadian investment vehicle. These instruments provide long-term maturity guarantees and often include complex option features. One controversial aspect is the reset feature, which provides the ability to lock in market gains. Recently, regulators have announced that firms offering these products will be subject to new capital requirements. This paper discusses the effects of volatility, interest rates, investor optimality, and product design on the cost of providing a segregated fund guarantee. For each scenario, the authors provide the appropriate management expense ratio (MER) that should be charged and demonstrate the current liability using a given fixed MER. The paper also investigates intuitive reasons that cause the reset feature to require such a dramatic increase in the hedging costs. Finally, an approximate method for handling the reset feature is presented that can be computed very efficiently, provided the correct proportional fee is charged. Journal: North American Actuarial Journal Pages: 107-124 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596047 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596047 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:107-124 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Klieber Author-X-Name-First: Eric Author-X-Name-Last: Klieber Title: “Macroeconomic Aspects of Private Retirement Programs,” Krzysztof M. Ostaszewski, July 2001 Journal: North American Actuarial Journal Pages: 125-127 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596049 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596049 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:125-127 Template-Type: ReDIF-Article 1.0 Author-Name: Allan Brender Author-X-Name-First: Allan Author-X-Name-Last: Brender Title: The Use of Internal Models for Determining Liabilities and Capital Requirements Abstract: Statutory capital requirements for insurers exist in several jurisdictions. They are generally formulabased and do not reflect the specific nature of a company’s asset or liability portfolio. Capital requirements for banks in the developed countries follow the Basel Capital Accord. In certain circumstances, the Accord permits the use of internal models to determine portions of a bank’s required capital. The Canadian federal regulator, OSFI, is beginning to allow life insurers to use internal models for the determination of certain components of its overall capital requirement, the MCCSR. This paper describes the risks that can be covered by these models and the conditions that must be satisfied before these models can be used. Journal: North American Actuarial Journal Pages: 1-10 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596039 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596039 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:1-10 Template-Type: ReDIF-Article 1.0 Author-Name: Esther Frostig Author-X-Name-First: Esther Author-X-Name-Last: Frostig Title: Comparison Between Future Lifetime Distribution and Its Approximations Abstract: Life tables contain data on survival probabilities only for integral ages. The actuarial literature offers several approximation schemes to evaluate survival probabilities for nonintegral ages: the uniform, exponential, and Balducci approximations. This paper shows that, if the real survival model has an increasing hazard rate, the last two approximations are stochastically smaller than the real survival model. Conditions are given on the real survival model, under which it is smaller in convex ordering than the uniform approximation. The paper shows how this result can be applied to give bounds on continuous whole life insurance and whole life annuity. It also investigates the kinds of dependency between the integral part of the lifetime and the fractional portion of the lifetime in the exponential and Balducci approximations. Journal: North American Actuarial Journal Pages: 11-17 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596040 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596040 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:11-17 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Link Author-X-Name-First: Robert Author-X-Name-Last: Link Title: “Principal Applications of Bayesian Methods in Actuarial Science: A Perspective” Udi E. Makov, October 2001 Journal: North American Actuarial Journal Pages: 129-129 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596051 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596051 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:129-129 Template-Type: ReDIF-Article 1.0 Author-Name: J. Peter Duran Author-X-Name-First: J. Author-X-Name-Last: Peter Duran Title: “An Approach to Fair Valuation of Insurance Liabilities Using the Firm’s Cost of Capital”, Luke N. Girard, July 2002 Journal: North American Actuarial Journal Pages: 41-46 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596042 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596042 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:41-46 Template-Type: ReDIF-Article 1.0 Author-Name: Luke Girard Author-X-Name-First: Luke Author-X-Name-Last: Girard Title: An Approach to Fair Valuation of Insurance Liabilities Using the Firm’s Cost of Capital Abstract: There are two competing and seemingly different methodologies for calculating fair values—the direct and indirect methods. The direct approach has the advantage of providing a more reliable assessment of the risk of financial leverage. The indirect method can be structured to adjust for financial leverage, however, the methodology becomes excessively complex. The advantage of the indirect method is that it can be more easily related to exit prices. Intuitively, an exit price should reflect both the creditworthiness of the firm and the cost of capital of the firm. How are these two concepts related? This paper attempts to advance the fair valuation methodology by addressing these questions and presenting a methodology for deriving the firm or own credit risk assumption (to be used with the direct method) that is consistent with the cost of capital assumption used with the indirect method. Journal: North American Actuarial Journal Pages: 18-41 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596041 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596041 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:18-41 Template-Type: ReDIF-Article 1.0 Author-Name: Harry Satanove Author-X-Name-First: Harry Author-X-Name-Last: Satanove Title: “Macroeconomic Aspects of Private Retirement Programs,” Krzysztof M. Ostaszewski, and “The Shift to Defined Contribution Pension Plans: Why Did It Not Happen in Canada?” Robert L. Brown and Jianxun Liu, July 2001 Journal: North American Actuarial Journal Pages: 127-129 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596050 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596050 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:127-129 Template-Type: ReDIF-Article 1.0 Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Alexandros Zimbidis Author-X-Name-First: Alexandros Author-X-Name-Last: Zimbidis Title: An Investigation of the Pay-As-You-Go Financing Method Using a Contingency Fund and Optimal Control Techniques Abstract: In many countries, aging populations are expected to lead to substantial rises in the cost of public pension systems financed by the pay-as-you-go (PAYGO) method. These systems will need to be adapted to cope with these changes. This paper considers one approach to reform, described in the literature as “parametric” (see, e.g., Disney 2000), and develops a model for adapting the PAYGO method using a contingency fund and optimal control techniques. The solution of the original model is investigated within two different frameworks: a deterministic-continuous one and a stochastic-discrete one. Finally, a case study applied to Greece is discussed, leading to a potentially acceptable proposal of a smooth path for contribution rates and the age of eligibility for the normal retirement pension. Journal: North American Actuarial Journal Pages: 60-75 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596044 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596044 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:60-75 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: The Evolving Role of the Actuary in Financial Reporting of Insurance Abstract: The demands that financial reporting of insurance companies present to actuaries are great and growing. With the prospects of change in the rules for financial reporting becoming more likely and insurance products becoming more complex, it is desirable to examine the evolving roles of the actuary and the actuarial profession. This paper describes these changes and the value that actuaries bring to financial reporting. The challenges presented are significant. As the methods of assessing and managing risk change are becoming more complex, the best efforts of the profession and individual actuaries will be needed to ensure that the actuary’s role is enhanced and expanded. Not only will the techniques used evolve, but the audiences served by the actuary will become even more demanding. The actuarial profession is better situated than other professions to meet these demands. Journal: North American Actuarial Journal Pages: 47-59 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596043 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596043 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:47-59 Template-Type: ReDIF-Article 1.0 Author-Name: Henk van Broekhoven Author-X-Name-First: Henk Author-X-Name-Last: van Broekhoven Title: Market Value of Liabilities Mortality Risk Abstract: Market values of the invested assets are frequently published. For most insurance liabilities, there are no published market values and, therefore, these have to be constructed. This construction can be based on a best estimate and a price for the risks in the liabilities. This paper presents a model explaining how the best estimate and the price of mortality risk can be constructed. Several methods to describe the risks are already known. The purpose of this paper is to describe a method to determine the mortality risk in a practical way. Journal: North American Actuarial Journal Pages: 95-106 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596046 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596046 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:95-106 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Margus Author-X-Name-First: Paul Author-X-Name-Last: Margus Title: Generalized Frasier Claim Rates Under Survivorship Life Insurance Policies Abstract: This paper proposes two modifications to the well-known Frasier formula, often used in the pricing, design, and valuation of survivorship life insurance policies: (1) allowing lapse rates to change after the first death and (2) reflecting simultaneous exposure to the same hazards, such as infectious diseases and common accidents, and possibly higher mortality among survivors. The purpose is to improve the pricing and valuation of survivorship life insurance. The paper will be of interest to actuaries doing pricing, GAAP valuation, self-support certifications, and to illustration actuaries. The results are important to reinsurers and direct writers. The paper includes numerical examples and compares the claim rates with and without the suggested modifications. The modified survivorship claim rates are considerably higher than those developed using pure Frasier, emphasizing the importance of learning to use these or similar methods. Journal: North American Actuarial Journal Pages: 76-94 Issue: 2 Volume: 6 Year: 2002 X-DOI: 10.1080/10920277.2002.10596045 File-URL: http://hdl.handle.net/10.1080/10920277.2002.10596045 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:76-94 Template-Type: ReDIF-Article 1.0 Author-Name: X. Sheldon Lin Author-X-Name-First: X. Author-X-Name-Last: Sheldon Lin Author-Name: Xiaoming Liu Author-X-Name-First: Xiaoming Author-X-Name-Last: Liu Title: “Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin Under the Sparre Andersen Model,”, Andrew C. Y. Ng and Hailiang Yang, July 2005 Journal: North American Actuarial Journal Pages: 102-107 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596205 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596205 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:102-107 Template-Type: ReDIF-Article 1.0 Author-Name: Grzegorz Rempala Author-X-Name-First: Grzegorz Author-X-Name-Last: Rempala Author-Name: Richard Derrig Author-X-Name-First: Richard Author-X-Name-Last: Derrig Title: Modeling Hidden Exposures in Claim Severity Via the Em Algorithm Abstract: We consider the issue of modeling the latent or hidden exposure occurring through either incomplete data or an unobserved underlying risk factor. We use the celebrated expectationmaximization (EM) algorithm as a convenient tool in detecting latent (unobserved) risks in finite mixture models of claim severity and in problems where data imputation is needed. We provide examples of applicability of the methodology based on real-life auto injury claim data and compare, when possible, the accuracy of our methods with that of standard techniques. Sample data and an EM algorithm program are included to allow readers to experiment with the EM methodology themselves. Journal: North American Actuarial Journal Pages: 108-128 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596206 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596206 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:108-128 Template-Type: ReDIF-Article 1.0 Author-Name: B. John Manistre Author-X-Name-First: B. Author-X-Name-Last: John Manistre Author-Name: Geoffrey Hancock Author-X-Name-First: Geoffrey Author-X-Name-Last: Hancock Title: Variance of the CTE Estimator Abstract: The Conditional Tail Expectation (CTE), also called Expected Shortfall or Tail-VaR, is a robust, convenient, practical, and coherent measure for quantifying financial risk exposure. The CTE is quickly becoming the preferred measure for statutory balance sheet valuation whenever real-world stochastic methods are used to set liability provisions. We look at some statistical properties of the methods that are commonly used to estimate the CTE and develop a simple formula for the variance of the CTE estimator that is valid in the large sample limit. We also show that the formula works well for finite sample sizes. Formula results are compared with sample values from realworld Monte Carlo simulations for some common loss distributions, including equity-linked annuities with investment guarantees, whole life insurance and operational risks. We develop the CTE variance formula in the general case using a system of biased weights and explore importance sampling, a form of variance reduction, as a way to improve the quality of the estimators for a given sample size. The paper closes with a discussion of practical applications. Journal: North American Actuarial Journal Pages: 129-156 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596207 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596207 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:129-156 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: We Are All “Actuaries Of The Third Kind” Now Journal: North American Actuarial Journal Pages: iii-v Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596208 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596208 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:iii-v Template-Type: ReDIF-Article 1.0 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: “The Time Value of Ruin in a Sparre Andersen Model,” Hans U. Gerber and Elias S. W. Shiu, July 2005 Journal: North American Actuarial Journal Pages: 78-80 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596201 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596201 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:78-80 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: “Authors’ Reply: The Time Value of Ruin in a Sparre Andersen Model,” Hans U. Gerber and Elias S. W. Shiu, July 2005 - Discussions by Hanspeter Schmidli, Hansjörg Albrecher, Cary Chi-Liang Tsai, Shuanming Li Journal: North American Actuarial Journal Pages: 80-84 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596202 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596202 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:80-84 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin Under the Sparre Andersen Model Abstract: In this paper we consider the Sparre Andersen insurance risk model. Three cases are discussed: the ordinary renewal risk process, stationary renewal risk process, and s-delayed renewal risk process. In the first part of the paper we study the joint distribution of surplus immediately before and at ruin under the renewal insurance risk model. By constructing an exponential martingale, we obtain Lundberg-type upper bounds for the joint distribution. Consequently we obtain bounds for the distribution of the deficit at ruin and ruin probability. In the second part of the paper, we consider the special case of phase-type claims and rederive the closed-form expression for the distribution of the severity of ruin, obtained by Drekic et al. (2003, 2004). Finally, we present some numerical results to illustrate the tightness of the bounds obtained in this paper. Journal: North American Actuarial Journal Pages: 85-100 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596203 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596203 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:85-100 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: “Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin Under the Sparre Andersen Model,”, Andrew C. Y. Ng and Hailiang Yang, July 2005 Journal: North American Actuarial Journal Pages: 100-102 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596204 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596204 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:100-102 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Title: “The Time Value of Ruin in a Sparre Andersen Model,” Hans U. Gerber and Elias S. W. Shiu, July 2005 Journal: North American Actuarial Journal Pages: 71-73 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596199 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596199 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:71-73 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Title: The Time Value of Ruin in a Sparre Andersen Model Abstract: This paper considers a Sparre Andersen collective risk model in which the distribution of the interclaim time is that of a sum of n independent exponential random variables; thus, the Erlang(n) model is a special case. The analysis is focused on the function φ(u), the expected discounted penalty at ruin, with u being the initial surplus. The penalty may depend on the deficit at ruin and possibly also on the surplus immediately before ruin. It is shown that the function φ(u) satisfies a certain integro-differential equation and that this equation can be solved in terms of Laplace transforms, extending a result found in Lin (2003). As a consequence, a closed-form expression is obtained for the discounted joint probability density of the deficit at ruin and the surplus just before ruin, if the initial surplus is zero. For this formula and other results, the roots of Lundberg’s fundamental equation in the right half of the complex plane play a central role. Also, it is shown that φ(u) satisfies Li’s (2003) renewal equation. Under the assumption that the penalty depends only on the deficit at ruin and that the individual claim amount density is a combination of exponential densities, a closed-form expression for φ(u) is derived. In this context, known results of the Cauchy matrix are useful. Surprisingly, certain results are best expressed in terms of divided differences, a topic deleted from the actuarial examinations at the end of last century. Journal: North American Actuarial Journal Pages: 49-69 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596197 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596197 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:49-69 Template-Type: ReDIF-Article 1.0 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Author-X-Name-Last: Chi-Liang Tsai Title: “The Time Value of Ruin in a Sparre Andersen Model,” Hans U. Gerber and Elias S. W. Shiu, July 2005 Journal: North American Actuarial Journal Pages: 74-77 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596200 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596200 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:74-77 Template-Type: ReDIF-Article 1.0 Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: “The Time Value of Ruin in a Sparre Andersen Model,” Hans U. Gerber and Elias S. W. Shiu, July 2005 Journal: North American Actuarial Journal Pages: 69-70 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596198 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596198 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:69-70 Template-Type: ReDIF-Article 1.0 Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: On the Moments of the Time of Ruin with Applications to Phase-Type Claims Abstract: We describe an approach to the evaluation of the moments of the time of ruin in the classical Poisson risk model. The methodology employed involves the expression of these moments in terms of linear combinations of convolutions involving compound negative binomial distributions. We then adapt the results for use in the practically important case involving phase-type claim size distributions. We present numerical examples to illuminate the influence of claim size variability on the moments of the time of ruin. Journal: North American Actuarial Journal Pages: 17-30 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596195 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596195 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:17-30 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Ping Wang Author-X-Name-First: Ping Author-X-Name-Last: Wang Title: Credibility Using Copulas Abstract: Credibility is a form of insurance pricing that is widely used, particularly in North America. The theory of credibility has been called a “cornerstone” in the field of actuarial science. Students of the North American actuarial bodies also study loss distributions, the process of statistical inference of relating a set of data to a theoretical (loss) distribution. In this work, we develop a direct link between credibility and loss distributions through the notion of a copula, a tool for understanding relationships among multivariate outcomes.This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross section of risk classes (towns) with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time; specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution; like the univariate tdistributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.We present an illustrative example of Massachusetts automobile claims, and compare our new credibility estimates with those currently existing in the literature. Journal: North American Actuarial Journal Pages: 31-48 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596196 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596196 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:31-48 Template-Type: ReDIF-Article 1.0 Author-Name: C. Allen Pinkham Author-X-Name-First: C. Author-X-Name-Last: Allen Pinkham Author-Name: Brian Ivanovic Author-X-Name-First: Brian Author-X-Name-Last: Ivanovic Author-Name: Marianne Cumming Author-X-Name-First: Marianne Author-X-Name-Last: Cumming Title: 2003 Swiss Re Blood Pressure Study of Insured Lives Abstract: Blood pressure, one of the most important mortality risk factors, is a common life insurance underwriting tool for classification of preferred, standard, and substandard risks. In order to assess changes in mortality risk associated with blood pressure since the last major intercompany study, Swiss Re’s Research & Development and Medical Departments conducted a longitudinal study of blood pressure readings collected at the time of policy issue. Mortality risk associated with different blood pressure levels on nearly 300,000 life insurance policies issued without any other ratable impairments was evaluated. The study cohort was formed by policies issued from 1975 through 2001, which generated over 8,600 claims within the study period. Univariate and bivariate blood pressure mortality results are shown along with results for other key covariates (sex, smoking status, issue year period, policy duration, and cardiovascular family history) for a subset of the cohort that had blood pressure readings of 120/80 mm Hg or lower. Journal: North American Actuarial Journal Pages: 1-16 Issue: 2 Volume: 9 Year: 2005 X-DOI: 10.1080/10920277.2005.10596194 File-URL: http://hdl.handle.net/10.1080/10920277.2005.10596194 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:9:y:2005:i:2:p:1-16 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Bebbington Author-X-Name-First: Mark Author-X-Name-Last: Bebbington Author-Name: Chin-Diew Lai Author-X-Name-First: Chin-Diew Author-X-Name-Last: Lai Author-Name: Ričardas Zitikis Author-X-Name-First: Ričardas Author-X-Name-Last: Zitikis Title: “An Extreme Value Analysis of Advanced Age Mortality Data,” Kathryn A. Watts, Debbie J. Dupuis, and Bruce L. Jones, October 2006 Journal: North American Actuarial Journal Pages: 173-174 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597478 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597478 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:173-174 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: The Impact of DC Pension Systems on Population Dynamics - Discussion by Mark Malnati Journal: North American Actuarial Journal Pages: 172-172 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597477 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:172-172 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Malnati Author-X-Name-First: Mark Author-X-Name-Last: Malnati Title: “The Impact of DC Pension Systems on Population Dynamics,” Bonnie-Jeanne MacDonald and Andrew J. G. Cairns, January 2007 Journal: North American Actuarial Journal Pages: 172-172 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597476 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597476 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:172a-172a Template-Type: ReDIF-Article 1.0 Author-Name: Edward Furman Author-X-Name-First: Edward Author-X-Name-Last: Furman Author-Name: Ričardas Zitikis Author-X-Name-First: Ričardas Author-X-Name-Last: Zitikis Title: “An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets”, Zinoviy Landsman and Michael Sherris, January 2007 Journal: North American Actuarial Journal Pages: 174-176 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597479 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597479 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:174-176 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment Abstract: This article considers the compound Poisson insurance risk model perturbed by diffusion with investment. We assume that the insurance company can invest its surplus in both a risky asset and the risk-free asset according to a fixed proportion. If the surplus is negative, a constant debit interest rate is applied. The absolute ruin probability function satisfies a certain integro-differential equation. In various special cases, closed-form solutions are obtained, and numerical illustrations are provided. Journal: North American Actuarial Journal Pages: 159-169 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597474 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597474 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:159-169 Template-Type: ReDIF-Article 1.0 Author-Name: Harald Dornheim Author-X-Name-First: Harald Author-X-Name-Last: Dornheim Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Title: Robust and Efficient Methods for Credibility When Claims Are Approximately Gamma-Distributed Abstract: As is well known in actuarial practice, excess claims (outliers) have a disturbing effect on the ratemaking process. To obtain better estimators of premiums, which are based on credibility theory, Künsch and Gisler and Reinhard suggested using robust methods. The estimators proposed by these authors are indeed resistant to outliers and serve as an excellent example of how useful robust models can be for insurance pricing. In this article we further refine these procedures by reducing the degree of heuristic arguments they involve. Specifically we develop a class of robust estimators for the credibility premium when claims are approximately gamma-distributed and thoroughly study their robustness-efficiency trade-offs in large and small samples. Under specific datagenerating scenarios, this approach yields quantitative indices of estimators’ strength and weakness, and it allows the actuary (who is typically equipped with information beyond the statistical model) to choose a procedure from a full menu of possibilities. Practical performance of our methods is illustrated under several simulated scenarios and by employing expert judgment. Journal: North American Actuarial Journal Pages: 138-158 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597473 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597473 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:138-158 Template-Type: ReDIF-Article 1.0 Author-Name: Bangwon Ko Author-X-Name-First: Bangwon Author-X-Name-Last: Ko Author-Name: Andrew Ng Author-X-Name-First: Andrew Author-X-Name-Last: Ng Title: “Stochastic Annuities,” Daniel Dufresne, January 2007 Journal: North American Actuarial Journal Pages: 170-171 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597475 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597475 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:170-171 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Powers Author-X-Name-First: Michael Author-X-Name-Last: Powers Title: Using Aumann-Shapley Values to Allocate Insurance Risk Abstract: The problem of allocating responsibility for risk among members of a portfolio arises in a variety of financial and risk-management contexts. Examples are particularly prominent in the insurance sector, where actuaries have long sought methods for distributing capital (net worth) across a number of distinct exposure units or accounts according to their relative contributions to the total “risk” of an insurer’s portfolio. Although substantial work has been done on this problem, no satisfactory solution has yet been presented for the case of inhomogeneous loss distributions— that is, losses X ∼ FX|λ such that FX|tλ (X) ≠ FtX|λ (X) for some t > 0. The purpose of this article is to show that the value-assignment method of nonatomic cooperative games proposed in 1974 by Aumann and Shapley may be used to solve risk-allocation problems involving losses of this type. This technique is illustrated by providing analytical solutions for a useful class of multivariatenormal loss distributions. Journal: North American Actuarial Journal Pages: 113-127 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597470 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597470 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:113-127 Template-Type: ReDIF-Article 1.0 Author-Name: Bangwon Ko Author-X-Name-First: Bangwon Author-X-Name-Last: Ko Title: “The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model”, Jiandong Ren, July 2007 Journal: North American Actuarial Journal Pages: 136-137 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597472 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597472 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:136-137 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Title: “A Risk Model with Multilayer Dividend Strategy”, Hansjorg Albrecher and Jürgen Hartinger, April 2007 Journal: North American Actuarial Journal Pages: 176-183 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597480 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597480 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:176-183 Template-Type: ReDIF-Article 1.0 Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model Abstract: In this article, we consider the risk model with phase-type interclaim times. We first derive a simple matrix-form expression for the discounted joint density of the surplus prior to ruin and the deficit at ruin when the initial surplus is zero. Then we express the discounted joint density in terms of certain expected discounted penalty functions when the initial surplus is greater than zero. This result generalizes that in Gerber and Shiu (1997). Journal: North American Actuarial Journal Pages: 128-136 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597471 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597471 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:128-136 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel Cox Author-X-Name-First: Samuel Author-X-Name-Last: Cox Author-Name: Yijia Lin Author-X-Name-First: Yijia Author-X-Name-Last: Lin Title: Natural Hedging of Life and Annuity Mortality Risks Abstract: The values of life insurance and annuity liabilities move in opposite directions in response to a change in the underlying mortality. Natural hedging utilizes this to stabilize aggregate liability cash flows. We find empirical evidence that suggests that annuity writing insurers who have more balanced business in life and annuity risks also tend to charge lower premiums than otherwise similar insurers. This indicates that insurers who have a natural hedge have a competitive advantage. In addition, we show how a mortality swap might be used to provide the benefits of natural hedging. Journal: North American Actuarial Journal Pages: 1-15 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597464 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597464 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:1-15 Template-Type: ReDIF-Article 1.0 Author-Name: Eric Stallard Author-X-Name-First: Eric Author-X-Name-Last: Stallard Title: Trajectories of Morbidity, Disability, and Mortality among the U.S. Elderly Population Abstract: This article employs a longitudinal form of the Grade of Membership (GoM) model to specify and estimate a multivariate model of the trajectories of morbidity, disability, and mortality among longitudinally followed elderly respondents to the National Long-Term Care Survey (NLTCS) of 1984, 1989, 1994, and 1999. A distinct trajectory was constructed for each individual respondent to the survey. The trajectories described the progressive declines over time in physical and cognitive functioning among a nationally representative sample of the U.S. elderly population.The model was structured to represent simultaneously the essential features of the fixed frailty model of Vaupel, Manton, and Stallard and Strehler and Mildvan’s model of linearly declining vitality. Unlike those models, however, the longitudinal GoM model was designed for easy and direct application to existing longitudinal data sets.The measurement space in the NLTCS application included from one to four sets of repeated measures for each survey respondent on 95 independent variables characterizing the nature and intensity of limitations in activities of daily living (ADLs), instrumental activities of daily living (IADLs), physical functioning, and cognitive functioning, as well as indicators of behavioral characteristics, medical conditions, subjective health, age, race, sex, institutional status, and survival status.The application showed that the model can be fitted to existing data and that the results were interpretable as generalizations of fixed frailty with linearly declining vitality. Journal: North American Actuarial Journal Pages: 16-53 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597465 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597465 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:16-53 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Edward Frees Author-X-Name-First: Edward Author-X-Name-Last: Frees Author-Name: Jiafeng Sun Author-X-Name-First: Jiafeng Author-X-Name-Last: Sun Author-Name: Paul Johnson Author-X-Name-First: Paul Author-X-Name-Last: Johnson Author-Name: Jim Robinson Author-X-Name-First: Jim Author-X-Name-Last: Robinson Title: Predictive Modeling with Longitudinal Data Abstract: The recent development and availability of sophisticated computer software has facilitated the use of predictive modeling by actuaries and other financial analysts. Predictive modeling has been used for several applications in both the health and property and casualty sectors. Often these applications employ extensions of industry-specific techniques and do not make full use of information contained in the data. In contrast, we employ fundamental statistical methods for predictive modeling that can be used in a variety of disciplines. As demonstrated in this article, this methodology permits a disciplined approach to model building, including model development and validation phases. This article is intended as a tutorial for the analyst interested in using predictive modeling by making the process more transparent.This article illustrates the predictive modeling process using State of Wisconsin nursing home cost reports. We examine utilization of approximately 400 nursing homes from 1989 to 2001. Because the data vary both in the cross section and over time, we employ longitudinal models. This article demonstrates many of the common difficulties that analysts face in analyzing longitudinal health care data, as well as techniques for addressing these difficulties. We find that longitudinal methods, which use historical trend information, significantly outperform regression models that do not take advantage of historical trends. Journal: North American Actuarial Journal Pages: 54-69 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597466 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597466 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:54-69 Template-Type: ReDIF-Article 1.0 Author-Name: Greg Taylor Author-X-Name-First: Greg Author-X-Name-Last: Taylor Author-Name: Gráinne McGuire Author-X-Name-First: Gráinne Author-X-Name-Last: McGuire Title: A Synchronous Bootstrap to Account for Dependencies Between Lines of Business in the Estimation of Loss Reserve Prediction Error Abstract: In this article we consider the situation in which an insurer requires a loss reserve, together with the estimated prediction error, in respect of a number of stochastically dependent lines of business, individually and in aggregate. We suppose that generalized linear models are used to estimate each of the individual loss reserves, and that bootstrapping is used to estimate prediction errors. Specialized forms of the bootstrap, referred to as synchronous bootstraps, are constructed to capture the dependencies. Numerical examples are given in which loss reserve forecasts and their prediction errors are obtained for individual lines of business and in aggregate. Journal: North American Actuarial Journal Pages: 70-88 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597467 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597467 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:70-88 Template-Type: ReDIF-Article 1.0 Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Title: Normalized Exponential Tilting Abstract: This article discusses methods of risk-neutralizing multivariate probability distributions by applying exponential tilting to the joint probability density function with respect to a set of reference risks. To ensure consistent interpretations of the exponential tilting parameters, a normalization procedure is performed on the reference risks via percentile mapping to standard normal variables. The article establishes links between normalized exponential tilting and multivariate probability distortions. It provides efficient methods for computing risk-neutralized multivariate probability distributions, and it gives illustrative examples in pricing contingent claims on multiple risks. Journal: North American Actuarial Journal Pages: 89-99 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597468 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597468 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:89-99 Template-Type: ReDIF-Article 1.0 Author-Name: Gopi Goda Author-X-Name-First: Gopi Author-X-Name-Last: Goda Author-Name: Colin Ramsay Author-X-Name-First: Colin Author-X-Name-Last: Ramsay Title: Determining the Optimum Guarantee Period for a One-Life Retirement Annuity Abstract: We consider a risk averse retiree from a defined contribution plan who decides to purchase a onelife annuity with a guarantee period. Given the retiree has a bequest motive, we focus on the problem of determining the optimum length of the guarantee period. Assuming the retiree’s bequest function is proportional to his or her utility function, we determine necessary and/or sufficient conditions under which the retiree would choose an annuity with (i) no guarantee period, (ii) the maximum guarantee period, or (iii) an intermediate guarantee period. Journal: North American Actuarial Journal Pages: 100-112 Issue: 3 Volume: 11 Year: 2007 X-DOI: 10.1080/10920277.2007.10597469 File-URL: http://hdl.handle.net/10.1080/10920277.2007.10597469 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:100-112 Template-Type: ReDIF-Article 1.0 Author-Name: Ian Duncan Author-X-Name-First: Ian Author-X-Name-Last: Duncan Author-Name: H. E. Frech Author-X-Name-First: H. E. Author-X-Name-Last: Frech Title: Measuring Healthcare Efficiency Journal: North American Actuarial Journal Pages: 443-444 Issue: 4 Volume: 18 Year: 2014 Month: 10 X-DOI: 10.1080/10920277.2014.984563 File-URL: http://hdl.handle.net/10.1080/10920277.2014.984563 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:443-444 Template-Type: ReDIF-Article 1.0 Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Title: A Comparative Study of Risk Measures for Guaranteed Minimum Maturity Benefits by a PDE Method Abstract: The stochastic modeling and determination of reserves and risk capitals for variable annuity guarantee products are relatively new developments in the insurance industry. The current market practice is largely based on Monte Carlo simulations, which have great engineering flexibility, but the demand for heavy computational power can be prohibitive in many cases. In this article we distinguish and compare two types of risk models to determine the commonly used risk measures for reserving and capital calculations. Using an example of the guaranteed minimum maturity benefit, we investigate alternative numerical methods that require less computational resources and yet achieve high accuracy and efficiency. Journal: North American Actuarial Journal Pages: 445-461 Issue: 4 Volume: 18 Year: 2014 Month: 10 X-DOI: 10.1080/10920277.2014.922031 File-URL: http://hdl.handle.net/10.1080/10920277.2014.922031 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:445-461 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Title: Positive Weights on the Efficient Frontier Abstract: One of the fundamental insights of the Capital Asset Pricing Model is that the market portfolio is mean variance efficient. Since the market portfolio has positive weights on all assets, the conditions under which frontier portfolios have this property are of interest. This article derives a simple explicit solution for an efficient portfolio with positive weights. Assuming the covariance matrix is given, we obtain an expected return vector such that there is a compatible frontier portfolio. This portfolio is derived from the dominant eigenvector of the correlation matrix and provides a proxy for the market portfolio. Examples are provided to illustrate the basic idea. Journal: North American Actuarial Journal Pages: 462-477 Issue: 4 Volume: 18 Year: 2014 Month: 10 X-DOI: 10.1080/10920277.2014.922032 File-URL: http://hdl.handle.net/10.1080/10920277.2014.922032 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:462-477 Template-Type: ReDIF-Article 1.0 Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Title: Health Care Reform, Efficiency of Health Insurers, and Optimal Health Insurance Markets Abstract: This research examines the efficiency of the U.S. health insurers. It shows that more insurers are less efficient than in the previous sample year; however, the results suggest that the federal health care reform has no significant effect on the overall efficiency of all insurers as a whole, which is very low but does not change much over time. This research explores how to improve the efficiency of the health insurance market by proposing state, regional, and national efficiency-based goal-oriented market models and an efficiency duplicating system, and it discusses important implications to the health care compacts, the health insurance exchanges or marketplaces, and the national multistate programs. It also analyzes further moves for efficiency enhancement with regard to payment methods and the health care delivery system. One interesting finding is that the Medicaid program is very efficient because it provides support to the offering of Medicaid coverage and further expansion, which enhances the health welfare of society with fewer resources inputs from the perspective of efficiency. This research should provide important insights for state and federal governments, policy makers, regulators, the health insurance industry, and consumers. Journal: North American Actuarial Journal Pages: 478-500 Issue: 4 Volume: 18 Year: 2014 Month: 10 X-DOI: 10.1080/10920277.2014.935438 File-URL: http://hdl.handle.net/10.1080/10920277.2014.935438 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:478-500 Template-Type: ReDIF-Article 1.0 Author-Name: Anatoliy Belaygorod Author-X-Name-First: Anatoliy Author-X-Name-Last: Belaygorod Author-Name: Atilio Zardetto Author-X-Name-First: Atilio Author-X-Name-Last: Zardetto Author-Name: Yuanjin Liu Author-X-Name-First: Yuanjin Author-X-Name-Last: Liu Title: Bayesian Modeling of Shock Lapse Rates Provides New Evidence for Emergency Fund Hypothesis Abstract: This article considers the problem of estimating shock lapse rates in term life products. Four models are estimated using Bayesian Multiple-Block Gibbs sampling. Goodness-of-fit was compared using weighted average lapse rate fitted error. A simulated data setting was employed to validate the algorithm. Among the methodological contributions to the literature we introduce Bayesian estimation for the lapse rate parameters permitting the identification of parameter distributions as opposed to point estimates. Also we introduce a flexible panel data model accommodating both mixed effects and cross-effects between explanatory variables. The data are weighted in the likelihood function according to their relevance as measured by policy counts. Finally, we utilize a large proprietary dataset of U.S. postlevel premium period term policies that enables superior inference over the parameter estimates. Building on the above improvements and recent data covering the 2008 crisis, we find strong evidence in favor of the Emergency Fund Hypothesis as a driver of shock lapses. Journal: North American Actuarial Journal Pages: 501-514 Issue: 4 Volume: 18 Year: 2014 Month: 10 X-DOI: 10.1080/10920277.2014.938545 File-URL: http://hdl.handle.net/10.1080/10920277.2014.938545 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:501-514 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board EOV Journal: North American Actuarial Journal Pages: ebi-ebi Issue: 4 Volume: 18 Year: 2014 Month: 10 X-DOI: 10.1080/10920277.2014.987571 File-URL: http://hdl.handle.net/10.1080/10920277.2014.987571 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: Michel Jacques Author-X-Name-First: Michel Author-X-Name-Last: Jacques Title: “Skewness and Stock Option Prices”, Hans U. Gerber; Bruno Landry, July 1997 Journal: North American Actuarial Journal Pages: 59-60 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595629 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595629 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:59-60 Template-Type: ReDIF-Article 1.0 Author-Name: Terence Chan Author-X-Name-First: Terence Author-X-Name-Last: Chan Title: “Skewness and Stock Option Prices”, Hans U. Gerber; Bruno Landry, July 1997 Journal: North American Actuarial Journal Pages: 58-59 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595628 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595628 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:58-59 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Bruno Landry Author-X-Name-First: Bruno Author-X-Name-Last: Landry Title: Skewness and Stock Option Prices Abstract: In the classical Black-Scholes model, the logarithm of the stock price has a normal distribution, which excludes skewness. In this paper we consider models that allow for skewness. We propose an option-pricing formula that contains a linear adjustment to the Black-Scholes formula. This approximation is derived in the shifted Poisson model, which is a complete market model in which the exact option price has some undesirable features. The same formula is obtained in some incomplete market models in which it is assumed that the price of an option is defined by the Esscher method. For a European call option, the adjustment for skewness can be positive or negative, depending on the strike price. Journal: North American Actuarial Journal Pages: 50-58 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595627 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595627 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:50-58 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Strommen Author-X-Name-First: Stephen Author-X-Name-Last: Strommen Title: An Object-Oriented Design for Dynamic Simulation Models Abstract: Object-oriented design has evolved as a means for dealing with very complex software systems. This paper outlines some of the fundamental concepts of the object-oriented approach and applies them to the design of a dynamic simulation model of a financial institution. A sample design for a simulation model is presented, including a description of the objects involved and the way they interact.The paper closes with a discussion of the advantages of object-oriented design, not only in the context of the model presented here but also in the broader context of dynamic modeling in general. Journal: North American Actuarial Journal Pages: 38-49 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595626 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595626 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:38-49 Template-Type: ReDIF-Article 1.0 Author-Name: Hans Gerber Author-X-Name-First: Hans Author-X-Name-Last: Gerber Author-Name: Bruno Landry Author-X-Name-First: Bruno Author-X-Name-Last: Landry Title: Author’s Reply: Skewness and Stock Option Prices - Discussion by Terence Chan, Michel Jacques, Heinz H. Mu¨ller, Geérard Pafumi, Elias S.W. Shiu, and Serena Tiong, July 1997 Journal: North American Actuarial Journal Pages: 64-65 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595633 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:64-65 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Title: Introduction to Actuarial Modeling Journal: North American Actuarial Journal Pages: 1-5 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595621 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:1-5 Template-Type: ReDIF-Article 1.0 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: Current Actuarial Modeling Practice and Related Issues and Questions Journal: North American Actuarial Journal Pages: 24-35 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595624 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595624 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:24-35 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Strommen Author-X-Name-First: Stephen Author-X-Name-Last: Strommen Title: “Current Actuarial Modeling Practice and Related Issues and Questions”, Angus S. Macdonald, July 1997 Journal: North American Actuarial Journal Pages: 35-37 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595625 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595625 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:35-37 Template-Type: ReDIF-Article 1.0 Author-Name: Heinz Mu¨ller Author-X-Name-First: Heinz Author-X-Name-Last: Mu¨ller Title: “Skewness and Stock Option Prices”, Hans U. Gerber; Bruno Landry, July 1997 Journal: North American Actuarial Journal Pages: 60-61 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595630 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595630 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:60-61 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Day Author-X-Name-First: Richard Author-X-Name-Last: Day Title: Complex Dynamics, Market Mediation and Stock Price Behavior Abstract: Most exchanges in a decentralized economy are mediated by agents who make markets. This paper applies the elementary theory of such mechanisms to equity markets. Based on stylized institutional and behavioral facts and exploiting the methods of nonlinear dynamics, it explains salient properties of stock market dynamics. Journal: North American Actuarial Journal Pages: 1-16 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595622 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595622 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:1-16 Template-Type: ReDIF-Article 1.0 Author-Name: Geérard Pafumi Author-X-Name-First: Geérard Author-X-Name-Last: Pafumi Title: “Skewness and Stock Option Prices”, Hans U. Gerber; Bruno Landry, July 1997 Journal: North American Actuarial Journal Pages: 61-62 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595631 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595631 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:61-62 Template-Type: ReDIF-Article 1.0 Author-Name: Irwin Vanderhoof Author-X-Name-First: Irwin Author-X-Name-Last: Vanderhoof Title: “Complex Dynamics, Market Mediation and Stock Price Behavior”, Richard H. Day, July 1997 Journal: North American Actuarial Journal Pages: 21-23 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595623 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595623 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:21-23 Template-Type: ReDIF-Article 1.0 Author-Name: Elias Shiu Author-X-Name-First: Elias Author-X-Name-Last: Shiu Author-Name: Serena Tiong Author-X-Name-First: Serena Author-X-Name-Last: Tiong Title: “Skewness and Stock Option Prices”, Hans U. Gerber; Bruno Landry, July 1997 Journal: North American Actuarial Journal Pages: 62-63 Issue: 3 Volume: 1 Year: 1997 X-DOI: 10.1080/10920277.1997.10595632 File-URL: http://hdl.handle.net/10.1080/10920277.1997.10595632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:1:y:1997:i:3:p:62-63 Template-Type: ReDIF-Article 1.0 Author-Name: Benjamin Wurzburger Author-X-Name-First: Benjamin Author-X-Name-Last: Wurzburger Title: “An Actuarial Index of the Right-Tail Risk,” Shaun Wang, April 1998 Journal: North American Actuarial Journal Pages: 139-141 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595760 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595760 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:139-141 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Goss Author-X-Name-First: Stephen Author-X-Name-Last: Goss Author-Name: Alice Wade Author-X-Name-First: Alice Author-X-Name-Last: Wade Author-Name: Felicitie Bell Author-X-Name-First: Felicitie Author-X-Name-Last: Bell Author-Name: Bernard Dussault Author-X-Name-First: Bernard Author-X-Name-Last: Dussault Title: Historical and Projected Mortality for Mexico, Canada, and the United States Abstract: This paper presents historical death rates for Canada, Mexico, and the U.S. by sex and broad age group. The time period for this historical analysis begins with 1900 (1930 for Mexico). These data provide a quite consistent basis from which experts can develop and contrast their expectations for future mortality trends. Official mortality projections developed by government agencies of each of the three countries provide a starting point for this discussion.During this century, death rates declined fairly rapidly in all three countries. However, the rate of mortality improvement has varied considerably across time periods: distinct periods of rapid and slow improvement are evident in the data, but are not consistent across the countries and have not yet been explained.The historical rates of improvement in mortality have also varied greatly by age and sex: younger age groups have shown the most rapid proportional improvement in mortality in all three countries, and mortality improvement during this century has generally been greater for females than for males. However, the data provide evidence that this difference in the rates of mortality improvement between men and women has recently slowed, and even reversed, in the U.S. and Canada. Historical experience and projections are provided in graphs, in which death rates are plotted on a logarithmic scale. This approach allows easy detection of the extent to which rates of improvement have been changing (death rates with constant rates of improvement would be plotted as straight lines).The official projections supplied for comparison provide strikingly similar outlooks for future potential mortality improvement. In each case, the relatively average rapid rate of mortality improvement experienced so far this century is assumed to slow in the future. In addition, rates of improvement are projected to be much more similar for all three countries across age groups and between the sexes. Journal: North American Actuarial Journal Pages: 108-126 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595757 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595757 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:108-126 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sze Author-X-Name-First: Michael Author-X-Name-Last: Sze Author-Name: Stephen Goss Author-X-Name-First: Stephen Author-X-Name-Last: Goss Author-Name: José de León Author-X-Name-First: José Author-X-Name-Last: de León Title: Effect of Aging Population with Declining Mortality on Social Security of Nafta Countries Abstract: This paper summarizes the results of Phase 3 of a three-phase study by the Society of Actuaries on the impact of mortality decline on social security systems in Canada, Mexico, and the U.S. (the NAFTA countries). Responding to an aging population, each NAFTA country has proposed solutions to its social security problem. It is important to analyze whether the proposed solutions would work under changing demography. It is equally important to ensure that social security financing would not be jeopardized by a greater-than-expected mortality decline. We attempt to analyze these critical issues in this phase of the study.Using assumptions obtained from responses to a questionnaire distributed to experts on mortality in Phase 2 of the study, we tested the impact of mortality decline on social security in each of the NAFTA countries. To ensure that we covered a wide range of possible mortality decline rates, we performed the test under four scenarios based on: current social ecurity assumptions, a measure of the best guess of expert opinion, a measure of the high end of expert opinion, and a measure of the low end of expert opinion. Under each scenario and for each country, the study examined the mortality rate at each age and sex, the projected population, the cash flow, and the financed status for each future year. Based on these analyses, we derived the constant contribution rate required to maintain the sustainability of the system for each country.Results of the study show that social security financing is adequate for Mexico and Canada under their respective social security reforms, and the systems are less volatile with respect to mortality fluctuation than expected. Even though social security financing is heavily affected by demographic changes, the rapid increase in the dependency ratios (defined as the ratio of the size of the population over age 65 to the population at working ages) in Canada and Mexico is mainly due to aging of the current population. Graphically, this is demonstrated by an upward shift in the shape of the current population. We show that the additional impact of mortality decline on the dependency ratio and the shape of the population graph is not as significant as is generally believed. Consequently, the difference between government actuaries’ and experts’ views on social security has less effect on social security financing than many experts expect.Although no definite formula for social security reform has yet been adopted in the U.S., our study shows that the impact of mortality decline on social security funding there is also relatively small. However, the study also points out other important elements to consider, including demographic factors such as retirement, disability rates, fertility, and immigration rates, and economic factors such as inflation, investment return, and real wage increases. These are subjects for future research. Journal: North American Actuarial Journal Pages: 83-107 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595756 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595756 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:83-107 Template-Type: ReDIF-Article 1.0 Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Warren Luckner Author-X-Name-First: Warren Author-X-Name-Last: Luckner Title: Summary of Results of Survey of Seminar Attendees Abstract: The Society of Actuaries undertook a three-phase research project on mortality improvement in the three NAFTA countries: Canada, Mexico, and the U.S. Phase 1 consisted of a literature review of papers on projecting mortality levels in the future and a study of the trend in mortality improvement during this century. Phase 2 consisted of a discussion of different facets of modeling mortality rates at a seminar attended by 79 experts (actuaries, demographers, economists, and medical researchers) representing different countries. The last session of the seminar consisted of the completion of a survey by the attendees to obtain input for Phase 3, which would analyze the impact of mortality improvement on the social security system of each country. This paper summarizes the results of the survey.The survey results illustrate the difficulty in forecasting mortality levels, because the effects of many factors that could have significant impact on mortality rates are unknown. This suggests the need for dynamic forecasting, which allows for the possibility of random shocks. A majority of the survey respondents believe that stochastic forecasting models, despite their complexity, have significant potential to add value. Respondents also believe that both historical data and cause-specific mortality forecasts are useful as input and also in validating forecasts of the aggregate levels of mortality. The challenge is to develop more sophisticated forecasting models to produce results that are relatively easy to interpret and to communicate these results to the desired audiences, including the public and policymakers.The survey results suggest that the aggregate effect of lifestyle changes, medical advances, diseases, catastrophe, and physical environmental changes is an increase in life span. However, there is much uncertainty about the future. Respondents expect that beyond the year 2020 the mean annual rate of reduction in mortality for males age 65 and over will average about 0.58% for Canada, 0.76% for Mexico, and 0.67% for the U.S. The results for the female age 65 and over population are 0.64%, 0.83%, and 0.70%, respectively. The age 65 and over population is expected to see larger percentage reductions in mortality than the 0–14 and 15–64 populations. The reductions in male and female mortality will be ultimately the same, and the mortality levels in the three countries will ultimately converge, although differences may persist for decades. Journal: North American Actuarial Journal Pages: 64-82 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595755 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:64-82 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Morrison Author-X-Name-First: Richard Author-X-Name-Last: Morrison Title: “Life Expectancy in the Future: A Summary of a Discussion among Experts”, Robert B. Friedland, October 1998 Journal: North American Actuarial Journal Pages: 61-63 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595754 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595754 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:61-63 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Friedland Author-X-Name-First: Robert Author-X-Name-Last: Friedland Title: Life Expectancy in the Future Abstract: Prior to the twentieth century, survival to a very old age meant living to 50 or 60 years; now, it means living beyond age 95. What will life expectancy be in the twenty-first century? Will life expectancy continue to increase as it has over the course of this century, or will the rate of increase eventually slow and perhaps stop as life expectancy approaches the limits of the life span? Longevity has had a direct impact on the cost of public pension systems; thus, forecasting mortality improvement in the future is an important component of projecting the financial health of public pension programs.On October 30, 1997, the SOA organized a day-long seminar entitled “Impact of Mortality Improvement on Social Security: Canada, Mexico, and the U.S.” The purpose of the seminar was to bring together experts on mortality rates from different disciplines to examine factors affecting mortality change and mortality assumptions throughout North America and to provide advice about forecasting mortality rates in the future. Presenters and participants included a wide array of experts from around the world and across disciplines: actuaries, biologists, demographers, and economists, as well as actuaries representing the governments of Canada, Mexico, the U.S., and Great Britain. This paper summarizes their day-long discussion, which addressed comparisons of mortality rates over time, across nations, and even across species. Causes of changes in mortality rates ranging from changes in the physical environment to socioeconomic considerations were discussed and debated, as were expectations about mortality rates in the future. Methods for projecting mortality rates were also presented and debated.The seminar was organized, in part, to respond to background papers commissioned by the SOA. These papers analyzed the current literature and compared mortality improvement in Canada, Mexico, and the U.S. The seminar also served as a source of information for estimating the impact of mortality improvement on the financial status of public pension programs in these countries. Journal: North American Actuarial Journal Pages: 48-61 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595753 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595753 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:48-61 Template-Type: ReDIF-Article 1.0 Author-Name: Liviana Picech Author-X-Name-First: Liviana Author-X-Name-Last: Picech Author-Name: Patrizia Gigante Author-X-Name-First: Patrizia Author-X-Name-Last: Gigante Author-Name: Luciano Sigalotti Author-X-Name-First: Luciano Author-X-Name-Last: Sigalotti Title: “Bonus-Malus Systems: The European and Asian Approach to Merit Rating,” Jean Lemaire, January 1998 Journal: North American Actuarial Journal Pages: 143-147 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595762 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595762 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:143-147 Template-Type: ReDIF-Article 1.0 Author-Name: Shripad Tuljapurkar Author-X-Name-First: Shripad Author-X-Name-Last: Tuljapurkar Author-Name: Carl Boe Author-X-Name-First: Carl Author-X-Name-Last: Boe Title: Mortality Change and Forecasting Abstract: Prospects of longer life are viewed as a positive change for individuals and as a substantial social achievement but have led to concern over their implications for public spending on old-age support. This paper makes a critical assessment of knowledge about mortality change. It is oriented toward the problem of forecasting the course of mortality change and the potential of existing work to contribute to the development of useful forecasts in Canada, Mexico, and the U.S.We first examine broad patterns in the historical decline in death rates in the three countries, the effect of these on trends in life expectancy, and the epidemiological transition. Next we review theories of the age pattern and evolution of mortality, including graduations, evolutionary theory, reliability models, dynamic models, and relational models.The analysis and forecasting of mortality change have been shaped largely by some key historical lessons, which we summarize next. We emphasize issues that have been or are likely to be significant in mortality analysis, especially the questions of the age pattern and time trend in mortality at old ages; we distinguish patterns and facts that are established from those that remain uncertain. Next, we consider mortality differentials in characteristics such as sex, marital status, education, and socioeconomic variables; we summarize their key features and also point to the substantial gaps in our understanding of their determinants.Finally, we review methods of forecasting, including the scenario method used by the U.S. Social Security Administration and the time series method of Lee and Carter. We set out some important recommendations for forecasters: forecasting assumptions should be made more formal and explicit; there should be retrospective evaluations of forecast performance; and greater attention should be paid to the assessment and consequences of forecast uncertainty. Journal: North American Actuarial Journal Pages: 13-47 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595752 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595752 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:13-47 Template-Type: ReDIF-Article 1.0 Author-Name: James Berberian Author-X-Name-First: James Author-X-Name-Last: Berberian Title: “An Actuarial Index of the Righttail Risk,” Shaun Wang, April 1998 Journal: North American Actuarial Journal Pages: 140-143 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595761 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595761 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:140-143 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sze Author-X-Name-First: Michael Author-X-Name-Last: Sze Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Title: Overview Journal: North American Actuarial Journal Pages: 10-12 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595751 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595751 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:10-12 Template-Type: ReDIF-Article 1.0 Author-Name: Liviana Picech Author-X-Name-First: Liviana Author-X-Name-Last: Picech Author-Name: Luciano Sigalotti Author-X-Name-First: Luciano Author-X-Name-Last: Sigalotti Title: “Bonus-Malus Systems: The European and Asian Approach to Merit-Rating,” Jean Lemaire, January 1998 Journal: North American Actuarial Journal Pages: 147-149 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595763 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595763 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:147-149 Template-Type: ReDIF-Article 1.0 Author-Name: James Hickman Author-X-Name-First: James Author-X-Name-Last: Hickman Author-Name: Linda Heacox Author-X-Name-First: Linda Author-X-Name-Last: Heacox Title: Actuaries in History Abstract: The NAAJ is honoring the Society of Actuaries as it approaches the half-century mark in 1999 by publishing a series of articles on the contributions of actuaries to the development of ideas. In this issue, we look at operations research, an idea born in war and now applied to peace-time pursuits including business. We begin with a short essay by james Hickman, F SA, ACA S , Ph.D , Dean Emeritus of the School of Business of the University of Wisconsin We conclude with comments by the actuaries who helped developed operations research and contributed so much to the winning of World War II. Journal: North American Actuarial Journal Pages: 1-9 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595750 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595750 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:1-9 Template-Type: ReDIF-Article 1.0 Author-Name: Shripad Tuljapurkar Author-X-Name-First: Shripad Author-X-Name-Last: Tuljapurkar Title: Forecasting Mortality Change Abstract: This paper enumerates questions about the assumptions, methods, and interpretation of mortality projections that are made for policy applications. These questions are of practical concern to people who make and use projections, and cover a much narrower scope than the review by Tuljapurkar and Boe (pp. 13–47). The objective in circulating this paper was to provide an initial focus for participants at the SOA meeting. Journal: North American Actuarial Journal Pages: 127-134 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595758 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595758 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:127-134 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Author-Name: Irwin Vanderhoof Author-X-Name-First: Irwin Author-X-Name-Last: Vanderhoof Title: Forecasting Changes in Mortality Abstract: In this article, we express a concern that certain commonly accepted methods of predicting mortality will likely prove to be inadequate in the future. Specifically, the Lee-Carter method, which overall has been empirically successful, uses auto-regressive moving average (ARMA) technology and contains no structural mortality equation. This structure means that no information other than previous history can be introduced. We argue that rapid advances in medical science are taking place and that failure to reflect this information in our projection methodology will make resulting projections unsuitable. Journal: North American Actuarial Journal Pages: 135-138 Issue: 4 Volume: 2 Year: 1998 X-DOI: 10.1080/10920277.1998.10595759 File-URL: http://hdl.handle.net/10.1080/10920277.1998.10595759 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:2:y:1998:i:4:p:135-138 Template-Type: ReDIF-Article 1.0 Author-Name: David C. M. Dickson Author-X-Name-First: David C. M. Author-X-Name-Last: Dickson Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Author-Name: David A. Stanford Author-X-Name-First: David A. Author-X-Name-Last: Stanford Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Title: “Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately before and at Ruin under the Sparre Andersen Model”, Andrew C. Y. Ng and Hailiang Yang, April 2005 Journal: North American Actuarial Journal Pages: 111-112 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596242 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596242 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:111-112 Template-Type: ReDIF-Article 1.0 Author-Name: Russell Gerrard Author-X-Name-First: Russell Author-X-Name-Last: Gerrard Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Elena Vigna Author-X-Name-First: Elena Author-X-Name-Last: Vigna Title: The Management of Decumulation Risks in a Defined Contribution Pension Plan Abstract: The aim of the paper is to lay the theoretical foundations for the construction of a flexible tool that can be used by pensioners to find optimal investment and consumption choices in the distribution phase of a defined contribution pension plan. The investment/consumption plan is adopted until the time of compulsory annuitization, taking into account the possibility of earlier death. The effect of the bequest motive and the desire to buy a higher annuity than the one purchasable at retirement are included in the objective function. The mathematical tools provided by dynamic programming techniques are applied to find closed-form solutions: numerical examples are also presented. In the model, the tradeoff between the different desires of the individual regarding consumption and final annuity can be dealt with by choosing appropriate weights for these factors in the setting of the problem. Conclusions are twofold. First, we find that there is a natural time-varying target for the size of the fund, which acts as a sort of safety level for the needs of the pensioner. Second, the personal preferences of the pensioner can be translated into optimal choices, which in turn affect the distribution of the consumption path and of the final annuity. Journal: North American Actuarial Journal Pages: 84-110 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596241 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596241 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:84-110 Template-Type: ReDIF-Article 1.0 Author-Name: David X. Li Author-X-Name-First: David X. Author-X-Name-Last: Li Title: It Is All About Credit Abstract: Journal: North American Actuarial Journal Pages: iii-iv Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596244 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596244 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Authors’ Reply: Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately before and at Ruin under the Sparre Andersen Model,” Andrew C. Y. Ng and Hailiang Yang, April 2005 - Discussion by David C. M. Dickson, Steve Drekic, David A. Stanford, and Gordon E. Willmot Journal: North American Actuarial Journal Pages: 112-112 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596243 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596243 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:112-112 Template-Type: ReDIF-Article 1.0 Author-Name: Stuart Klugman Author-X-Name-First: Stuart Author-X-Name-Last: Klugman Author-Name: Jacques Rioux Author-X-Name-First: Jacques Author-X-Name-Last: Rioux Title: Toward a Unified Approach to Fitting Loss Models Abstract: There are four components to fitting models: selecting a set of candidate distributions, estimating parameters, evaluating the appropriateness of a model, and determining which member fits best. It is important to have the candidate set be small to avoid overfitting. Finite mixture models using a small number of base distributions provide an ideal set. Because actuaries fit models for a variety of situations, particularly with regard to data modifications, it is useful to have a single approach. Although not optimal or exact for a particular model or data structure, the method should be reasonable for most all settings. Such a method is proposed in this article. Journal: North American Actuarial Journal Pages: 63-83 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596240 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596240 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:63-83 Template-Type: ReDIF-Article 1.0 Author-Name: Marsha Wallace Author-X-Name-First: Marsha Author-X-Name-Last: Wallace Title: The Problem with Current Accounting Abstract: In recent decades, as the use of derivatives by financial institutions has expanded, the shortcomings of historical cost accounting approaches have become increasingly apparent. Since derivatives can create large exposures to risk that go unnoticed under historical standards, the accounting industry has focused on how to change the standards so that these risks are reflected appropriately in a company’s accounting statements. New standards such as SFAS 115 and SFAS 133 have been adopted in part to achieve this goal. However, both of these standards use a piecemeal approach to risk measurement that may be adding to the problem rather than creating a solution. This paper will use a simple equity-indexed annuity to illustrate the problem with historical cost accounting and with the standards that have been adopted to correct it. The paper then argues that the only legitimate means of reflecting risk properly on a company’s accounting statements is to adopt full fair value accounting for all assets and liabilities on the company’s books. Journal: North American Actuarial Journal Pages: 11-29 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596237 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596237 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:11-29 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Finkelstein Author-X-Name-First: Mark Author-X-Name-Last: Finkelstein Author-Name: Howard G. Tucker Author-X-Name-First: Howard G. Author-X-Name-Last: Tucker Author-Name: Jerry Alan Veeh Author-X-Name-First: Jerry Author-X-Name-Last: Alan Veeh Title: Pareto Tail Index Estimation Revisited Abstract: An estimator of the tail index of a Pareto distribution is given that is based on the use of the probability integral transform. This new estimator provides performance that is comparable to the best robust estimators, while retaining conceptual and computational simplicity. A tuning parameter in the new estimator can be adjusted to control the tradeoff between robustness and efficiency. The method used to compute the estimator also can be used to find a confidence interval for the tail index that is guaranteed to have the nominal confidence level for any given sample size. Guidelines for the use of the new estimator are provided. Journal: North American Actuarial Journal Pages: 1-10 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596236 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596236 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:1-10 Template-Type: ReDIF-Article 1.0 Author-Name: Vincent Goulet Author-X-Name-First: Vincent Author-X-Name-Last: Goulet Author-Name: Antoni Forgues Author-X-Name-First: Antoni Author-X-Name-Last: Forgues Author-Name: Jiatao Lu Author-X-Name-First: Jiatao Author-X-Name-Last: Lu Title: Credibility for Severity Revisited Abstract: It is basic actuarial knowledge that the pure premium of an insurance contract can be written as the product of the expected claim number and the expected claim amount. Actuaries use credibility theory to incorporate the contract’s individual experience into this calculation in a statistically optimal way. For many years, however, the use of credibility was limited to the frequency component. Starting with the paper by Hewitt (1971), there have been various suggestions as to how credibility theory also can be applied to the severity component of the pure premium. The latest such suggestion, Frees (2003), revived the interest in the problem.In this paper, we review four different formulas incorporating frequency and severity into credibility calculations. We then compare by simulation which one is most accurate at predicting a contract’s next-year outcome. It is found that the classical formula of Bühlmann (1967) is as good as the other ones in many cases. Alternatives, however, may offer easier analysis of the separate effects of frequency and severity on the premium.We also show that all the formulas reviewed in this paper stem from the same minimization problem, and we present a general, integrated, solution. At the same time, we complete Gerber (1972) by providing a proof to the main result of this paper and by stating required additional assumptions. Journal: North American Actuarial Journal Pages: 49-62 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596239 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596239 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:49-62 Template-Type: ReDIF-Article 1.0 Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Author-Name: Jan Beirlant Author-X-Name-First: Jan Author-X-Name-Last: Beirlant Author-Name: Tom Hoedemakers Author-X-Name-First: Tom Author-X-Name-Last: Hoedemakers Author-Name: Robert Verlaak Author-X-Name-First: Robert Author-X-Name-Last: Verlaak Title: Lognormal Mixed Models for Reported Claims Reserves Abstract: Traditional claims-reserving techniques are based on so-called run-off triangles containing aggregate claim figures. Such a triangle provides a summary of an underlying data set with individual claim figures. This contribution explores the interpretation of the available individual data in the framework of longitudinal data analysis. Making use of the theory of linear mixed models, a flexible model for loss reserving is built. Whereas traditional claims-reserving techniques don’t lead directly to predictions for individual claims, the mixed model enables such predictions on a sound statistical basis with, for example, confidence regions. Both a likelihood-based as well as a Bayesian approach are considered. In the frequentist approach, expressions for the mean squared error of prediction of an individual claim reserve, origin year reserves, and the total reserve are derived. Using MCMC techniques, the Bayesian approach allows simulation from the complete predictive distribution of the reserves and the calculation of various risk measures. The paper ends with an illustration of the suggested techniques on a data set from practice, consisting of Belgian automotive third-party liability claims. The results for the mixed-model analysis are compared with those obtained from traditional claims-reserving techniques for run-off triangles. For the data under consideration, the lognormal mixed model fits the observed individual data well. It leads to individual predictions comparable to those obtained by applying chain-ladder development factors to individual data. Concerning the predictive power on the aggregate level, the mixed model leads to reasonable predictions and performs comparable to and often better than the stochastic chain ladder for aggregate data. Journal: North American Actuarial Journal Pages: 30-48 Issue: 1 Volume: 10 Year: 2006 X-DOI: 10.1080/10920277.2006.10596238 File-URL: http://hdl.handle.net/10.1080/10920277.2006.10596238 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:30-48 Template-Type: ReDIF-Article 1.0 Author-Name: Anatoliy I. Yashin Author-X-Name-First: Anatoliy I. Author-X-Name-Last: Yashin Author-Name: Konstantin G. Arbeev Author-X-Name-First: Konstantin G. Author-X-Name-Last: Arbeev Author-Name: Deqing Wu Author-X-Name-First: Deqing Author-X-Name-Last: Wu Author-Name: Liubov Arbeeva Author-X-Name-First: Liubov Author-X-Name-Last: Arbeeva Author-Name: Alexander Kulminski Author-X-Name-First: Alexander Author-X-Name-Last: Kulminski Author-Name: Irina Kulminskaya Author-X-Name-First: Irina Author-X-Name-Last: Kulminskaya Author-Name: Igor Akushevich Author-X-Name-First: Igor Author-X-Name-Last: Akushevich Author-Name: Svetlana V. Ukraintseva Author-X-Name-First: Svetlana V. Author-X-Name-Last: Ukraintseva Title: How Genes Modulate Patterns of Aging-Related Changes on the Way to 100: Biodemographic Models and Methods in Genetic Analyses of Longitudinal Data Abstract: In this article we clarify mechanisms of genetic regulation of human aging and longevity traits. The objective of this article is to address the issues in previous research of not reaching a genome-wide level of statistical significance and lack of replication in the studies of independent populations. We performed GWAS of human life span using different subsets of data from the original Framingham Heart Study cohort corresponding to different quality control procedures, and we used one subset of selected genetic variants for further analyses. We used a simulation study to show that this approach to combining data improves the quality of GWAS with FHS longitudinal data to compare average age trajectories of physiological variables in carriers and noncarriers of selected genetic variants. We used a stochastic process model of human mortality and aging to investigate genetic influence on hidden biomarkers of aging and on dynamic interaction between aging and longevity. We investigated properties of genes related to selected variants and their roles in signaling and metabolic pathways and showed that the use of different quality control procedures results in different sets of genetic variants associated with life span. We selected 24 genetic variants negatively associated with life span and showed that the joint analyses of genetic data at the time of biospecimen collection and follow-up data substantially improved significance of associations of 24 selected SNPs with life span. We also showed that aging-related changes in physiological variables and in hidden biomarkers of aging differ for the groups of carriers and noncarriers of selected variants. The results of these analyses demonstrated benefits of using biodemographic models and methods in genetic association studies of these traits. Our findings showed that the absence of a large number of genetic variants with deleterious effects may make substantial contribution to exceptional longevity. These effects are dynamically mediated by a number of physiological variables and hidden biomarkers of aging. The results of these research demonstrated benefits of using integrative statistical models of mortality risks in genetic studies of human aging and longevity. Journal: North American Actuarial Journal Pages: 201-232 Issue: 3 Volume: 20 Year: 2016 Month: 7 X-DOI: 10.1080/10920277.2016.1178588 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1178588 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:3:p:201-232 Template-Type: ReDIF-Article 1.0 Author-Name: Linda L. Golden Author-X-Name-First: Linda L. Author-X-Name-Last: Golden Author-Name: Patrick L. Brockett Author-X-Name-First: Patrick L. Author-X-Name-Last: Brockett Author-Name: Jing Ai Author-X-Name-First: Jing Author-X-Name-Last: Ai Author-Name: Bruce Kellison Author-X-Name-First: Bruce Author-X-Name-Last: Kellison Title: Empirical Evidence on the Use of Credit Scoring for Predicting Insurance Losses with Psycho-social and Biochemical Explanations Abstract: An important development in personal lines of insurance in the United States is the use of credit history data for insurance risk classification to predict losses. This research presents the results of collaboration with industry conducted by a university at the request of its state legislature. The purpose was to see the viability and validity of the use of credit scoring to predict insurance losses given its controversial nature and criticism as redundant of other predictive variables currently used. Working with industry and government, this study analyzed more than 175,000 policyholders’ information for the relationship between credit score and claims. Credit scores were significantly related to incurred losses, evidencing both statistical and practical significance. We investigate whether the revealed relationship between credit score and incurred losses was explainable by overlap with existing underwriting variables or whether the credit score adds new information about losses not contained in existing underwriting variables. The results show that credit scores contain significant information not already incorporated into other traditional rating variables (e.g., age, sex, driving history). We discuss how sensation seeking and self-control theory provide a partial explanation of why credit scoring works (the psycho-social perspective). This article also presents an overview of biological and chemical correlates of risk taking that helps explain why knowing risk-taking behavior in one realm (e.g., risky financial behavior and poor credit history) transits to predicting risk-taking behavior in other realms (e.g., automobile insurance incurred losses). Additional research is needed to advance new nontraditional loss prediction variables from social media consumer information to using information provided by technological advances. The evolving and dynamic nature of the insurance marketplace makes it imperative that professionals continue to evolve predictive variables and for academics to assist with understanding the whys of the relationships through theory development. Journal: North American Actuarial Journal Pages: 233-251 Issue: 3 Volume: 20 Year: 2016 Month: 7 X-DOI: 10.1080/10920277.2016.1209118 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1209118 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:3:p:233-251 Template-Type: ReDIF-Article 1.0 Author-Name: Andreas Milidonis Author-X-Name-First: Andreas Author-X-Name-Last: Milidonis Title: An Empirical Investigation of CDS Spreads Using a Regime-Switching Default Risk Model Abstract: Default risk in equity returns can be measured by structural models of default. In this article we propose a credit warning signal (CWS) based on the Merton Default Risk (MDR) model and a Regime-Switching Default Risk (RSDR) model. The RSDR model is a generalization of the MDR model, comprises regime-switching asset distribution dynamics, and thus produces more realistic default probability estimates in cases of deteriorating credit quality. Alternatively, it reduces to the MDR model. Using a dataset of U.S. credit default swap (CDS) contracts around the 2007-8 crisis we construct rating-based indices to investigate the MDR and RSDR implied probabilities of default in relation to the market-observed CDS spreads. The proposed CWS measure indicates an increase in implied default probabilities several months ahead of notable increases in CDS spreads. Journal: North American Actuarial Journal Pages: 252-275 Issue: 3 Volume: 20 Year: 2016 Month: 7 X-DOI: 10.1080/10920277.2016.1180996 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1180996 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:3:p:252-275 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Canudas-Romo Author-X-Name-First: Vladimir Author-X-Name-Last: Canudas-Romo Author-Name: Eva DuGoff Author-X-Name-First: Eva Author-X-Name-Last: DuGoff Author-Name: Albert W. Wu Author-X-Name-First: Albert W. Author-X-Name-Last: Wu Author-Name: Saifuddin Ahmed Author-X-Name-First: Saifuddin Author-X-Name-Last: Ahmed Author-Name: Gerard Anderson Author-X-Name-First: Gerard Author-X-Name-Last: Anderson Title: Life Expectancy in 2040: What Do Clinical Experts Expect? Abstract: We use expert clinical and public health opinion to estimate likely changes in the prevention and treatment of important disease conditions and how they will affect future life expectancy. Focus groups were held including clinical and public health faculty with expertise in the six leading causes of death in the United States. Mortality rates and life tables for 2040 were derived by sex and age. Life expectancy at age 20 and 65 was compared to figures published by the Social Security Administration and to estimates from the Lee-Carter method. There was agreement among all three approaches that life expectancy at age 20 will increase by approximately one year per decade for females and males between now and 2040. According to the clinical experts, 70% of the improvement in life expectancy will occur in cardiovascular disease and cancer, while in the last 30 years most of the improvement has occurred in cardiovascular disease. Expert opinion suggests that most of the increase in life expectancy will be attributable to the already achieved reduction in smoking rates, especially for women. Journal: North American Actuarial Journal Pages: 276-285 Issue: 3 Volume: 20 Year: 2016 Month: 7 X-DOI: 10.1080/10920277.2016.1179123 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1179123 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:3:p:276-285 Template-Type: ReDIF-Article 1.0 Author-Name: Zeinab Amin Author-X-Name-First: Zeinab Author-X-Name-Last: Amin Title: Quantification of Operational Risk: A Scenario-Based Approach Abstract: In this article, I identify challenges to the loss distribution approach in modeling operational risk. I propose a scenario-based methodology for operational risk assessment, which recognizes that each risk can occur under a number of wide-ranging scenarios and that association between risks may behave differently for different scenarios. The model that is developed internally in the company provides a practical quantitative assessment of risk exposure that reflects a deep understanding of the company and its environment, making the risk calculation more responsive to the actual state, ensuring that the company is attending to its key operational risks. In this model qualitative and quantitative approaches are combined to build a loss distribution for individual and aggregate operational risk exposure. The model helps to portray the company's internal control systems and aspects of business environment. These features can help the company increase its operational efficiency, reduce loss from undesirable incidents, and maintain the integrity of internal control. Journal: North American Actuarial Journal Pages: 286-297 Issue: 3 Volume: 20 Year: 2016 Month: 7 X-DOI: 10.1080/10920277.2016.1176581 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1176581 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:3:p:286-297 Template-Type: ReDIF-Article 1.0 Author-Name: Michael R. Powers Author-X-Name-First: Michael R. Author-X-Name-Last: Powers Author-Name: Joseph Qiu Author-X-Name-First: Joseph Author-X-Name-Last: Qiu Author-Name: April Shen Author-X-Name-First: April Author-X-Name-Last: Shen Author-Name: Zhan Shen Author-X-Name-First: Zhan Author-X-Name-Last: Shen Title: Effects of Competition on Insurance Contract Formation Abstract: For an insurance transaction between a single risk-averse buyer and single risk-neutral seller with positive transaction costs, it is well known that the buyer will prefer a policy contract with an ordinary deductible. More detailed results demonstrate the Pareto optimality of an insurance contract characterized by a deductible (followed by coinsurance) for a single risk-averse buyer and single risk-averse seller. In the present work, we employ a market-game model to solve for the equilibrium insurance contract. This formulation, which approximates the behavior of excess property insurance and property catastrophe reinsurance markets, reveals that the equilibrium policy is described by full insurance up to a given policy limit, with no deductible or coinsurance. Our analysis shows further that this solution persists regardless of the numbers of buyers and sellers in the market, and in particular that the market-game equilibrium does not converge to a Pareto-optimal result because of boundary constraints on the number of sellers. Finally, we test our price-formation mechanism against an important generalization, and find that the policy-limit contract persists. Journal: North American Actuarial Journal Pages: 298-312 Issue: 3 Volume: 20 Year: 2016 Month: 7 X-DOI: 10.1080/10920277.2016.1191995 File-URL: http://hdl.handle.net/10.1080/10920277.2016.1191995 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:20:y:2016:i:3:p:298-312 Template-Type: ReDIF-Article 1.0 Author-Name: Diana Chisholm Author-X-Name-First: Diana Author-X-Name-Last: Chisholm Author-Name: Rob Brown Author-X-Name-First: Rob Author-X-Name-Last: Brown Title: Negative Effects of the Canadian GIS Clawback and Possible Mitigating Alternatives Abstract: In Canada there are three main sources of government-provided retirement income: the Canada/Quebec Pension Plans (C/QPP), which have benefits and contributions based on earnings up to the Yearly Maximum Pensionable Earnings; Old Age Security (OAS), which is a fixed amount for most but does include a “clawback” of benefits for high-income individuals; and the Guaranteed Income Supplement (GIS), which is designed to supplement those persons with extremely low income. The annual GIS benefit is reduced, or clawed back, by 50 cents for every dollar of annual income the person has in retirement, including C/QPP and income from Registered Retirement Savings Plans (RRSPs) and other savings. OAS benefits are not included in determining the GIS clawback.The result of this is that low-income individuals who attempt to enhance their retirement replacement ratio actually see a decrease in government-provided support the more they save for retirement. Savings in an RRSP can effectively be taxed at more than 100% through corresponding reductions in the GIS, social housing, home care, GAINS (Ontario’s Guaranteed Annual Income Supplement), and other benefits that are based on one’s personal retirement income.This paper explores alternatives to the 50% GIS clawback, including a basic GIS exemption, a GIS clawback rate lower than 50%, and a combination of the two. The goal is to improve the fairness of the GIS and reduce the disincentive to save for retirement, without increasing the overall cost of the program significantly. Journal: North American Actuarial Journal Pages: 372-383 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597530 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597530 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:372-383 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: Kristen Moore Author-X-Name-First: Kristen Author-X-Name-Last: Moore Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Minimizing the Probability of Lifetime Ruin under Random Consumption Abstract: We determine the optimal investment strategy in a financial market for an individual whose random consumption is correlated with the price of a risky asset. Bayraktar and Young consider this problem and show that the minimum probability of lifetime ruin is the unique convex, smooth solution of its corresponding Hamilton-Jacobi-Bellman equation. In this paper we focus on determining the probability of lifetime ruin and the corresponding optimal investment strategy. We obtain approximations for the probability of lifetime ruin for small values of certain parameters and demonstrate numerically that they are reasonable ones. We also obtain numerical results in cases for which those parameters are not small. Journal: North American Actuarial Journal Pages: 384-400 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597531 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597531 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:384-400 Template-Type: ReDIF-Article 1.0 Author-Name: Liang Wang Author-X-Name-First: Liang Author-X-Name-Last: Wang Author-Name: Emiliano Valdez Author-X-Name-First: Emiliano Author-X-Name-Last: Valdez Author-Name: John Piggott Author-X-Name-First: John Author-X-Name-Last: Piggott Title: Securitization of Longevity Risk in Reverse Mortgages Abstract: The reverse mortgage market has been expanding rapidly in developed economies in recent years. The onset of demographic transition places a rapidly rising number of households in an age window in which reverse mortgages have potential appeal. Increasing prices for residential real estate over the last decade have further stimulated interest.Reverse mortgages involve various risks from the provider-s perspective that may hinder the further development of these financial products. This paper addresses one method of transferring and financing the risks associated with these products through the form of securitization. Securitization is becoming a popular and attractive alternative form of risk transfer of insurance liabilities. Here we demonstrate how to construct a securitization structure for reverse mortgages similar to the one applied in traditional insurance products.Specifically, we investigate the merits of developing survivor bonds and survivor swaps for reverse mortgage products. In the case of survivor bonds, for example, we are able to compute premiums, both analytically and numerically through simulations, and to examine how the longevity risk may be transferred to the financial investors. Our numerical calculations provide an indication of the economic benefits derived from developing survivor bonds to securitize the “longevity risk component” of reverse mortgage products. Moreover, some sensitivity analysis of these economic benefits indicates that these survivor bonds provide for a promising tool for investment diversification. Journal: North American Actuarial Journal Pages: 345-371 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597529 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597529 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:345-371 Template-Type: ReDIF-Article 1.0 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: “On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals,” Jiandong Ren, April 2008 Journal: North American Actuarial Journal Pages: 443-445 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597536 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597536 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:443-445 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Editorial Journal: North American Actuarial Journal Pages: iii-iv Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597537 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597537 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:iii-iv Template-Type: ReDIF-Article 1.0 Author-Name: Vincent Goulet Author-X-Name-First: Vincent Author-X-Name-Last: Goulet Author-Name: Louis-Philippe Pouliot Author-X-Name-First: Louis-Philippe Author-X-Name-Last: Pouliot Title: Simulation of Compound Hierarchical Models in R Abstract: Hierarchical probability models are widely used in insurance applications for data classified in a tree-like structure and in Bayesian inference. We propose an R function to simulate data from compound models in which both the frequency component and the severity component can have a hierarchical structure. The model description method is based solely on R expressions, and it allows for models with any number of levels and nodes per level, as well as with very general conditional probability structures. The function is part of the R package actuar. Journal: North American Actuarial Journal Pages: 401-412 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597532 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597532 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:401-412 Template-Type: ReDIF-Article 1.0 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model Abstract: Phase-type distributions are one of the most general classes of distributions permitting a Markovian interpretation. Sparre Andersen risk models with phase-type claim interarrival times or phase-type claims can be analyzed using Markovian techniques, and results can be expressed in compact matrix forms. Computations involved are readily programmable in practice.This paper studies some quantities associated with the first passage time and the time of ruin in a Sparre Andersen risk model with phase-type interclaim times. In an earlier discussion the present author obtained a matrix expression for the Laplace transform of the first time that the surplus process reaches a given target from the initial surplus. Using this result, we analyze (1) the Laplace transform of the recovery time after ruin, (2) the probability that the surplus attains a certain level before ruin, and (3) the distribution of the maximum severity of ruin. We also give a matrix expression for the expected discounted dividend payments prior to ruin for the Sparre Andersen model in the presence of a constant dividend barrier. Journal: North American Actuarial Journal Pages: 413-425 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597533 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597533 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:413-425 Template-Type: ReDIF-Article 1.0 Author-Name: Xueyuan Wu Author-X-Name-First: Xueyuan Author-X-Name-Last: Wu Title: “The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model,” Shuanming Li, October 2008 Journal: North American Actuarial Journal Pages: 425-427 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597534 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597534 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:425-427 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Minimizing the Probability of Ruin When Consumption is Ratcheted Abstract: We assume that an agent’s rate of consumption is ratcheted; that is, it forms a nondecreasing process. We assume that the agent invests in a financial market with one riskless and one risky asset, with the latter’s price following geometric Brownian motion as in the Black-Scholes model. Given the rate of consumption, we act as financial advisers and find the optimal investment strategy for the agent who wishes to minimize his probability of ruin. To solve this minimization problem, we use techniques from stochastic optimal control. Journal: North American Actuarial Journal Pages: 428-442 Issue: 4 Volume: 12 Year: 2008 X-DOI: 10.1080/10920277.2008.10597535 File-URL: http://hdl.handle.net/10.1080/10920277.2008.10597535 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:428-442 Template-Type: ReDIF-Article 1.0 Author-Name: Kyeonghee Kim Author-X-Name-First: Kyeonghee Author-X-Name-Last: Kim Author-Name: Marjorie A. Rosenberg Author-X-Name-First: Marjorie A. Author-X-Name-Last: Rosenberg Title: Determinants of Persistent High Utilizers in U.S. Adults Using Nationally Representative Data Abstract: High utilizers of health care are those individuals in the upper tail of the distribution each year. The main purpose of our work is to identify determinants of persistent high utilizers in adults, those with high utilization in two consecutive years. Our secondary purpose is to specifically examine the effect of multiple unhealthy behaviors on high health care utilization. In our study, high utilizers are defined as those whose expenditures exceed $10,000 in 2012 dollars. We link 2007–2010 National Health Interview Survey data to the corresponding two-year longitudinal panel of the Medical Expenditure Panel Survey. Our outcome is a three-category variable called “utilization group” consisting of low utilizer, one-time high utilizer, and persistent high utilizer. One-time high utilizers are high utilizers for only one of two years, persistent high utilizers are high utilizers for both years, and low utilizers are the remainder. A partial proportional ordinal logistic regression prospectively predicts the utilization group controlling for the number of unhealthy behaviors, sociodemographic predictors such as age, gender, marital status, insurance status, and income, and individual-level health-related items. The number of unhealthy behaviors is based on physical inactivity, smoking, heavy drinking, and inadequate sleeping habits. Our study found that social determinants, such as education and income, access to insurance, and health-related issues, are significant predictors of being a persistent high utilizer over the next two years. Individuals with two or more unhealthy behaviors are significantly more likely to be a persistent high utilizer relative to those with fewer unhealthy behaviors. Journal: North American Actuarial Journal Pages: 1-21 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1585880 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1585880 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:1-21 Template-Type: ReDIF-Article 1.0 Author-Name: Nan Li Author-X-Name-First: Nan Author-X-Name-Last: Li Title: Estimating Complete Life Tables for Populations with Limited Size: From Graduation to Equivalent Construction Abstract: Reliable complete life tables cannot be directly calculated for small populations, but they are necessary to improve population projections that are the basis of various programs such as social security. Estimating complete life tables for small populations is a solution and is related to mortality graduation. In the rich literature of mortality graduation, various life-table functions are graduated using different smoothing models, but a definition of the true age patterns of life-table functions can hardly be found. The vagueness about the true age patterns of life-table functions is the essential difficulty in mortality graduation. This article removes the essential difficulty by analyzing the computational structure of a life table and by constructing a complete life table that is equivalent to the input abridged life table. Inputting an abridged life table to equivalently construct a complete life table refers to that, using the constructed complete life table to compute an abridged life table, the result is identical to the input life table. For a constructed complete life table, the true age pattern between the abridged age groups is defined as the observed age pattern of the input abridged life table. Within the abridged age groups, the true age pattern is defined as the smoothest pattern using the variation of functionals. The basis of these definitions is the law of large numbers. Utilizing these definitions, equivalent constructions and construction-based graduations are proposed and applied successfully to the data of women in Iceland and Estonia. Journal: North American Actuarial Journal Pages: 22-35 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1585879 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1585879 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:22-35 Template-Type: ReDIF-Article 1.0 Author-Name: Jiahua Xu Author-X-Name-First: Jiahua Author-X-Name-Last: Xu Title: Dating Death: An Empirical Comparison of Medical Underwriters in the U.S. Life Settlements Market Abstract: The value of a life settlement investment, manifested through a traded life insurance policy, is highly dependent on the insured’s life expectancy (LE). LE estimation in life settlements relies heavily on medical underwriting. Employing different evaluation processes, underwriters rarely agree on LE estimates, leading to valuation disparities. We use the natural logarithm of the implied mortality multiplier (ln k) to compare the underwriting results of the four major U.S. medical underwriters (ITM, AVS, Fasano, and LSI). ln k is normalized in terms of gender, age, and smoking status, and is therefore a more suitable indicator than LE estimates for high-level comparisons, especially when the compared groups have a heterogeneous make-up. Based on the analysis of life settlement samples from 2011 to 2016, we trace patterns of underwriters’ ln k in both secondary and tertiary markets of life settlements, and investigate systematic differences in their estimation. Our results show that an underwriter can, relative to peers, act more conservatively (issuing longer LE estimates) for one cohort while more aggressively (issuing shorter LE estimates) for another. We also detect signs of intermediaries’ cherry-picking behavior and discuss additional theories that shed light on the convoluted LE landscape. Journal: North American Actuarial Journal Pages: 36-56 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1585881 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1585881 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:36-56 Template-Type: ReDIF-Article 1.0 Author-Name: Colin M. Ramsay Author-X-Name-First: Colin M. Author-X-Name-Last: Ramsay Author-Name: Victor I. Oguledo Author-X-Name-First: Victor I. Author-X-Name-Last: Oguledo Title: Doubly Enhanced Annuities (DEANs) and the Impact of Quality of Long-Term Care under a Multi-State Model of Activities of Daily Living (ADL) Abstract: The relatively small size of global voluntary immediate life annuity markets seemingly contradicts a well-known result that, under certain conditions, utility-maximizing retirees should annuitize all of their wealth upon retirement. This apparent contradiction contributes to what is called the “annuity puzzle.” The main explanations for the annuity puzzle include adverse selection, bequest motives, and retirees’ fear of health shocks that may require them to need long-term care. To explore a potential solution to this puzzle in the U.S. annuity market, we consider a cohort of retirees who are independent and identical except for a hidden immutable health parameter, θ>0, that identifies the retiree’s risk type. We assume that the “average” or “standard” retiree has θ = 1, with larger values of θ denoting less healthy individuals. Because private insurers fear that annuitants may live well beyond their life expectancy—that is, they fear adverse selection—voluntary immediate life annuities are generally priced in a manner that makes them attractive mainly to retirees who believe themselves to be healthier than average. These retirees, however, typically represent a small fraction of their cohort of retirees. To expand annuity markets, we are proposing a hybrid voluntary fixed immediate annuity product called a doubly enhanced annuity (DEAN), which we feel will be attractive to the larger retiree population; that is, retirees with θ>1. DEANs are medically underwritten to provide greater annual benefits to annuitants with shorter than average life expectancies, they provide long-term care benefits, and they satisfy a bequest motive through a death benefit. Our underlying model of retiree mortality and morbidity is based on a multi-state Markov process with states representing various levels of an insured retiree’s ability to perform activities of daily living (ADL). A major contribution of our research is to explicitly include in our multi-state Markov model a parameter, α, that reflects the level of quality of long-term care a retiree receives over her lifetime. Our main objectives are to develop a theoretical basis for pricing DEANs for the U.S. market, to determine a retiree’s expected discounted utility gained from these annuities, to determine the optimal choice of quality of care, and to explore some of the quality of life implications. A numerical example is provided. Journal: North American Actuarial Journal Pages: 57-99 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1598270 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1598270 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:57-99 Template-Type: ReDIF-Article 1.0 Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: Valuation of Large Variable Annuity Portfolios with Rank Order Kriging Abstract: Metamodels, which simplify the simulation models used in the valuation of large variable annuity portfolios, have recently increased in popularity. The ordinary kriging and the GB2 (generalized beta of the second kind) regression models are examples of metamodels used to predict fair market values of variable annuity guarantees. It is well known that the distribution of fair market values is highly skewed. Ordinary kriging does not fit skewed data well but depends on only a few parameters that can be estimated straightforwardly. GB2 regression can handle skewed data but parameter estimation can be quite challenging. In this article, we explore the rank order kriging method, which can handle highly skewed data and depends only on a single parameter, for the valuation of large variable annuity portfolios. Our numerical results demonstrate that the rank order kriging method performs remarkably well in terms of fitting the skewed distribution and producing accurate estimates of fair market values at the portfolio level. Journal: North American Actuarial Journal Pages: 100-117 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1617169 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1617169 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:100-117 Template-Type: ReDIF-Article 1.0 Author-Name: Tzuling Lin Author-X-Name-First: Tzuling Author-X-Name-Last: Lin Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Title: Hedging Mortality/Longevity Risks for Multiple Years Abstract: In this article, we develop strategies of hedging multiyear mortality (longevity) risk for a life insurer (an annuity provider) through purchasing some mortality-linked securities from a financial intermediary. Under the multiyear hedges for a life insurer (an annuity provider) involving two uncertain factors—the mortality rate and the number of life insureds (annuity recipients)—we derive closed-form formulas for the optimal units of purchasing underlying mortality-linked securities. Numerical illustrations show that the downside risk of loss because of mortality (longevity) risk for the life insurer (annuity provider) can be significantly hedged by purchasing the optimal units of mortality-linked securities, and the sample risk can be reduced by increasing the number of life insureds (annuity recipients) at issue. For a financial intermediary, adopting an optimal weight of a portfolio of life and annuity business can reduce extreme losses from the longevity risk but could slightly increase losses from the mortality risk, and the sample risk cannot necessarily be eliminated by increasing the number of life insureds/annuity recipients at issue. Journal: North American Actuarial Journal Pages: 118-140 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1625789 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1625789 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:118-140 Template-Type: ReDIF-Article 1.0 Author-Name: Montserrat Guillen Author-X-Name-First: Montserrat Author-X-Name-Last: Guillen Author-Name: Jens Perch Nielsen Author-X-Name-First: Jens Perch Author-X-Name-Last: Nielsen Author-Name: Ana M. Pérez-Marín Author-X-Name-First: Ana M. Author-X-Name-Last: Pérez-Marín Author-Name: Valandis Elpidorou Author-X-Name-First: Valandis Author-X-Name-Last: Elpidorou Title: Can Automobile Insurance Telematics Predict the Risk of Near-Miss Events? Abstract: Telematics data from usage-based motor insurance provide valuable information – including vehicle usage, attitude toward speeding, and time and proportion of urban/nonurban driving, which can be used for ratemaking. Additional information on acceleration, braking, and cornering can likewise be usefully employed to identify near-miss events, a concept taken from aviation that denotes a situation that might have resulted in an accident. We analyze near-miss events from a sample of drivers in order to identify the risk factors associated with a higher risk of near-miss occurrence. Our empirical application with a pilot sample of real usage-based insurance data reveals that certain factors are associated with a higher expected number of near-miss events, but that the association differs depending on the type of near miss. We conclude that nighttime driving is associated with a lower risk of cornering events, urban driving increases the risk of braking events, and speeding is associated with acceleration events. These results are relevant for the insurance industry in order to implement dynamic risk monitoring through telematics, as well as preventive actions. Journal: North American Actuarial Journal Pages: 141-152 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1627221 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1627221 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:141-152 Template-Type: ReDIF-Article 1.0 Author-Name: Xiyue Liao Author-X-Name-First: Xiyue Author-X-Name-Last: Liao Author-Name: Guoqiang Chen Author-X-Name-First: Guoqiang Author-X-Name-Last: Chen Author-Name: Ben Ku Author-X-Name-First: Ben Author-X-Name-Last: Ku Author-Name: Rahul Narula Author-X-Name-First: Rahul Author-X-Name-Last: Narula Author-Name: Janet Duncan Author-X-Name-First: Janet Author-X-Name-Last: Duncan Title: Text Mining Methods Applied to Insurance Company Customer Calls: A Case Study Abstract: The purpose of this case study is to develop a process for a U.S. personal lines insurance company to improve its customer service, make call center operations more efficient, and reduce costs by analyzing customer calls. Text mining methods such as topic modeling and sentiment analysis are used to study approximately 10,000 nonclaim customer calls from 2016. Results show the most frequent topics of calls and how customer sentiment differs between topics, which will allow the company to adjust its customer service accordingly. Journal: North American Actuarial Journal Pages: 153-163 Issue: 1 Volume: 24 Year: 2020 Month: 1 X-DOI: 10.1080/10920277.2019.1649155 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1649155 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:1:p:153-163 Template-Type: ReDIF-Article 1.0 Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Author-Name: Tony Wirjanto Author-X-Name-First: Tony Author-X-Name-Last: Wirjanto Title: Advances in Predictive Analytics Journal: North American Actuarial Journal Pages: 165-167 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2020.1737495 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1737495 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:165-167 Template-Type: ReDIF-Article 1.0 Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: Data Clustering with Actuarial Applications Abstract: Data clustering refers to the process of dividing a set of objects into homogeneous groups or clusters such that the objects in each cluster are more similar to each other than to those of other clusters. As one of the most popular tools for exploratory data analysis, data clustering has been applied in many scientific areas. In this article, we give a review of the basics of data clustering, such as distance measures and cluster validity, and different types of clustering algorithms. We also demonstrate the applications of data clustering in insurance by using two scalable clustering algorithms, the truncated fuzzy c-means (TFCM) algorithm and the hierarchical k-means algorithm, to select representative variable annuity contracts, which are used to build predictive models. We found that the hierarchical k-means algorithm is efficient and produces high-quality representative variable annuity contracts. Journal: North American Actuarial Journal Pages: 168-186 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1575242 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1575242 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:168-186 Template-Type: ReDIF-Article 1.0 Author-Name: Ou Dang Author-X-Name-First: Ou Author-X-Name-Last: Dang Author-Name: Mingbin Feng Author-X-Name-First: Mingbin Author-X-Name-Last: Feng Author-Name: Mary R. Hardy Author-X-Name-First: Mary R. Author-X-Name-Last: Hardy Title: Efficient Nested Simulation for Conditional Tail Expectation of Variable Annuities Abstract: Monte Carlo simulations—in particular, nested Monte Carlo simulations—are commonly used in variable annuity (VA) risk modeling. However, the computational burden associated with nested simulations is substantial. We propose an Importance-Allocated Nested Simulation (IANS) method to reduce the computational burden, using a two-stage process. The first stage uses a low-cost analytic proxy to identify the tail scenarios most likely to contribute to the Conditional Tail Expectation risk measure. In the second stage we allocate the entire inner simulation computational budget to the scenarios identified in the first stage. Our numerical experiments show that, in the VA context, IANS can be up to 30 times more efficient than a standard Monte Carlo experiment, measured by relative mean squared errors, when both are given the same computational budget. Journal: North American Actuarial Journal Pages: 187-210 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1636399 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1636399 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:187-210 Template-Type: ReDIF-Article 1.0 Author-Name: Edward W. Frees Author-X-Name-First: Edward W. Author-X-Name-Last: Frees Author-Name: Lisa Gao Author-X-Name-First: Lisa Author-X-Name-Last: Gao Title: Predictive Analytics and Medical Malpractice Abstract: Insurance as a discipline has long embraced analytics, and market trends signal an even stronger relationship going forward. This article is a case study on the use of predictive analytics in the context of medical errors. Analyzing medical errors helps improve health care systems, and through a type of insurance known as medical malpractice insurance, we have the ability to analyze medical errors using data external to the health care system. In the spirit of modern analytics, this paper describes the application of data from several different sources. These sources give different insights into a specific problem facing the medical malpractice community familiar to actuaries: the relative importance of upper limits (or caps) on insurance payouts for noneconomic damages (e.g., pain and suffering). This topic is important to the industry in that many courts are considering the legality of such limitations. All stakeholders, including patients, physicians, hospitals, lawyers, and the general public, are interested in the implications of removing limitations on caps. This article demonstrates how we can use data and analytics to inform the many different stakeholders on this issue. Journal: North American Actuarial Journal Pages: 211-227 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1634597 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1634597 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:211-227 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny S.-H. Li Author-X-Name-First: Johnny S.-H. Author-X-Name-Last: Li Author-Name: Rui Zhou Author-X-Name-First: Rui Author-X-Name-Last: Zhou Author-Name: Yanxin Liu Author-X-Name-First: Yanxin Author-X-Name-Last: Liu Author-Name: George Graziani Author-X-Name-First: George Author-X-Name-Last: Graziani Author-Name: R. Dale Hall Author-X-Name-First: R. Dale Author-X-Name-Last: Hall Author-Name: Jennifer Haid Author-X-Name-First: Jennifer Author-X-Name-Last: Haid Author-Name: Andrew Peterson Author-X-Name-First: Andrew Author-X-Name-Last: Peterson Author-Name: Laurence Pinzur Author-X-Name-First: Laurence Author-X-Name-Last: Pinzur Title: Drivers of Mortality Dynamics: Identifying Age/Period/Cohort Components of Historical U.S. Mortality Improvements Abstract: The goal of this article is to obtain an age/period/cohort (A/P/C) decomposition of historical U.S. mortality improvement. Two different routes to achieving this goal are considered. In the first route, the desired components are obtained by fitting an A/P/C model directly to historical mortality improvement rates. In the second route, an A/P/C model is estimated to historical crude death rates and the desired components are then obtained by differencing the estimated model parameters. For each route, various possible A/P/C model structures are tested and evaluated on the basis of their robustness to several factors (e.g., changes in the calibration window) and their ability to explain historical changes in mortality improvement. Based on the evaluation results, an A/P/C decomposition for each gender is recommended. The decomposition will be examined in a follow-up project, in which the linkages between the A/P/C components and certain intrinsic factors will be identified. Journal: North American Actuarial Journal Pages: 228-250 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2020.1716808 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1716808 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:228-250 Template-Type: ReDIF-Article 1.0 Author-Name: Mathieu Boudreault Author-X-Name-First: Mathieu Author-X-Name-Last: Boudreault Author-Name: Patrick Grenier Author-X-Name-First: Patrick Author-X-Name-Last: Grenier Author-Name: Mathieu Pigeon Author-X-Name-First: Mathieu Author-X-Name-Last: Pigeon Author-Name: Jean-Mathieu Potvin Author-X-Name-First: Jean-Mathieu Author-X-Name-Last: Potvin Author-Name: Richard Turcotte Author-X-Name-First: Richard Author-X-Name-Last: Turcotte Title: Pricing Flood Insurance with a Hierarchical Physics-Based Model Abstract: Floods account for a large part of global economic losses from natural disasters. As a result, the private insurance sector is increasingly participating in the financial risk sharing, thus expanding the role of actuaries to flood risk management. In this article, we investigate pricing and spatial segmentation of flood risk in the context of private insurance, meaning that individual risk assessment should minimize adverse selection. As such, we design a hierarchical flood risk model that allows an assessment at the individual level. Our model relies on a chain of physics-based climate, hydrological, and hydraulics modules combined with civil engineering methods to map the distribution of individual flood losses at high resolution. Building on such approach, we design pricing and segmentation methods tailored for flood risk management. We then apply the methods to study flood risk in a small city in the province of Quebec. We calculate premiums, analyze the impacts of risk sharing, set pricing territories consistent with the spatial flood risk, and finally, quantify the impact of greenhouse gas emission scenarios on individual and aggregate losses, premiums, and tail risk measures. Journal: North American Actuarial Journal Pages: 251-274 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1667830 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1667830 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:251-274 Template-Type: ReDIF-Article 1.0 Author-Name: Ben Mingbin Feng Author-X-Name-First: Ben Mingbin Author-X-Name-Last: Feng Author-Name: Zhenni Tan Author-X-Name-First: Zhenni Author-X-Name-Last: Tan Author-Name: Jiayi Zheng Author-X-Name-First: Jiayi Author-X-Name-Last: Zheng Title: Efficient Simulation Designs for Valuation of Large Variable Annuity Portfolios Abstract: The valuation of large variable annuity portfolios is an important enterprise risk management task but is computationally challenging due to the need for simulation. Existing methods in the literature only use simple experimental designs with significant room for improvement. This article identifies three major components in an efficient valuation framework. In addition, we propose optimal experimental designs and provides analytical insights for each component. Our numerical results show that our proposal achieves significantly higher accuracy than state-of-the-art alternatives without requiring any additional computational resource. Journal: North American Actuarial Journal Pages: 275-289 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1685394 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1685394 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:275-289 Template-Type: ReDIF-Article 1.0 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Author-Name: Adelaide Di Wu Author-X-Name-First: Adelaide Di Author-X-Name-Last: Wu Title: Bühlmann Credibility-Based Approaches to Modeling Mortality Rates for Multiple Populations Abstract: Inspired by the ideas of the joint-k, the co-integrated, the common factor, and the augmented common factor Lee-Carter models, in this article, we propose four corresponding Bühlmann credibility-based mortality models for multiple populations. Our models and the four Lee-Carter models are fitted with mortality data from the Human Mortality Database for both genders of the United States, the United Kingdom, and Japan to forecast mortality rates for three forecasting periods. Based on the measure of AMAPE (average of mean absolute percentage error), numerical illustrations show that our Bühlmann credibility-based models contribute to more accurate forecasts than the Lee-Carter-based models in all three forecasting periods. Finally, we also propose a stochastic version of the multi-population Bühlmann credibility-based mortality models, which can be used to construct predictive intervals on the projected mortality rates and to conduct stochastic simulations for applications. Journal: North American Actuarial Journal Pages: 290-315 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1614463 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1614463 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:290-315 Template-Type: ReDIF-Article 1.0 Author-Name: Min Ji Author-X-Name-First: Min Author-X-Name-Last: Ji Author-Name: Mostafa Aminzadeh Author-X-Name-First: Mostafa Author-X-Name-Last: Aminzadeh Author-Name: Min Deng Author-X-Name-First: Min Author-X-Name-Last: Deng Title: Predictive Modeling of Threshold Life Tables Abstract: Accurate modeling of mortality at advanced ages is crucial to the valuation of pension plans and life annuities, especially longevity annuities for which annuity payments start very late in life, say age 85. Parametric regression models extrapolate lifetime distribution to the advanced ages but do not guarantee goodness fit. Threshold life tables offer an alternative solution to this problem using piecewise distribution via the peaks-over-threshold approach in the extreme value family. However, parameter estimation of this model is challenging, especially the determination of the threshold. Regular estimation methods do not guarantee a smooth life table. In this research, we impose parameter constraints to achieve a smooth threshold life table and propose a Bayesian approach to obtain Bayes estimates of the parameters and approximate predictive density via simulation, which can be used to compute life expectancy and other measures of interest in a Bayesian framework. Journal: North American Actuarial Journal Pages: 316-332 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2019.1633929 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1633929 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:316-332 Template-Type: ReDIF-Article 1.0 Author-Name: C. Brock Porth Author-X-Name-First: C. Author-X-Name-Last: Brock Porth Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Author-Name: Milton Boyd Author-X-Name-First: Milton Author-X-Name-Last: Boyd Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Kai Liu Author-X-Name-First: Kai Author-X-Name-Last: Liu Title: Remote Sensing Applications for Insurance: A Predictive Model for Pasture Yield in the Presence of Systemic Weather Abstract: A robust predictive model for crop yield is essential for designing a commercially viable index-based insurance policy. Index-based insurance for crops is still at a relatively infant stage, and more research and development is needed in order to address a main limitation, which is referred to as basis risk. Traditionally, ground weather station measurements have been the most common approach used in weather indices, and this approach has often led to high levels of basis risk. Recent advances in satellite-based remote sensing provide new opportunities to use publicly available and transparent “big data,” to potentially make index-based insurance policies more relevant by reducing basis risk. This is the first article to provide a comprehensive comparison of 13 pasture production indices (PPIs), including those developed based on satellite-derived vegetation and biophysical parameter indices using data products from the Moderate Resolution Imaging Spectroradiometer (MODIS). A validation protocol is established, and a unique dataset covering the period 2002 to 2016 from a network of pasture clip sites in the province of Alberta, Canada, is used to demonstrate new applications for insurance based on remote sensing–derived data. The results of the satellite-derived PPIs are compared to PPIs based on ground weather station data as benchmarks, which to date are the most common design for index-based insurance. Overall, the satellite-based indices report higher correlations with the ground truth forage yield data compared to the weather station PPIs. As an example, in 2015 and 2016 the best performing satellite-based PPIs produced correlations close to 90%. When considering the whole sample period, the highest overall average correlation is 62.0% for the biophysical parameter PPI based on FPAR 500-m MODIS, and the lowest overall average correlation is 43.8% for the vegetation PPI based on EVI 250-m MODIS. Comparatively, the highest correlation reported for the weather station indices is for precipitation, at 12.51%. Other predictive models based on principal component analysis and shrinkage methods (such as lasso, ridge regression, and elastic net) are considered to address the issues of variable selection and dimension reduction in insurance design. This research makes an important contribution to the field of actuarial science and insurance, because it highlights potential new opportunities for insurance design and predictive analytics using large and comprehensive satellite datasets that remain relatively unexplored to date in insurance practice. Though forage is used as the example here, the research could be extended to other crops, and other areas in the property and casualty sector, including for fire and flood. Journal: North American Actuarial Journal Pages: 333-354 Issue: 2 Volume: 24 Year: 2020 Month: 4 X-DOI: 10.1080/10920277.2020.1717345 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1717345 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:2:p:333-354 Template-Type: ReDIF-Article 1.0 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Author-X-Name-Last: Chi-Liang Tsai Author-Name: Xinying Liang Author-X-Name-First: Xinying Author-X-Name-Last: Liang Title: Application of Relational Models in Mortality Immunization Abstract: The prediction of future mortality rates by any existing mortality models is hardly exact, which causes an exposure to mortality (longevity) risk for life insurers (annuity providers). Since a change in mortality rates has opposite impacts on the surpluses of life insurance and annuity, hedging strategies of mortality and longevity risks can be implemented by creating an insurance portfolio of both life insurance and annuity products. In this article, we apply relational models to capture the mortality movements by assuming that the realized mortality sequence is a proportional change and/or a constant shift of the expected one, and the size of the changes varies in the length of the sequences. Then we create a variety of non-size-free matching strategies to determine the weights of life insurance and annuity products in an insurance portfolio for mortality immunization, where the weights depend on the sizes of the proportional and/or constant changes. Comparing the hedging performances of four non-size-free matching strategies with corresponding size-free ones proposed by Lin and Tsai, we demonstrate with simulation illustrations that the non-size-free matching strategies can hedge against mortality and longevity risks more effectively than the size-free ones. Journal: North American Actuarial Journal Pages: 509-532 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1462715 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1462715 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:509-532 Template-Type: ReDIF-Article 1.0 Author-Name: Giacomo Nebbia Author-X-Name-First: Giacomo Author-X-Name-Last: Nebbia Author-Name: Lisa Nussbaum Author-X-Name-First: Lisa Author-X-Name-Last: Nussbaum Author-Name: Annie Helmkamp Author-X-Name-First: Annie Author-X-Name-Last: Helmkamp Author-Name: Stacy Andersen Author-X-Name-First: Stacy Author-X-Name-Last: Andersen Author-Name: Thomas Perls Author-X-Name-First: Thomas Author-X-Name-Last: Perls Author-Name: Paola Sebastiani Author-X-Name-First: Paola Author-X-Name-Last: Sebastiani Title: Manual and Automated Procedures for Compiling a Very Large Sample of Centenarian Pedigrees Abstract: A large portion of the baby boomer population will live beyond the age of 90 years, and entitlement programs and various insurance products have thus become interested in longevity risk. Beyond cohort life table predictions, actuaries have little to go on in determining which individuals or portions of populations are at increased risk of living to 90 or 100 or even older. We and others have noted strong familial risk for living beyond the oldest one percentile of survival, and we developed an algorithm that uses information about relatives’ longevity to compute the chance of an individual surviving to extreme old age. An important step of this work is to compile large samples of pedigrees with and without long-lived family members. Here we describe our process of hand curation of centenarian pedigrees and software that we have developed for the automated construction of such pedigrees using internet-based resources that can support the manual process. Journal: North American Actuarial Journal Pages: 591-599 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1462716 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1462716 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:591-599 Template-Type: ReDIF-Article 1.0 Author-Name: Lukas Reichel Author-X-Name-First: Lukas Author-X-Name-Last: Reichel Author-Name: Hato Schmeiser Author-X-Name-First: Hato Author-X-Name-Last: Schmeiser Title: The Liability Regime of Insurance Pools and Its Impact on Pricing Abstract: This work formally derives fairly priced premiums for the policyholder of an insurance pool and the risk-adequate equity contributions of the pool insurers’ equity holders in a contingent claims approach. The approach distinguishes between two liability regimes: joint liability and several liability. These regimes regulate the pool’s indemnification when one or more of the pool insurers cannot meet their full obligations because of insolvency. Joint liability is deduced to be the preferable regime for the policyholder in cost-savings terms if corporate income taxation is introduced as a market friction. This regime advantage vanishes if the pool insurers’ asset correlation is substantial or if their risk sharing becomes unbalanced. Additionally, we address risk-shifting problems and their regime-dependent effects on both stakeholder groups. Journal: North American Actuarial Journal Pages: 533-553 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1462717 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1462717 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:533-553 Template-Type: ReDIF-Article 1.0 Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: Fat-Tailed Regression Modeling with Spliced Distributions Abstract: Insurance claims data usually contain a large number of zeros and exhibits fat-tail behavior. Misestimation of one end of the tail impacts the other end of the tail of the claims distribution and can affect both the adequacy of premiums and needed reserves to hold. In addition, insured policyholders in a portfolio are naturally non-homogeneous. It is an ongoing challenge for actuaries to be able to build a predictive model that will simultaneously capture these peculiar characteristics of claims data and policyholder heterogeneity. Such models can help make improved predictions and thereby ease the decision-making process. This article proposes the use of spliced regression models for fitting insurance loss data. A primary advantage of spliced distributions is their flexibility to accommodate modeling different segments of the claims distribution with different parametric models. The threshold that breaks the segments is assumed to be a parameter, and this presents an additional challenge in the estimation. Our simulation study demonstrates the effectiveness of using multistage optimization for likelihood inference and at the same time the repercussions of model misspecification. For purposes of illustration, we consider three-component spliced regression models: the first component contains zeros, the second component models the middle segment of the loss data, and the third component models the tail segment of the loss data. We calibrate these proposed models and evaluate their performance using a Singapore auto insurance claims dataset. The estimation results show that the spliced regression model performs better than the Tweedie regression model in terms of tail fitting and prediction accuracy. Journal: North American Actuarial Journal Pages: 554-573 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1462718 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1462718 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:554-573 Template-Type: ReDIF-Article 1.0 Author-Name: Saisai Zhang Author-X-Name-First: Saisai Author-X-Name-Last: Zhang Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Author-Name: David Saunders Author-X-Name-First: David Author-X-Name-Last: Saunders Title: Updating Wilkie’s Economic Scenario Generator for U.S. Applications Abstract: The Wilkie economic scenario generator has had a significant influence on economic scenario generators since the first formal publication in 1986 by Wilkie. In this article we update the model parameters using U.S. data to 2014, and review the model performance. In particular, we consider stationarity assumptions, parameter stability, and structural breaks. Journal: North American Actuarial Journal Pages: 600-622 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1466713 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1466713 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:600-622 Template-Type: ReDIF-Article 1.0 Author-Name: Moshe A. Milevsky Author-X-Name-First: Moshe A. Author-X-Name-Last: Milevsky Author-Name: Huaxiong Huang Author-X-Name-First: Huaxiong Author-X-Name-Last: Huang Title: The Utility Value of Longevity Risk Pooling: Analytic Insights Abstract: The consensus among researchers is that (some) longevity risk pooling is the optimal strategy for drawing down wealth in retirement, and a robust literature has developed around its measurement via annuity equivalent wealth. However, most of the published work is conducted numerically, and authors usually report only a handful of limited values. In this article we derive closed-form expressions for the value of longevity risk pooling with fixed life annuities under constant relative risk aversion preferences. We show, for example, that this value converges to e−1≈65% when the interest rate happens to be the inverse of life expectancy, remaining lifetimes are exponentially distributed, and utility is logarithmic. In general the various formula we derive match previously published numerical results when properly calibrated to discrete time and tables. More importantly, we focus attention on the incremental utility from annuitization when the retiree is already endowed with preexisting pension income such as Social Security benefits. Indeed, because of the difficulty in working with the so-called wealth depletion time in lifecycle models, we believe this is an area that hasn’t received proper attention in the literature. Overall, our article offers an assortment of tools to help explain the value of longevity risk pooling. Journal: North American Actuarial Journal Pages: 574-590 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1467271 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1467271 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:574-590 Template-Type: ReDIF-Article 1.0 Author-Name: Colin M. Ramsay Author-X-Name-First: Colin M. Author-X-Name-Last: Ramsay Author-Name: Victor I. Oguledo Author-X-Name-First: Victor I. Author-X-Name-Last: Oguledo Title: The Annuity Puzzle and an Outline of Its Solution Abstract: In his seminal 1965 paper, Yaari showed that, assuming actuarially fair annuity prices, uncertain lifetimes, and no bequest motives, utility-maximizing retirees should annuitize all of their wealth on retirement. Nevertheless, the markets for individual immediate life annuities in the United States, the United Kingdom, and several other developed countries have been small relative to other financial investment outlets competing for retirement savings. Researchers have found this situation puzzling, hence the so-called “annuity puzzle.” There are many possible explanations for the annuity puzzle, including “rational” explanations such as adverse selection, bequest motives, and incomplete markets; and “behaviorial” explanations, such as mental accounting, cumulative prospect theory, and mortality salience. We review the literature on the various plausible explanations given for the existence of the annuity puzzle, suggest ways of stimulating the demand for annuities, and suggest a few of the ingredients needed for further development of hybrid annuity products that may provide a solution to the puzzle. Journal: North American Actuarial Journal Pages: 623-645 Issue: 4 Volume: 22 Year: 2018 Month: 10 X-DOI: 10.1080/10920277.2018.1470936 File-URL: http://hdl.handle.net/10.1080/10920277.2018.1470936 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:22:y:2018:i:4:p:623-645 Template-Type: ReDIF-Article 1.0 Author-Name: Milton Boyd Author-X-Name-First: Milton Author-X-Name-Last: Boyd Author-Name: Brock Porth Author-X-Name-First: Brock Author-X-Name-Last: Porth Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Author-Name: Ken Seng Tan Author-X-Name-First: Ken Author-X-Name-Last: Seng Tan Author-Name: Shuo Wang Author-X-Name-First: Shuo Author-X-Name-Last: Wang Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Title: The Design of Weather Index Insurance Using Principal Component Regression and Partial Least Squares Regression: The Case of Forage Crops Abstract: Weather index insurance is a relatively new alternative to traditional agricultural insurance such as individual yield-based crop insurance. It is still mostly at the experimental stage, rather than in widespread use like traditional crop insurance. A major challenge for weather insurance is basis risk, where the loss estimated by the index differs from the actual loss, and this is generally believed to be the main limitation in the use of weather index insurance for crops. Variable basis risk is an important type of basis risk that occurs when there are incorrect variables or missing variables for the design of the weather index. In agriculture, there is a relatively small sample size of yields, and therefore, as the number of considered weather variables increases, the problems of limited degrees of freedom for predictive models must be overcome. The objective of this article is to demonstrate two possible approaches that could be used to construct a multivariable weather index to reduce variable basis risk. Forage insurance is used as an example, and a main focus of the research is on reducing the dimensionality of the predictive model and resolving the problem of multicollinearity among weather variables. The research uses daily weather information and county-level forage yield data from Ontario, Canada. Two multivariable indices are developed based on principal component regression (PCR) and partial least squares regression (PLSR) methods, and they are evaluated against a single-variable benchmark index based on cumulative precipitation (SVCP) using several basis risk metrics. The results show that both the PCR and PLSR models are superior compared to the single-variable weather index based on cumulative rainfall (SVCR) index and can be used to achieve the objective of reducing the dimensionality of the weather variable matrix and addressing the issue of multicollinearity. Though the PLSR indices perform better than the PCR and SVCR indices in terms of average value of basis risk (E(BRLoss)),(rom) the PCR method produces a smaller percentage of mismatch, suggesting that the PCR method may be superior in correctly detecting when the insurance payment should be triggered. The methods demonstrated in this article will assist in the development of weather index–based crop insurance. Journal: North American Actuarial Journal Pages: 355-369 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1669055 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1669055 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:355-369 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Eling Author-X-Name-First: Martin Author-X-Name-Last: Eling Author-Name: Werner Schnell Author-X-Name-First: Werner Author-X-Name-Last: Schnell Title: Capital Requirements for Cyber Risk and Cyber Risk Insurance: An Analysis of Solvency II, the U.S. Risk-Based Capital Standards, and the Swiss Solvency Test Abstract: Cyber risk is becoming more significant for insurance companies in both underwriting and operational risk terms, but the characteristics of cyber risk are still not yet well understood. We contribute to the literature by analyzing the role of cyber risk in insurance regulation frameworks. The aggregated cyber risk exposure of an insurer is estimated by fitting different marginal distributions and dependence models to historical cyber losses. This aggregated cyber exposure allows us to derive the insurer’s survival probability and compare it with the goals of regulatory frameworks, such as the U.S. Risk Based Capital (RBC) or Solvency II (SII). Our findings indicate that regulatory models underestimate the potential risks associated with cyber threats. This is especially true for small cyber insurance portfolios, which are predominant in practice today. Regulatory models should be adapted to account for the heavy tails and dependence structure specific to cyber risks, instead of assuming “one size fits all.” Journal: North American Actuarial Journal Pages: 370-392 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1641416 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1641416 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:370-392 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Hatzopoulos Author-X-Name-First: Peter Author-X-Name-Last: Hatzopoulos Author-Name: Aliki Sagianou Author-X-Name-First: Aliki Author-X-Name-Last: Sagianou Title: Introducing and Evaluating a New Multiple-Component Stochastic Mortality Model Abstract: This work introduces and evaluates a new multiple-component stochastic mortality model. Our proposal is based on a parameter estimation methodology that aims to reveal significant and distinct age clusters by identifying the optimal number of incorporated period and cohort effects. Our methodology adopts sparse principal component analysis and generalized linear models (GLMs), first introduced in Hatzopoulos and Haberman (2011), and it incorporates several novelties. Precisely, our approach is driven by the unexplained variance ratio (UVR) metric to maximize the captured variance of the mortality data and to regulate the sparsity of the model with the aim of acquiring distinct and significant stochastic components. In this way, our model gains a highly informative structure in an efficient way, and it is able to designate an identified mortality trend to a unique age cluster. We also provide an extensive experimental testbed to evaluate the efficiency of the proposed model in terms of fitting and forecasting performance over several datasets (Greece, England and Wales, France, and Japan), and we compare our results to those of well-known mortality models (Lee-Carter, Renshaw-Haberman, Currie, and Plat). Our model is able to achieve high scores over diverse qualitative and quantitative evaluation metrics and outperforms the rest of the models in the majority of the experiments. Our results show the beneficial characteristics of the proposed model and come into agreement with well-established findings in the mortality literature. Journal: North American Actuarial Journal Pages: 393-445 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1658606 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1658606 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:393-445 Template-Type: ReDIF-Article 1.0 Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Title: The Affordability of the Individual Markets in the Affordable Care Act: Analyses of Premium Increases and Cost Reductions from an Expanded Cross-Subsidization Perspective Abstract: In response to the significant premium increases and the “death spiral” concern, this research examines the stability and affordability of the ACA individual markets by quantifying appropriate premium increases in expanded cross-subsidization groups and determining cost reduction potentials. The results indicate that the required premium increases of the Marketplace insurers are definitely affordable when spreading among the enrollees in expanded cross-subsidization groups. Furthermore, premium increases or government subsidies are actually unnecessary if conservative cost reductions are achieved through efficiency improvement. This research suggests that premium increases and cost reductions be implemented through a subsidized reinsurance program or an individual market guaranty fund, financed by shared assessments from customers, providers, and insurers, or government subsidies. The estimated premium increases and cost reductions of this research provide important targets for financing assessments and government subsidies. Journal: North American Actuarial Journal Pages: 446-462 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1664914 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1664914 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:446-462 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Le Courtois Author-X-Name-First: Olivier Author-X-Name-Last: Le Courtois Author-Name: Jacques Lévy-Véhel Author-X-Name-First: Jacques Author-X-Name-Last: Lévy-Véhel Author-Name: Christian Walter Author-X-Name-First: Christian Author-X-Name-Last: Walter Title: Regulation Risk Abstract: Market risk regulations adopted in response to recent crises aim to reduce financial risks. Nevertheless, a large number of practitioners feel that even, if these rules seem to succeed in lowering volatility, they appear to rigidify the financial structure of the economic system and tend to increase the probability of large jumps: prudential rules seem to produce an unexpected effect, the swap between volatility risk and jump risk. The attempt at reduction in volatility is accompanied by an increase in the intensity of jumps. The new regulations seem create a new risk. This article discusses this idea in three ways. First, we introduce a conventionalist framework to shed some light on this unexpected effect. Second, we precisely define volatility risk and the intensity of jumps to document the risk swap effect by analyzing a daily time series of the S&P 500. Third, we propose a model that allows one to appreciate a practical consequence of this swap on the risk measures. We conclude by challenging the main objective of regulation: we argue that concentrating on reducing volatility can create a new type of risk that increases the potential losses, which we term regulation risk. Journal: North American Actuarial Journal Pages: 463-474 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1679189 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1679189 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:463-474 Template-Type: ReDIF-Article 1.0 Author-Name: Hossein Nadeb Author-X-Name-First: Hossein Author-X-Name-Last: Nadeb Author-Name: Hamzeh Torabi Author-X-Name-First: Hamzeh Author-X-Name-Last: Torabi Author-Name: Ali Dolati Author-X-Name-First: Ali Author-X-Name-Last: Dolati Title: Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model Abstract: Let Xλ1,…,Xλn be independent and non-negative random variables belong to the transmuted-G model and let Yi=IpiXλi,i=1,…,n, where Ip1,…,Ipn are independent Bernoulli random variables independent of Xλis, with E[Ipi]=pi,i=1,…,n. In actuarial sciences, Yi corresponds to the claim amount in a portfolio of risks. In this article, we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of the usual stochastic order, hazard rate order, and dispersive order, when the variables in one set have the parameters λ1,…,λn and the variables in the other set have the parameters λ1*,…,λn*. For illustration we apply the results to transmuted exponential and the transmuted Weibull models. Journal: North American Actuarial Journal Pages: 475-487 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1671203 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1671203 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:475-487 Template-Type: ReDIF-Article 1.0 Author-Name: Kenneth W. Faig Author-X-Name-First: Kenneth W. Author-X-Name-Last: Faig Title: Discussion on “Manual and Automated Procedures for Compiling a Very Large Sample of Centenarian Pedigrees,” by Giacomo Nebbia, Lisa Nussbaum, Annie Helmkamp, Stacy Anderson, Thomas Perls, and Paola Sebastiani, Volume 22(4) Journal: North American Actuarial Journal Pages: 488-490 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1625790 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1625790 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:488-490 Template-Type: ReDIF-Article 1.0 Author-Name: Hans U. Gerber Author-X-Name-First: Hans U. Author-X-Name-Last: Gerber Author-Name: Elias S. W. Shiu Author-X-Name-First: Elias S. W. Author-X-Name-Last: Shiu Title: Discussion on “A General Semi-Markov Model for Coupled Lifetimes,” by Min Ji and Rui Zhou, Volume 23(1) Journal: North American Actuarial Journal Pages: 491-494 Issue: 3 Volume: 24 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2019.1627222 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1627222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:491-494 Template-Type: ReDIF-Article 1.0 Author-Name: Raoufeh Asghari Author-X-Name-First: Raoufeh Author-X-Name-Last: Asghari Author-Name: Amin Hassan Zadeh Author-X-Name-First: Amin Author-X-Name-Last: Hassan Zadeh Title: Mortality Modeling of Skin Cancer Patients with Actuarial Applications Abstract: In this article, the Markovian aging process is used to model mortality of patients with skin cancer. The time until death is assumed to have a phase-type distribution (which is defined in a Markov chain environment) with interpretable parameters. The underlying continuous-time Markov chain has one absorbing state (death) and nx +1 (x is the age when the patient is diagnosed with cancer) transient states. Each transient state represents a physiological age, and aging is a transition from one physiological age to the next until the process reaches its end. The transition can occur from any other state to the absorbing state. For patients with skin cancer in the United States, we estimate unknown parameters related to the aging process that can be useful for comparing the physiological aging processes of patients with cancer and healthy people. For different age intervals, we estimate physiological age parameters for both males and females. The index of conditional expected physiological age of the patients with skin cancer at given ages is calculated and compared with the total U.S. population. By using bootstrap techniques, confidence bands and confidence intervals are constructed for the estimated survival curves and aging process parameters, respectively. The fitting results have been used for pricing substandard annuities. Journal: North American Actuarial Journal Pages: 495-511 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2019.1670070 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1670070 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:495-511 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Size-Biased Risk Measures of Compound Sums Abstract: The size-biased, or length-biased transform is known to be particularly useful in insurance risk measurement. The case of continuous losses has been extensively considered in the actuarial literature. Given their importance in insurance studies, this article concentrates on compound sums. The zero-augmented distributions that naturally appear in the individual model of risk theory are obtained as particular cases when the claim frequency distribution is concentrated on {0, 1}. The general results derived in this article help actuaries to understand how risk measurement proceeds because the formulas make explicit the loadings corresponding to each source of randomness. Some simple and explicit expressions are obtained when losses are modeled by independent compound Poisson sums and compound mixed Poisson sums, including the compound negative binomial sums. Extensions to correlated risks are briefly discussed in the concluding section. Journal: North American Actuarial Journal Pages: 512-532 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2019.1676787 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1676787 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:512-532 Template-Type: ReDIF-Article 1.0 Author-Name: Jie Wen Author-X-Name-First: Jie Author-X-Name-Last: Wen Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Author-Name: Andrew J. G. Cairns Author-X-Name-First: Andrew J. G. Author-X-Name-Last: Cairns Title: Trends in Canadian Mortality by Pension Level: Evidence from the CPP and QPP Abstract: This article looks at the mortality of Canadian pensioners subdivided by pension level using data from the Canada Pension Plan (CPP) and Québec Pension Plan (QPP). Differing pension levels (11 groups) are found to give rise to significant levels of mortality inequality at age 65, with a declining inequality gap as cohorts get older. We also find that levels of inequality have increased slightly over time, and that the QPP pensioners exhibit greater levels of inequality than CPP. Additionally, we find strong, but indirect, evidence among the lowest pension groups for a healthy immigrant effect.We fit a range of multipopulation stochastic mortality models to the CPP and QPP data and find that the common age effect model satisfies a range of quantitative and qualitative criteria. The model allows us to distill further detail from the underlying mortality data as well as provide a coherent basis for forecasting mortality and assessing uncertainty in these forecasts.Lastly, we use clustering methods to consider how significant the differences are between the 11 groups. Journal: North American Actuarial Journal Pages: 533-561 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2019.1679190 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1679190 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:533-561 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: E-Cigarettes: A Hazard or a Help? Abstract: A global debate has arisen regarding the relative benefits and harm resulting from the use of electronic cigarettes (“e-cigarettes”). In some countries, such as the United Kingdom, the use of e-cigarettes (“vaping”) has been shown to help reduce addiction to combustible tobacco cigarette (“smoking”), which represents the leading preventable health hazard in many countries. In contrast, in other countries, such as the United States, e-cigarettes, which have attracted many adolescents and young adults who would not otherwise have started to smoke, represent an alternative delivery vehicle for nicotine or cannabis (marijuana) by expanding their markets, reducing nicotine cessation rates by means of a more convenient, healthier, and less offensive product. Although considered less harmful health-wise than smoking, the expected net effect of vaping remains controversial, as sufficient experience has not yet been accumulated to confirm the health impacts, especially over the long term. Nevertheless, viewed by themselves, e-cigarettes do represent a health hazard, with growing information regarding their adverse effects. The stakes of this debate are high—for individuals, society and the e-cigarette, tobacco, insurance, and health care industries. After highlighting the current use of e-cigarettes by adults and adolescents, this article summarizes current issues associated with e-cigarettes, highlighting their health effects; nicotine and addiction; initiation; smoking cessation and harm reduction; gateway to smoking; modifications; flavorings; secondhand aerosol; and new product innovations. It discusses the sources of disagreements and reactions from regulators and life insurers. In addition, the modeling, estimates, and uncertainties associated with mortality resulting from vaping are addressed. For life and health insurance, actuaries are assessing whether to treat e-cigarette users in a manner similar to those who smoke combustible tobacco cigarettes. Journal: North American Actuarial Journal Pages: 562-592 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2019.1683040 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1683040 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:562-592 Template-Type: ReDIF-Article 1.0 Author-Name: J. Bradley Karl Author-X-Name-First: J. Bradley Author-X-Name-Last: Karl Author-Name: Charles Nyce Author-X-Name-First: Charles Author-X-Name-Last: Nyce Title: The Effect of Distracted Driving Laws on Automobile Liability Insurance Claims Abstract: We examine whether laws designed to reduce distracted driving have consequences for the automobile liability insurance market. Our research is motivated by prior studies that suggest distracted driving laws lead to improvements in traffic safety. Following these studies, we propose that distracted driving laws should also lead to reductions in the frequency and cost of injury liability insurance claims. Consistent with this expectation, we provide evidence that cellphone bans lead to approximately 3,400 fewer injury liability insurance claims, on average, in any given state enacting a ban. Our analysis also suggests that cellphone bans lead to reductions in injury liability loss costs, and we estimate the total statewide savings to the insurance industry, on average, is approximately $32 million per year in any given state enacting a ban. Additional analysis that further considers other types of distracted driving laws confirms that laws designed to limit distracted driving lead to substantial reductions in the frequency and cost of injury liability insurance claims. Finally, we also present analysis that suggests the reduction in claims frequency and injury liability loss costs attributable to distracted driving laws leads to statewide automobile liability insurance premium savings of approximately 4.7%. Journal: North American Actuarial Journal Pages: 593-610 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2019.1683041 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1683041 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:593-610 Template-Type: ReDIF-Article 1.0 Author-Name: Zhuoli Jin Author-X-Name-First: Zhuoli Author-X-Name-Last: Jin Author-Name: Robert J. Erhardt Author-X-Name-First: Robert J. Author-X-Name-Last: Erhardt Title: Incorporating Climate Change Projections into Risk Measures of Index-Based Insurance Abstract: We use regional climate model projections to quantify long-term projected changes to risk measures for an example set of temperature index–based insurance products in California. This region is a major agricultural producer for the United States and the world. The climate model projections are an ensemble of six regional climate model runs obtained from the North American Regional Climate Change Assessment Program. Hindcasts for the period of 1971–2000 are compared to historical observed temperature data for bias and variance corrections. Adjusted future model projections are used to estimate distributions of cooling degree days for 2041–2070, which are then used to estimate risk measures for index-based insurance products to demonstrate the scale of changes that climate models project through mid-century in actuarial terms. More broadly, this article provides an illustration of the use of climate data products to explore actuarial risks. Journal: North American Actuarial Journal Pages: 611-625 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2019.1690525 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1690525 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:611-625 Template-Type: ReDIF-Article 1.0 Author-Name: Patricia H. Born Author-X-Name-First: Patricia H. Author-X-Name-Last: Born Author-Name: Evan M. Eastman Author-X-Name-First: Evan M. Author-X-Name-Last: Eastman Author-Name: W. Kip Viscusi Author-X-Name-First: W. Kip Author-X-Name-Last: Viscusi Title: Reducing Medical Malpractice Loss Reserve Volatility Through Tort Reform Abstract: This study examines how tort reform affects uncertainty in insurance markets by testing whether noneconomic damage caps influence reserving volatility for medical malpractice insurers. Using a panel of insurers from 1986 to 2009, we estimate the determinants of loss reserve error volatility and focus on how this volatility is influenced by the percent of premiums an insurer writes that are subject to noneconomic damage caps. We find empirical evidence that tort reform reduces reserve volatility over the subsequent 3- and 5-year periods, consistent with tort reform improving insurers’ loss forecasting ability. Our findings address outcomes of tort reform that are prominent concerns of legislators, regulators, and policyholders. This article contributes both to the literature examining the insurance market effects of tort reform and to the literature examining loss reserving practices. Journal: North American Actuarial Journal Pages: 626-646 Issue: 4 Volume: 24 Year: 2020 Month: 10 X-DOI: 10.1080/10920277.2020.1733616 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1733616 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:24:y:2020:i:4:p:626-646 Template-Type: ReDIF-Article 1.0 Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Richard MacMinn Author-X-Name-First: Richard Author-X-Name-Last: MacMinn Title: Longevity Risk and Capital Markets: The 2016–2017 Update Journal: North American Actuarial Journal Pages: S1-S6 Issue: S1 Volume: 25 Year: 2020 Month: 12 X-DOI: 10.1080/10920277.2019.1652101 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1652101 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:S1:p:S1-S6 Template-Type: ReDIF-Article 1.0 Author-Name: Amy Kessler Author-X-Name-First: Amy Author-X-Name-Last: Kessler Title: New Solutions to an Age-Old Problem: Innovative Strategies for Managing Pension and Longevity Risk Abstract: The recent wave of innovation in the pension and longevity risk transfer market is barely a decade old, but more than U.S. $470 billion in global transaction activity has taken place, mainly in the United Kingdom, the United States, Canada, and the Netherlands. The main deals have been buy-outs, buy-ins, and longevity swaps for pension schemes. Similar derisking solutions have spread to the market for insured annuities. But transactions must be simplified, standardized, and made available to all pension schemes, regardless of size. They must also cover younger deferred scheme participants, as well as those in collective schemes where intergenerational risks are important. New investors must be brought in, and one way of doing this is via sidecars. Capital relief is important in reducing the costs of insurance-based solutions, such as those involving tail-risk protection; regulators need to become more comfortable with such deals. Journal: North American Actuarial Journal Pages: S7-S24 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1672566 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1672566 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S7-S24 Template-Type: ReDIF-Article 1.0 Author-Name: Nicholas Bugler Author-X-Name-First: Nicholas Author-X-Name-Last: Bugler Author-Name: Kirsty Maclean Author-X-Name-First: Kirsty Author-X-Name-Last: Maclean Author-Name: Vladimir Nicenko Author-X-Name-First: Vladimir Author-X-Name-Last: Nicenko Author-Name: Patrick Tedesco Author-X-Name-First: Patrick Author-X-Name-Last: Tedesco Title: Reinsurance Sidecars: The Next Stage in the Development of the Longevity Risk Transfer Market Abstract: The longevity risk transfer market in Europe and North America remains in its infancy despite rapid growth in recent years, and further qualitative progress is needed to develop a commoditized market. Reinsurance sidecars, which are commonly used in the property and casualty market in the United States, have enormous potential to play an important role in such development. Transaction structures involving reinsurance sidecars can be adapted to benefit cedants and sponsoring reinsurers and also to attract a broader spectrum of investors and participants by reducing the long-tail risk inherent in longevity risk transfer. While several transaction structures are possible, each would fundamentally provide additional capital to support transactions in a form that is not subject to a requirement to hold a regulatory solvency capital buffer, thereby enabling sponsoring reinsurers to offer keener pricing to cedants. As a result, a European Union-based cedant could gain considerable capital benefits by reinsuring longevity risk, market risk or both to a reinsurance sidecar. Journal: North American Actuarial Journal Pages: S25-S39 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1673183 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1673183 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S25-S39 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel H. Cox Author-X-Name-First: Samuel H. Author-X-Name-Last: Cox Author-Name: Yijia Lin Author-X-Name-First: Yijia Author-X-Name-Last: Lin Author-Name: Sheen Liu Author-X-Name-First: Sheen Author-X-Name-Last: Liu Title: Optimal Longevity Risk Transfer and Investment Strategies Abstract: Given the rising cost of maintaining defined benefit pensions, there has been a surge of activities in recent years by defined benefit plan sponsors to transfer their pension risk through strategies such as buy-ins and buy-outs. As buy-in and buy-out transaction pipelines grow, insurers actively participating in the buy-in and buy-out markets are exposed to significant longevity risk embedded in pension schemes. In this article, we investigate how to maximize a bulk annuity insurer’s value with reinsurance and/or longevity securities, subject to constraints that control longevity and investment risks as well as an overall risk. We apply duality and the martingale approach to derive an optimal longevity risk transfer strategy. Our results show that longevity risk transfer interacts with an insurer’s investment decision for value maximization. Our analysis also highlights the interdependence of different longevity risk management tools to achieve an overall risk target. Journal: North American Actuarial Journal Pages: S40-S65 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1692617 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1692617 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S40-S65 Template-Type: ReDIF-Article 1.0 Author-Name: Kenneth Q. Zhou Author-X-Name-First: Kenneth Q. Author-X-Name-Last: Zhou Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Title: Longevity Greeks: What Do Insurers and Capital Market Investors Need to Know? Abstract: Recently, it has been argued that capital markets may share some of the overwhelming longevity risk exposures borne by the pension and life insurance industries. The transfer of risk can be accomplished by trading standardized derivatives such as q-forwards that are linked to published mortality indexes. To strategize such trades, one may utilize longevity Greeks, which are analogous to equity Greeks that have been used extensively in managing stock price risk. In this article, we first derive three important longevity Greeks—delta, gamma, and vega—on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility. We then study the properties of each longevity Greek and estimate the levels of effectiveness that different longevity Greek hedges can possibly achieve. The results reveal several interesting facts; for example, in a delta–vega hedge formed by q-forwards, the choice of reference ages does not materially affect hedge effectiveness, but the choice of times to maturity does. These facts may aid insurers to better formulate their hedge portfolios and issuers of mortality-linked securities to determine what security structures are more likely to attract liquidity. Journal: North American Actuarial Journal Pages: S66-S96 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1650283 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1650283 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S66-S96 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew J. G. Cairns Author-X-Name-First: Andrew J. G. Author-X-Name-Last: Cairns Author-Name: Ghali El Boukfaoui Author-X-Name-First: Ghali Author-X-Name-Last: El Boukfaoui Title: Basis Risk in Index-Based Longevity Hedges: A Guide for Longevity Hedgers Abstract: This article considers the assessment of longevity basis risk in the context of a general index-based hedge. We develop a detailed framework for measuring the impact of a hedge on regulatory or economic capital that takes population basis risk explicitly into account. The framework is set up in a way that accommodates a variety of regulatory regimes such as Solvency II as well as local actuarial practice, attempting, therefore, to bridge the gap between academia and practice. This is followed by a detailed analysis of the capital relief resulting from a hedge that uses a call spread as the hedging instrument. We find that the impact of population basis risk on capital relief (expressed in terms of a “haircut” relative to the case with no population basis risk) depends strongly on the exhaustion point of the hedge instrument. In particular, in a Solvency II setting, if the exhaustion point lies well below the 99.5% Value-at-Risk, population basis risk has a negligible impact and the haircut is zero. Journal: North American Actuarial Journal Pages: S97-S118 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1651658 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1651658 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S97-S118 Template-Type: ReDIF-Article 1.0 Author-Name: Ming-Hua Hsieh Author-X-Name-First: Ming-Hua Author-X-Name-Last: Hsieh Author-Name: Chenghsien Jason Tsai Author-X-Name-First: Chenghsien Jason Author-X-Name-Last: Tsai Author-Name: Jennifer L. Wang Author-X-Name-First: Jennifer L. Author-X-Name-Last: Wang Title: Mortality Risk Management Under the Factor Copula Framework—With Applications to Insurance Policy Pools Abstract: Mortality risk is one of the core risks that life insurers undertake. The uncertain future lifetime of each insured represents one risk factor, and the dependence structure among these risk factors determines the aggregate risk of an insurance policy pool. We propose using factor copulas to describe the dependence structure among the future lifetimes of numerous insureds. This differs from Chen, MacMinn, and Sun (2015) in that their focus is on pricing the securities linked to several mortality indexes. To mitigate the systematic mortality risk associated with an insurance pool, the insurer may purchase an asset exposed to similar systematic risk. We thus set up a two-factor copula framework and solve for the optimal investment amount in the asset. In numerical illustrations, we employ real-case data from a life insurer and a life settlement market maker involving hundreds of policies. Journal: North American Actuarial Journal Pages: S119-S131 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1653201 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1653201 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S119-S131 Template-Type: ReDIF-Article 1.0 Author-Name: Sharon S. Yang Author-X-Name-First: Sharon S. Author-X-Name-Last: Yang Author-Name: Yu-Yun Yeh Author-X-Name-First: Yu-Yun Author-X-Name-Last: Yeh Author-Name: Jack C. Yue Author-X-Name-First: Jack C. Author-X-Name-Last: Yue Author-Name: Hong Chih Huang Author-X-Name-First: Hong Chih Author-X-Name-Last: Huang Title: Understanding Patterns of Mortality Homogeneity and Heterogeneity Across Countries and Their Role in Modeling Mortality Dynamics and Hedging Longevity Risk Abstract: Understanding patterns of mortality homogeneity and heterogeneity across countries can assist in modeling mortality dynamics and in hedging longevity risk. This study proposes a methodology, based on the graduation method, to detect differences in mortality rates across different populations. Using an index ĥ2 based on the partial standard mortality ratio, we measure mortality homogeneity and heterogeneity, then conduct an empirical study across countries with emerging and developed markets. The results of model fitting show that it is inappropriate to use a coherent mortality model for the mortality-heterogeneous populations. In an application, we demonstrate that a reinsurer can utilize information concerning mortality homogeneity/heterogeneity for pooling risk in its books of life insurance and annuity businesses and increase overall hedge effectiveness. The coherent mortality model can help reduce the volatility of the reinsurer’s profit and help the reinsurer diversify its longevity risk. Journal: North American Actuarial Journal Pages: S132-S155 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1662315 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1662315 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S132-S155 Template-Type: ReDIF-Article 1.0 Author-Name: Qiheng Guo Author-X-Name-First: Qiheng Author-X-Name-Last: Guo Author-Name: Daniel Bauer Author-X-Name-First: Daniel Author-X-Name-Last: Bauer Title: Different Shades of Risk: Mortality Trends Implied by Term Insurance Prices Abstract: To infer forward-looking, market-based mortality trends, we estimate a flexible affine stochastic mortality model based on a set of U.S. term life insurance prices using a generalized method of moments approach. We find that neither mortality shocks nor stochasticity in the aggregate trend seem to affect the prices. In contrast, allowing for heterogeneity in the mortality rates across carriers is crucial. We conclude that for life insurance, rather than aggregate mortality risk, the key risks emanate from the composition of the portfolio of policyholders. These findings have consequences for mortality risk management and emphasize important directions for mortality-related actuarial research. Journal: North American Actuarial Journal Pages: S156-S169 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1651656 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1651656 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S156-S169 Template-Type: ReDIF-Article 1.0 Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Author-Name: Andrew J. G. Cairns Author-X-Name-First: Andrew J. G. Author-X-Name-Last: Cairns Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: Hedging Annuity Risks with the Age-Period-Cohort Two-Population Gravity Model Abstract: We consider the effectiveness of an illustrative annuity hedging problem in which a forward annuity predicated on one population is hedged by a position in a forward annuity predicated on another population. Our analysis makes use of the age-period-cohort two-population gravity model that takes account of the observed interdependence between the two populations’ mortality rates; it also considers the implications of parameter uncertainty, individual death or Poisson risk, and interest-rate risk for hedge effectiveness. We consider horizons of up to 20 years. For the most part, our results are robust and indicate strong hedge effectiveness, with estimates of relative risk reduction varying from about 70% in the least effective case to well over 95% in the most effective cases. Journal: North American Actuarial Journal Pages: S170-S181 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1652102 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1652102 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S170-S181 Template-Type: ReDIF-Article 1.0 Author-Name: Ralph Rogalla Author-X-Name-First: Ralph Author-X-Name-Last: Rogalla Title: Optimal Portfolio Choice in Retirement With Participating Life Annuities Abstract: This article derives optimal consumption, investment, and annuitization patterns for retired households that have access to German-style participating payout life annuities (PLAs), allowing for capital market risks as well as idiosyncratic and systematic longevity risks. PLAs provide guaranteed minimum benefits in combination with participation in insurers’ surpluses. Minimum benefits are calculated based on conservative assumptions regarding capital market and mortality developments, while surpluses distributed to annuitants bridge the gap between the insurers’ actual investment and mortality experiences and the projections used in pricing. Through the participation scheme, systematic longevity risk is shared between insurers and annuitants, as unanticipated longevity shocks result in benefit adjustments via the surplus mechanism. We show that the retiree draws substantial utility from access to PLAs, equivalent to 20% of initial wealth in the presence of systematic longevity risk. We also find that stochasticity in mortality rates only has minor impact on the appeal of PLAs to the retiree. Even if the interest rate guarantee is reduced to zero in adverse capital market environments, PLAs prove to provide substantial utility for retirees. Overall, the participating life annuity design produces substantial welfare gains over a no-annuity world, while being an effective setup that helps providers manage long-term risks that are difficult to hedge otherwise, such as systematic longevity risks. Journal: North American Actuarial Journal Pages: S182-S195 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1650284 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1650284 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S182-S195 Template-Type: ReDIF-Article 1.0 Author-Name: Les Mayhew Author-X-Name-First: Les Author-X-Name-Last: Mayhew Author-Name: Ben Rickayzen Author-X-Name-First: Ben Author-X-Name-Last: Rickayzen Author-Name: David Smith Author-X-Name-First: David Author-X-Name-Last: Smith Title: Flexible and Affordable Methods of Paying for Long-Term Care Insurance Abstract: With the expected dramatic increase in the number of older people requiring care, and the tightening of public funding, individuals will be increasingly expected to contribute to, and plan for, their own care in later life. However, history shows us that people are very reluctant to save for their care to the extent that there are no longer any providers of traditional prefunded long-term care insurance products in the United Kingdom to help address this problem. In this article, we consider a a disability-linked annuity that provides benefit payments toward the cost of both domiciliary and residential nursing care. We investigate different ways in which individuals can purchase this product with the goal of minimizing the impact on their living standards, hence making the purchase of the product more palatable. In addition to the traditional methods of purchasing insurance out of income and savings, we show that this product can also be purchased by making use of assets such as residential property. This flexibility would allow individuals to have control over the timing of their payments to fit around their lifestyle, particularly for those with low retirement incomes. It follows that some people will be more attracted to particular payment methods than others, and a framework is presented that segments people according to individual circumstances. A model is developed showing how the annuity works and how premiums are calculated. Journal: North American Actuarial Journal Pages: S196-S214 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1651657 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1651657 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S196-S214 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Hunt Author-X-Name-First: Andrew Author-X-Name-Last: Hunt Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: On the Structure and Classification of Mortality Models Abstract: Recently there has been a huge increase in the use of models that examine the structure of mortality rates across the dimensions of age, period and cohort. This article reviews the major developments in the field, provides a holistic analysis of these models, and examines the models’ similarities and differences. Specifically, the article reviews the models that have been proposed to date, investigates the structure of age/period/cohort mortality models, introduces a classification scheme for existing models, and lists the key principles a model user should consider when constructing a new model in this class. Journal: North American Actuarial Journal Pages: S215-S234 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1649156 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1649156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S215-S234 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Hunt Author-X-Name-First: Andrew Author-X-Name-Last: Hunt Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: A Bayesian Approach to Modeling and Projecting Cohort Effects Abstract: One of the key motivations in the construction of ever more sophisticated mortality models was the realization of the importance of “cohort effects” in the historical data. However, these are often difficult to estimate robustly, due to the identifiability issues present in age/period/cohort mortality models, and exhibit spurious features for the most recent years of birth, for which we have little data. These can cause problems when we project the model into the future. In this study, we show how to ensure that projected mortality rates from the model are independent of the arbitrary identifiability constraints needed to identify the cohort parameters. We then go on to develop a Bayesian approach for projecting the cohort parameters that allows fully for uncertainty in the recent parameters due to the lack of information for these years of birth, which leads to more reasonable projections of mortality rates in future. Journal: North American Actuarial Journal Pages: S235-S254 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1649157 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1649157 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S235-S254 Template-Type: ReDIF-Article 1.0 Author-Name: Alexandre Boumezoued Author-X-Name-First: Alexandre Author-X-Name-Last: Boumezoued Title: Improving HMD Mortality Estimates with HFD Fertility Data Abstract: This article aims to improve mortality estimates using fertility data. Estimating the population exposed to risk, such as in the Human Mortality Database (HMD), can suffer from errors for cohorts born in years in which births fluctuate unevenly over the year. When comparing period and cohort mortality tables, we highlight the presence of anomalies in the period tables in the form of isolated cohort effects. Our investigation of the HMD methodology shows that it assumes a uniform distribution of births that is specific to the period tables, which is likely to lead to an asymmetry with the cohort tables. Building on the “Phantoms Never Die” study of Cairns et al. regarding the construction of a “data quality indicator,” we utilize the Human Fertility Database (HFD), which is the perfect counterpart to the HMD in terms of fertility. The indicator is then used to construct corrected period mortality tables for several countries, which are then analyzed from both historical and prospective points of view. The analysis has implications for the reduction of volatility of mortality improvement rates, the use of cohort parameters in stochastic mortality models, and the improved fit of corrected tables by classical mortality models. Journal: North American Actuarial Journal Pages: S255-S279 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1672567 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1672567 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S255-S279 Template-Type: ReDIF-Article 1.0 Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Author-Name: Richard MacMinn Author-X-Name-First: Richard Author-X-Name-Last: MacMinn Author-Name: Jason Chenghsien Tsai Author-X-Name-First: Jason Chenghsien Author-X-Name-Last: Tsai Author-Name: Jennifer Wang Author-X-Name-First: Jennifer Author-X-Name-Last: Wang Title: Longevity Risk and Capital Markets: The 2017–2018 Update Journal: North American Actuarial Journal Pages: S280-S308 Issue: S1 Volume: 25 Year: 2020 Month: 12 X-DOI: 10.1080/10920277.2019.1644469 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1644469 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:S1:p:S280-S308 Template-Type: ReDIF-Article 1.0 Author-Name: Yanxin Liu Author-X-Name-First: Yanxin Author-X-Name-Last: Liu Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Title: An Efficient Method for Mitigating Longevity Value-at-Risk Abstract: Many of the existing index-based longevity hedging strategies focus on the reduction in variance. However, solvency capital requirements are typically based on the τ-year-ahead Value-at-Risk, with τ = 1 under Solvency II. Optimizing a longevity hedge using variance minimization is particularly inadequate when the cost of hedging is nonzero and mortality improvements are driven by a skewed and/or heavy-tailed distribution. In this article, we contribute a method to formulate a value hedge that aims to minimize the Value-at-Risk of the hedged position over a horizon of τ years. The proposed method works with all stochastic mortality models that can be formulated in a state-space form, even when a non normal distributional assumption is made. We further develop a technique to expedite the evaluation of a value longevity hedge. By utilizing the generic assumption that the innovations in the stochastic processes for the period and cohort effects are not serially correlated, the proposed technique spares us from the need for nested simulations that are generally required when evaluating a value hedge. Journal: North American Actuarial Journal Pages: S309-S340 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1658607 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1658607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S309-S340 Template-Type: ReDIF-Article 1.0 Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Author-Name: Uditha Balasooriya Author-X-Name-First: Uditha Author-X-Name-Last: Balasooriya Author-Name: Kenneth Q. Zhou Author-X-Name-First: Kenneth Q. Author-X-Name-Last: Zhou Title: Constructing Out-of-the-Money Longevity Hedges Using Parametric Mortality Indexes Abstract: Proposed by Chan, Li, and Li, parametric mortality indexes (i.e., indexes created using the time-varying parameters in a suitable stochastic mortality model) can be used to develop tradable mortality-linked derivatives such as K-forwards. Compared to existing indexes such as the Life and Longevity Markets Association’s LifeMetrics, parametric mortality indexes are richer in information content, allowing the market to better concentrate liquidity. In this article, we further study this concept in several aspects. First, we consider options written on parametric mortality indexes. Such options enable hedgers to create out-of-the-money longevity hedges, which, compared to at-the-money-hedges created with q-/K-forwards, may better meet hedgers’ needs for protection against downside risk. Second, using the properties of the time series processes for the parametric mortality indexes, we derive analytical risk-neutral pricing formulas for K-forwards and options. In addition to convenience, the analytical pricing formulas remove the need for computationally intensive nested simulations that are entailed in, for example, the calculation of the hedging instruments’ values when a dynamic hedge is adjusted. Finally, we construct static and dynamic Greek hedging strategies using K-forwards and options, and demonstrate empirically the conditions under which an out-of-the-money hedge is more economically justifiable than an at-the-money one. Journal: North American Actuarial Journal Pages: S341-S372 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1650285 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1650285 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S341-S372 Template-Type: ReDIF-Article 1.0 Author-Name: Richard D. MacMinn Author-X-Name-First: Richard D. Author-X-Name-Last: MacMinn Author-Name: Nan Zhu Author-X-Name-First: Nan Author-X-Name-Last: Zhu Title: Hedging Longevity Risk: Does the Structure of the Financial Instrument Matter? Abstract: Longevity-linked securities can be constructed either as cash flow hedging instruments or as value hedging instruments. This article studies the interaction between the structure of longevity-linked securities and shareholder value. Relying on a strand of literature that investigates corporate risk management decisions made in the interests of shareholders, we present a framework that compares cash flow hedges with value hedges. Both our theoretical model and numerical experiments show that value hedging dominates cash flow hedging in the context of management decisions being made to maximize shareholder value. This finding provides an explanation for the failure of some attempted issues of longevity risk transfer instruments and suggests efficient alternate structures. Journal: North American Actuarial Journal Pages: S373-S384 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1650286 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1650286 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S373-S384 Template-Type: ReDIF-Article 1.0 Author-Name: David McCarthy Author-X-Name-First: David Author-X-Name-Last: McCarthy Author-Name: Po-Lin Wang Author-X-Name-First: Po-Lin Author-X-Name-Last: Wang Title: An Analysis of Period and Cohort Mortality Shocks in International Data Abstract: This article uses Bayesian maximum a posteriori (BMAP) estimation to fit a cohort-based mortality model that applies the Gompertz mortality law to fixed cohorts across different periods (rather than the more usual application to fixed periods across different cohorts). Period effects are then estimated as residuals. In this approach, cohort effects can be viewed as a proxy for causes of death with long latency, which have become relatively more important in recent decades in richer countries. We estimate the model independently using male and female adult population mortality data in 31 countries. We are able to associate historical events with many of the observed period and cohort shocks, most notably the 1918 flu epidemic, and find striking geographical and cultural correlations in the results. We find that after 1960, the variance of period mortality shocks has declined by an average factor of 5 in most of the countries we examine. Over the same period, cohort shocks appear to have become a more important factor causing changes in mortality than period shocks. We also find that period and cohort shocks appear to be driven by different underlying factors. Our results have important implications for stochastic mortality modeling, and may explain why stochastic mortality models that rely largely on period mortality shocks struggle to generate sufficient variation in mortality rates. Our results will also be useful to those who construct reinsurance portfolios, those who issue or trade longevity-linked securities, and those who study the origins of human mortality. Journal: North American Actuarial Journal Pages: S385-S409 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1650287 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1650287 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S385-S409 Template-Type: ReDIF-Article 1.0 Author-Name: Jack C. Yue Author-X-Name-First: Jack C. Author-X-Name-Last: Yue Author-Name: Hsin-Chung Wang Author-X-Name-First: Hsin-Chung Author-X-Name-Last: Wang Author-Name: Tzu-Yu Wang Author-X-Name-First: Tzu-Yu Author-X-Name-Last: Wang Title: Using Graduation to Modify the Estimation of Lee–Carter Model for Small Populations Abstract: Many mortality models, such as the Lee–Carter model, have unsatisfactory estimation in the case of small populations. Increasing population size is a natural choice to stabilize the estimation, if we can find a larger reference population that has a mortality profile similar to that of the small population. Aggregating historical data of the small populations is a fine candidate for the reference population. However, it is often not feasible in practice and we need to rely on other reference populations. In this study, we explore whether graduation methods can be used if the mortality profile of a small population differs from that of the reference population. To explore the appropriate occasion to use graduation methods, we create several mortality scenarios and similarity types between small and reference populations. We propose combining the graduation methods and mortality models, either graduating mortality rates first or applying the mortality model first, and determine whether they can improve the model fit. We use computer simulation to determine whether the proposed approach has better mortality estimation than the Lee–Carter model and the the Li–Lee model. We found that the Li–Lee model always has smaller estimation errors than the Lee–Carter model, and the proposed approach has smaller estimation errors than the Li–Lee model in most cases. Journal: North American Actuarial Journal Pages: S410-S420 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1650288 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1650288 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S410-S420 Template-Type: ReDIF-Article 1.0 Author-Name: Pintao Lyu Author-X-Name-First: Pintao Author-X-Name-Last: Lyu Author-Name: Anja De Waegenaere Author-X-Name-First: Anja Author-X-Name-Last: De Waegenaere Author-Name: Bertrand Melenberg Author-X-Name-First: Bertrand Author-X-Name-Last: Melenberg Title: A Multi-population Approach to Forecasting All-Cause Mortality Using Cause-of-Death Mortality Data Abstract: All-cause mortality is driven by various types of cause-specific mortality. Projecting all-cause mortality based on cause-of-death mortality allows one to understand the drivers of the recent changes in all-cause mortality. However, the existing literature has argued that all-cause mortality projections based on cause-specific mortality experience have a number of serious drawbacks, including the inferior cause-of-death mortality data and the complex dependence structure between causes of death. In this article, we use the recent World Health Organization causes-of-death data to address this issue in a multipopulation context. We construct a new model in the spirit of N. Li and Lee (2005) but in terms of cause-specific mortality. A new two-step beta convergence test is used to capture the cause-specific mortality dynamics between different countries and between different causes. We show that the all-cause mortality estimations produced by the new model perform in the sample similarly to the estimations by the Lee-Carter and Li-Lee all-cause mortality models. However, in contrast to results from earlier studies, we find that the all-cause mortality projections of the new model have better out-of-sample performance in a long forecast horizon. Moreover, for the case of The Netherlands, an approximately 1-year higher remaining life expectancy projection for a 67-year-old Dutch male in a 30-year forecast horizon is obtained by this new model, compared to the all-cause Li-Lee mortality model. Journal: North American Actuarial Journal Pages: S421-S456 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1662316 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1662316 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S421-S456 Template-Type: ReDIF-Article 1.0 Author-Name: Karen C. Su Author-X-Name-First: Karen C. Author-X-Name-Last: Su Author-Name: Jack C. Yue Author-X-Name-First: Jack C. Author-X-Name-Last: Yue Title: A Synthesis Mortality Model for the Elderly Abstract: Mortality improvement has been a common phenomenon since the 20th century, and the human longevity continues to prolong. Postretirement life receives a lot of attention, and modeling mortality rates of the elderly (ages 65 years and beyond) is essential because life expectancy has reached the highest level in history. Mortality models can be divided into two groups, relational and stochastic models, but there is no consensus on which model is better in modeling mortality rates of the elderly. In this study, instead of choosing either a relational or stochastic model, we propose a synthesis model, selecting and modifying appropriate models from both groups, which not only has a satisfactory estimation result but also can be used for mortality projection. We use the data from the United States, the United Kingdom, Japan, and Taiwan (data were from the Human Mortality Database) to evaluate the proposed approach. We found that the proposed model performs well and is a possible choice for modeling mortality rates of the elderly. Journal: North American Actuarial Journal Pages: S457-S481 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1651659 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1651659 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S457-S481 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Hunt Author-X-Name-First: Andrew Author-X-Name-Last: Hunt Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing Abstract: Many users of mortality models are interested in using them to place values on longevity-linked liabilities and securities. Modern regulatory regimes require that the values of liabilities and reserves are consistent with market prices (if available), though the gradual emergence of a traded market in longevity risk needs methods for pricing new types of longevity-linked securities quickly and efficiently. In this study, we develop a new forward mortality framework to enable the efficient pricing of longevity-linked liabilities and securities in a market-consistent fashion. This approach starts from the historical data of the observed mortality rates, i.e., the force of mortality. Building on the dynamics of age/period/cohort models of the observed force of mortality, we develop models of forward mortality rates and then use a change of measure to incorporate whatever market information is available. The resulting forward mortality rates are then used to value a number of different longevity-linked securities, such as q-forwards, s-forwards, and longevity swaps. Journal: North American Actuarial Journal Pages: S482-S507 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1649159 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1649159 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S482-S507 Template-Type: ReDIF-Article 1.0 Author-Name: Andrew Hunt Author-X-Name-First: Andrew Author-X-Name-Last: Hunt Author-Name: David Blake Author-X-Name-First: David Author-X-Name-Last: Blake Title: Forward Mortality Rates in Discrete Time II: Longevity Risk and Hedging Strategies Abstract: Longevity risk has emerged as an important risk in the early 21st century for the providers of pension benefits and annuities. Any changes in the assumptions for future mortality rates can have a major financial impact on the valuation of these liabilities and motivates many of the longevity-linked securities that have been proposed to hedge this risk. Using the framework developed in Hunt and Blake (2020c), we investigate how these assumptions can change over a one-year period and the potential for hedging longevity risk in an illustrative annuity portfolio and find that relatively simple hedging strategies can significantly mitigate longevity risk over a one-year period. Journal: North American Actuarial Journal Pages: S508-S533 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1649160 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1649160 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S508-S533 Template-Type: ReDIF-Article 1.0 Author-Name: Atsuyuki Kogure Author-X-Name-First: Atsuyuki Author-X-Name-Last: Kogure Author-Name: Takahiro Fushimi Author-X-Name-First: Takahiro Author-X-Name-Last: Fushimi Author-Name: Shinichi Kamiya Author-X-Name-First: Shinichi Author-X-Name-Last: Kamiya Title: Mortality Forecasts for Long-Term Care Subpopulations with Longevity Risk: A Bayesian Approach Abstract: This article aims to propose a new Bayesian methodology to forecast mortality rates of long-term care (LTC) subpopulations with longevity risk. A major obstacle to developing such a method is lack of data on the number of deaths in LTC subpopulations, which would prevent us from using conventional mortality models such as the Lee-Carter model. To overcome this difficulty, we propose an extended Lee-Carter model for mortality differential by LTC status that does not require data on the number of deaths in LTC subpopulations. We apply the proposed model to mortality forecasts for subpopulations under the public long-term care system in Japan. Our results show that the proposed method captures the heterogeneity in the mortality rates between the LTC statuses and provides reasonable forecasts. Journal: North American Actuarial Journal Pages: S534-S544 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1653202 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1653202 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S534-S544 Template-Type: ReDIF-Article 1.0 Author-Name: Les Mayhew Author-X-Name-First: Les Author-X-Name-Last: Mayhew Author-Name: David Smith Author-X-Name-First: David Author-X-Name-Last: Smith Title: An Investigation into Inequalities in Adult Lifespan Abstract: People in the United Kingdom are living longer than ever but the gap between the shortest and longest lived appears to be increasing. Based on data from the Human Mortality Database, we measure the differences in age between the first 10% of adult deaths and the top 5% of survivors. We find that in the period from 1879 to 1939 this gap steadily closed. We cite evidence that the reduction in inequalities in age at death was due to significant improvements in the health and condition of the population through better housing, sanitation, mass vaccination, occupational health, clearer air, and other public health improvements that disproportionately improved the lives of the poorest in society relative to the wealthiest. Although life expectancy continued to rise after 1950, the inequality gap remained roughly constant and in recent years has started to widen again—more so for men than for women. A key difference between pre-1939 and now is that deaths are much more likely to be from chronic rather than infectious diseases or environmental causes. Since chronic disease is often attributable to life choices such as smoking and diet, we maintain that the blame for the widening must be laid increasingly at the door of individual lifestyles rather than ambient risks and hazards. Journal: North American Actuarial Journal Pages: S545-S565 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1671874 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1671874 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S545-S565 Template-Type: ReDIF-Article 1.0 Author-Name: Geoffrey T. Sanzenbacher Author-X-Name-First: Geoffrey T. Author-X-Name-Last: Sanzenbacher Author-Name: Anthony Webb Author-X-Name-First: Anthony Author-X-Name-Last: Webb Author-Name: Candace M. Cosgrove Author-X-Name-First: Candace M. Author-X-Name-Last: Cosgrove Author-Name: Natalia Orlova Author-X-Name-First: Natalia Author-X-Name-Last: Orlova Title: Rising Inequality in Life Expectancy by Socioeconomic Status Abstract: Inequality in life expectancy is growing in the United States, but evidence is mixed regarding how much it has grown. Some studies have found that life expectancies have decreased for those with the lowest socioeconomic status (SES). Other studies have found that while inequality is rising, there have been life expectancy gains across the board. A primary difference in these studies is how SES is measured. Some studies use an absolute measure, such as years of school completed, while others use relative measures, such as a person’s ranking of years of school completed compared to others born at the same time. This study uses regression analysis to assign people a relative education ranking and, in doing so, attempts to isolate the changing relationship between SES and mortality from the fact that certain education-based groups, especially high school dropouts, actually have a lower SES level today than in the past. The study finds that when SES is defined in this way—relatively—inequality in mortality by SES is increasing but life expectancies have also increased across SES groups. The study also finds that white women in the bottom of the education distribution have experienced the least improvement of any group and that rectangularization of the mortality distribution has occurred much more in the top of the income distribution than at the bottom. Journal: North American Actuarial Journal Pages: S566-S581 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1676788 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1676788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S566-S581 Template-Type: ReDIF-Article 1.0 Author-Name: Chih-Kai Chang Author-X-Name-First: Chih-Kai Author-X-Name-Last: Chang Author-Name: Jack C. Yue Author-X-Name-First: Jack C. Author-X-Name-Last: Yue Author-Name: Chian-Jing Chen Author-X-Name-First: Chian-Jing Author-X-Name-Last: Chen Author-Name: Yen-Wen Chen Author-X-Name-First: Yen-Wen Author-X-Name-Last: Chen Title: Mortality Differential and Social Insurance: A Case Study in Taiwan Abstract: The mortality differential is important information for planning social insurance programs, such as health insurance and public pensions. It can be used to evaluate whether certain areas need more medical facilities and traffic infrastructure. The ignorance of mortality differentials can result in adverse selection and problems of pricing and liability. In this study, we use mortality models to estimate the mortality differentials of two social pension plans in Taiwan, National Pension Insurance (NPI) and Farmer Health Insurance (FHI), which account for more than one-third of the population of Taiwan (about 9 million). We compare the mortality profiles of the two pension groups in terms of economic status and geographic region. Empirical study leads to several policy implications, such as the feasibility of unifying the FHI and NPI systems, reallocating more premium subsidy according to mortality difference and corresponding annuity cost, and the antiselection effect in suburban areas with lower annuity costs and lower willingness to pay premiums. Journal: North American Actuarial Journal Pages: S582-S592 Issue: S1 Volume: 25 Year: 2021 Month: 2 X-DOI: 10.1080/10920277.2019.1651660 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1651660 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:S1:p:S582-S592 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Author-Name: Linda Golden Author-X-Name-First: Linda Author-X-Name-Last: Golden Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Author-Name: David Young Author-X-Name-First: David Author-X-Name-Last: Young Title: Medicaid Managed Care: Efficiency, Medical Loss Ratio, and Quality of Care Abstract: The recent final rule on Medicaid managed care establishes the minimum medical loss ratio (MLR) requirement for Medicaid managed care and contains several provisions to strengthen delivery and payment reforms and improve efficiency and quality of care. Accordingly, this research examines the quality of Medicaid managed care and the effect of MLR and efficiency. The results show that, medical services efficiency has an insignificant (but negative) effect on the quality of care, which indicates that there may be room to improve medical services efficiency without significantly reducing the quality of care. The MLR does have a significantly positive effect on the aggregate quality ratings, however the magnitude of this effect is very small. This indicates that a minimum MLR requirement of 80% or 85% does not make a large difference on quality ratings. Journal: North American Actuarial Journal Pages: 1-16 Issue: 1 Volume: 25 Year: 2021 Month: 1 X-DOI: 10.1080/10920277.2019.1678044 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1678044 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:1:p:1-16 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: Pengyu Wei Author-X-Name-First: Pengyu Author-X-Name-Last: Wei Title: A Multi-state Model of Functional Disability and Health Status in the Presence of Systematic Trend and Uncertainty Abstract: This article proposes a multi-state model of both functional disability and health status in the presence of systematic trend and uncertainty. We classify each individual observation along two dimensions health status (other than disability) and disability—and use the multi-state latent factor intensity model to estimate the transition rates. The model is then used to calculate (healthy) life expectancy and price a variety of insurance products. We illustrate the importance of various factors and quantify the potential losses from model misspecification. Our results suggest that insurers should pay great attention to health status, trend, and systematic uncertainty in disability/mortality modeling and insurance pricing. We also find that integrating long-term care (LTC) insurance with a life annuity can help to reduce systematic uncertainties. Journal: North American Actuarial Journal Pages: 17-39 Issue: 1 Volume: 25 Year: 2021 Month: 1 X-DOI: 10.1080/10920277.2019.1708755 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1708755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:1:p:17-39 Template-Type: ReDIF-Article 1.0 Author-Name: Lisa Gao Author-X-Name-First: Lisa Author-X-Name-Last: Gao Author-Name: Marjorie A. Rosenberg Author-X-Name-First: Marjorie A. Author-X-Name-Last: Rosenberg Title: Assessing the Causal Impact of Delayed Oral Health Care on Emergency Department Utilization Abstract: This study examines the causal effect of delayed oral health care on increased emergency department visits in the United States. We extend prior research by estimating the effect of delayed or forgone preventive and necessary dental care on emergency department utilization using a longitudinal, nationally representative data set. We incorporate the temporal structure of the data into a two-part model with a predictive component and an inferential component. The first part predicts propensity scores for delayed oral health care and the second stage incorporates the inverse weighted propensity scores in a logistic regression that assesses nationally representative estimates of any emergency department visits. We find a positive causal relationship between delaying oral health care and subsequent emergency department utilization. Our results have implications for actuaries, policymakers, and consumers, because unnecessary use of emergency department services for preventable conditions is a growing public health concern in the United States. Journal: North American Actuarial Journal Pages: 40-52 Issue: 1 Volume: 25 Year: 2021 Month: 1 X-DOI: 10.1080/10920277.2020.1735448 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1735448 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:1:p:40-52 Template-Type: ReDIF-Article 1.0 Author-Name: Brian Hartman Author-X-Name-First: Brian Author-X-Name-Last: Hartman Author-Name: Rebecca Owen Author-X-Name-First: Rebecca Author-X-Name-Last: Owen Author-Name: Zoe Gibbs Author-X-Name-First: Zoe Author-X-Name-Last: Gibbs Title: Predicting High-Cost Health Insurance Members through Boosted Trees and Oversampling: An Application Using the HCCI Database Abstract: Using the Health Care Cost Institute data (approximately 47 million members over seven years), we examine how to best predict which members will be high-cost next year. We find that cost history, age, and prescription drug coverage all predict high costs, with cost history being by far the most predictive. We also compare the predictive accuracy of logistic regression to extreme gradient boosting (XGBoost) and find that the added flexibility of the extreme gradient boosting improves the predictive power. Finally, we show that with extremely unbalanced classes (because high-cost members are so rare), oversampling the minority class provides a better XGBoost predictive model than undersampling the majority class or using the training data as is. Logistic regression performance seems unaffected by the method of sampling. Journal: North American Actuarial Journal Pages: 53-61 Issue: 1 Volume: 25 Year: 2020 Month: 7 X-DOI: 10.1080/10920277.2020.1754242 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1754242 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:1:p:53-61 Template-Type: ReDIF-Article 1.0 Author-Name: Zoe Gibbs Author-X-Name-First: Zoe Author-X-Name-Last: Gibbs Author-Name: Brian Hartman Author-X-Name-First: Brian Author-X-Name-Last: Hartman Title: Using Asymmetric Cost Matrices to Optimize Care Management Interventions Abstract: The majority of health care expenditures are incurred by a small portion of the population. Care management or intervention programs may help reduce medical costs, especially those of extremely high-cost members. For these programs to be effective, however, the insurer must identify and select potential high-cost members to be assigned to an intervention before they incur those costs. Because high medical costs are often connected to an accident or traumatic event that cannot be anticipated, it can be difficult to predict who will be high-cost in the future. In this article, we explore the use of machine learning in predicting high-cost members. Specifically, we use the extreme gradient boosting algorithm to develop risk scores for members based on demographic, medical, and financial histories. To select members for intervention, we develop asymmetric cost matrices that account for potentially unequal savings or losses for assigning interventions to members. We show how these matrices can be reduced to a function of the expected savings per dollar of intervention, which is easily used to optimize the risk score threshold at which members are assigned an intervention. These techniques, which can be tailored to the specific needs of an insurer, may help insurers select the optimal members for intervention programs, reduce overall costs, and improve member health outcomes. Journal: North American Actuarial Journal Pages: 62-72 Issue: 1 Volume: 25 Year: 2020 Month: 8 X-DOI: 10.1080/10920277.2020.1763811 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1763811 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:1:p:62-72 Template-Type: ReDIF-Article 1.0 Author-Name: Boquan Cheng Author-X-Name-First: Boquan Author-X-Name-Last: Cheng Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Author-Name: Xiaoming Liu Author-X-Name-First: Xiaoming Author-X-Name-Last: Liu Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: The Mathematical Mechanism of Biological Aging Abstract: Despite aging being a universal and ever-present biological phenomenon, describing this aging mechanism in accurate mathematical terms—in particular, how to model the aging pattern and quantify the aging rate—has been an unsolved challenge for centuries. In this article, we propose a class of Coxian-type Markovian models that can provide a quantitative description of the well-known aging characteristics—the genetically determined, progressive, and essentially irreversible process. Our model has a unique structure, including a constant transition rate for the aging process, and a functional form for the relationship between aging and death with a shape parameter to capture the biologically deteriorating effect due to aging. The force of moving from one state to another in the Markovian process indicates the intrinsic biological aging force. The associated increasing exiting rate captures the external force of stress due to mortality risk on a living organism. The idea of the article is developed from Lin and Liu's paper, “Markov Aging Process and Phase-type Law of Mortality,” that was published in 2007. A big difference is that, in this article, our model uses a functional form for model parameters, which allows a parsimonious yet flexible representation for various aging patterns. Our proposed mathematical framework can be used to classify the aging pattern and the key parameters of the model can be used to measure and compare how human aging evolves over time and across populations. Journal: North American Actuarial Journal Pages: 73-93 Issue: 1 Volume: 25 Year: 2020 Month: 9 X-DOI: 10.1080/10920277.2020.1775654 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1775654 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:1:p:73-93 Template-Type: ReDIF-Article 1.0 Author-Name: Charles C. Yang Author-X-Name-First: Charles C. Author-X-Name-Last: Yang Title: Health Expenditures and Quality Health Services: The Efficiency Analysis of Differential Risk Structures of Medicare Accountable Care Organizations (ACOs) Abstract: Medicare Accountable Care Organizations (ACOs) represent the nation’s largest initiative of Medicare alternative payment models toward value and health outcomes. The Centers for Medicare & Medicaid Services (CMS) have tested various ACO models with differential risk structures, and have issued a final rule to accelerate the ACOs to assume greater financial risks. In response, this research investigates whether superiority exists among various ACO models and determines their potential cost reductions. The results indicate that in minimizing health expenditures given quality services, or maximizing quality services given health expenditures, one-sided ACOs are more efficient than two-sided ACOs, so it might not be advisable to mandate the transition of ACOs from one-sided to two-sided. This research also shows that Medicare ACOs should be able to reduce expenditures significantly through efficiency improvement, without switching to two-sided tracks. Another finding is that the benchmark expenditures for a significant number of Medicare ACOs are below the efficient expenditures and should be adjusted upward. Journal: North American Actuarial Journal Pages: 94-114 Issue: 1 Volume: 25 Year: 2020 Month: 9 X-DOI: 10.1080/10920277.2020.1793783 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1793783 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:1:p:94-114 Template-Type: ReDIF-Article 1.0 Author-Name: Fanghao Zhong Author-X-Name-First: Fanghao Author-X-Name-Last: Zhong Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Joshua Agterberg Author-X-Name-First: Joshua Author-X-Name-Last: Agterberg Author-Name: Richard Crabb Author-X-Name-First: Richard Author-X-Name-Last: Crabb Title: Social Determinant–Based Profiles of U.S. Adults with the Highest and Lowest Health Expenditures Using Clusters Abstract: Using only social determinants, we employ an unsupervised clustering methodology that can differentiate high and low expenditure individuals. There are three major implications of this work: (1) clustering algorithms can produce meaningful results; (2) clustering on individuals, not specific variables, can produce predictive clusters; and (3) including comorbidities in cluster formation adds information to better separate the highest expenditure cluster profiles. Using nationally representative data, cluster expenditure distributions are wider for the most expensive clusters and smallest for the least expensive clusters. The clusters using comorbidities show larger separation between the highest two clusters and the remaining clusters than clusters developed excluding comorbidities. Though the profiles designed are representative of U.S. adults, the approach can be applied to any insured population to reveal the impact of the profiles on utilization. Clusters formed using the data without comorbidities can profile new insureds to allow prospective management of certain individuals. The same group profiles can be used in multiple studies with different outcomes, such as inpatient or drug expenditures. Journal: North American Actuarial Journal Pages: 115-133 Issue: 1 Volume: 25 Year: 2020 Month: 11 X-DOI: 10.1080/10920277.2020.1814819 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1814819 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2020:i:1:p:115-133 Template-Type: ReDIF-Article 1.0 Author-Name: Roel Henckaerts Author-X-Name-First: Roel Author-X-Name-Last: Henckaerts Author-Name: Marie-Pier Côté Author-X-Name-First: Marie-Pier Author-X-Name-Last: Côté Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Author-Name: Roel Verbelen Author-X-Name-First: Roel Author-X-Name-Last: Verbelen Title: Boosting Insights in Insurance Tariff Plans with Tree-Based Machine Learning Methods Abstract: Pricing actuaries typically operate within the framework of generalized linear models (GLMs). With the upswing of data analytics, our study puts focus on machine learning methods to develop full tariff plans built from both the frequency and severity of claims. We adapt the loss functions used in the algorithms such that the specific characteristics of insurance data are carefully incorporated: highly unbalanced count data with excess zeros and varying exposure on the frequency side combined with scarce but potentially long-tailed data on the severity side. A key requirement is the need for transparent and interpretable pricing models that are easily explainable to all stakeholders. We therefore focus on machine learning with decision trees: Starting from simple regression trees, we work toward more advanced ensembles such as random forests and boosted trees. We show how to choose the optimal tuning parameters for these models in an elaborate cross-validation scheme. In addition, we present visualization tools to obtain insights from the resulting models, and the economic value of these new modeling approaches is evaluated. Boosted trees outperform the classical GLMs, allowing the insurer to form profitable portfolios and to guard against potential adverse risk selection. Journal: North American Actuarial Journal Pages: 255-285 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2020.1745656 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1745656 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:255-285 Template-Type: ReDIF-Article 1.0 Author-Name: Hirbod Assa Author-X-Name-First: Hirbod Author-X-Name-Last: Assa Author-Name: Meng (Simon) Wang Author-X-Name-First: Meng (Simon) Author-X-Name-Last: Wang Title: Price Index Insurances in the Agriculture Markets Abstract: In this article, we introduce price index insurances on agricultural goods. Although these seem similar to derivatives, there are significant differences between price index insurances and derivatives. First, unlike derivatives, there are no entrance barriers for purchasing insurances, making them the risk management tools that are accessible to almost all farmers. Second, since insurances are issued in a certain number for any individual farm, unlike futures, for example, they cannot be used for speculation and are used solely for hedging price risk. Third, unlike forwards, they are heavily regulated and do not default and cause counterparty risk. In addition to all differences (or benefits), such products have just recently been introduced in the agricultural insurance market. In this article, we investigate if there could have been a financially viable market where these products are traded. More precisely, we investigate whether an insurance company can design a portfolio of optimal contracts that gives a higher Sharpe ratio than the financial market index prices (here, FTSE 100 and other three major indexes). To reach the article’s objective, we take three steps, in considering theoretical, practical, and corporation standpoints. In the first step, we show what an optimal contract would look like from the demand side in a theoretical setup and we obtain the optimal contract from the farmers' standpoint. In the second step, by adopting a more practical approach in meeting the Key Performance Indicators requirements set by the market participants (both demand and supply side), we find the optimal policies specifications from the first step, in the market equilibrium. This step also helps to determine some unobservable market parameters like volatility. Finally, by adopting a corporation standpoint we bring our model to the U.K. farm index prices and find an optimal portfolio of the products on products from 10 commodities. We demonstrate that investing in such a business is financially viable, as the optimal insurance portfolio produces a Sharpe ratio that outperforms the FTSE 100 and other major market indexes. Journal: North American Actuarial Journal Pages: 286-311 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2020.1755315 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1755315 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:286-311 Template-Type: ReDIF-Article 1.0 Author-Name: Tsz Chai Fung Author-X-Name-First: Tsz Chai Author-X-Name-Last: Fung Author-Name: Andrei L. Badescu Author-X-Name-First: Andrei L. Author-X-Name-Last: Badescu Author-Name: X. Sheldon Lin Author-X-Name-First: X. Sheldon Author-X-Name-Last: Lin Title: A New Class of Severity Regression Models with an Application to IBNR Prediction Abstract: Insurance loss severity data often exhibit heavy-tailed behavior, complex distributional characteristics such as multimodality, and peculiar links between policyholders’ risk profiles and claim amounts. To capture these features, we propose a transformed Gamma logit-weighted mixture of experts (TG-LRMoE) model for severity regression. The model possesses several desirable properties. The TG-LRMoE satisfies the denseness property that warrants its full versatility in capturing any distribution and regression structures. It may effectively extrapolate a wide range of tail behavior. The model is also identifiable, which further ensures its suitability for statistical inference. To make the TG-LRMoE computationally tractable, an expectation conditional maximization (ECM) algorithm with parameter penalization is developed for efficient and robust parameter estimation. The proposed model is applied to fit the severity and reporting delay components of a European automobile insurance dataset. In addition to obtaining excellent goodness of fit, the proposed model is shown to be useful and crucial for adequate prediction of incurred but not reported (IBNR) reserves through out-of-sample testing. Journal: North American Actuarial Journal Pages: 206-231 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2020.1729813 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1729813 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:206-231 Template-Type: ReDIF-Article 1.0 Author-Name: Hong Li Author-X-Name-First: Hong Author-X-Name-Last: Li Author-Name: Yang Lu Author-X-Name-First: Yang Author-X-Name-Last: Lu Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Title: Dynamic Bayesian Ratemaking: A Markov Chain Approximation Approach Abstract: We contribute to the non-life experience ratemaking literature by introducing a computationally efficient approximation algorithm for the Bayesian premium in models with dynamic random effects, where the risk of a policyholder is governed by an individual process of unobserved heterogeneity. Although intuitive and flexible, the biggest challenge of dynamic random effect models is that the resulting Bayesian premium typically lacks tractability. In this article, we propose to approximate the dynamics of the random effects process by a discrete (hidden) Markov chain and replace the intractable Bayesian premium of the original model by that of the approximate Markov chain model, for which concise, closed-form formula are derived. The methodology is general because it does not rely on any parametric distributional assumptions and, in particular, allows for the inclusion of both the cost and the frequency components in pricing. Numerical examples show that the proposed approximation method is highly accurate. Finally, a real data pricing example is used to illustrate the versatility of the approach. Journal: North American Actuarial Journal Pages: 186-205 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2020.1716809 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1716809 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:186-205 Template-Type: ReDIF-Article 1.0 Author-Name: Ning Zhang Author-X-Name-First: Ning Author-X-Name-Last: Zhang Author-Name: Yang-Che Wu Author-X-Name-First: Yang-Che Author-X-Name-Last: Wu Author-Name: Wan-Shiou Yang Author-X-Name-First: Wan-Shiou Author-X-Name-Last: Yang Title: Feasibility of Long-Term Interest Balance among Stakeholders in the Natural Catastrophe Insurance Market Abstract: This study establishes a stakeholder framework in the natural catastrophe insurance market: Insurers charge policyholders the full insurance premium and pay the public catastrophe insurance scheme (PCIS) contributions for the contingent bailout. The government subsidizes policyholders and taxes insurers. Then a series of accounting procedures is developed to illustrate how the stakeholders’ cash flows change. A numerical analysis reveals that both the PCIS and the subsidy policy can achieve long-term self-financing under special tax rates, contribution rates, and subsidy conditions. The results show that the short-term inequity of favoring insurers and policyholders can promote balanced long-term interests for all stakeholders. Journal: North American Actuarial Journal Pages: 163-185 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2019.1705169 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1705169 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:163-185 Template-Type: ReDIF-Article 1.0 Author-Name: Cassandra R. Cole Author-X-Name-First: Cassandra R. Author-X-Name-Last: Cole Author-Name: Stephen G. Fier Author-X-Name-First: Stephen G. Author-X-Name-Last: Fier Title: An Empirical Analysis of Insurer Participation in the U.S. Cyber Insurance Market Abstract: The U.S. property-casualty insurance industry has witnessed substantial growth in the cyber insurance market over the past decade, largely attributable to the proliferation of technology in the business world paired with the greater occurrence of cyber-related loss activity. While cyber insurance plays an increasingly important role both in the insurance industry and in the worldwide economy, relatively little is known about participation and performance in the cyber insurance market. Using a unique panel dataset made available through recent mandatory disclosures, we examine market trends, factors associated with market participation, and firm-specific characteristics related to performance. Among our findings, the results indicate that the cyber insurance market is highly concentrated and that firm-specific characteristics such as size, business mix, reinsurance, and organizational structure tend to impact both participation and the extent of participation in the market. Furthermore, we show that classification as an excess and surplus (E&S) lines insurer and group affiliation are particularly significant drivers of cyber market involvement. Finally, we offer evidence that while cyber insurance is a profitable line of business for market participants, factors such as insurer size, reinsurance use, diversification, group affiliation, organizational structure, and status as an E&S insurer each influence performance in different and important ways. Journal: North American Actuarial Journal Pages: 232-254 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2020.1733615 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1733615 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:232-254 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: José Carlos Araujo-Acuna Author-X-Name-First: José Carlos Author-X-Name-Last: Araujo-Acuna Author-Name: Jan Beirlant Author-X-Name-First: Jan Author-X-Name-Last: Beirlant Title: Fitting Nonstationary Cox Processes: An Application to Fire Insurance Data Abstract: In insurance practice, claims often occur in clusters and their arrivals may depend on various external and time-dependent factors. In this article, we propose a statistical approach for modeling claim arrivals by considering clustered arrivals and non-stationarity simultaneously. To this end, we extend the Cox process methodology with Lévy subordinators presented in Selch and Scherer (2018) relaxing the stationarity of increments assumption. A particular special case of the proposed approach is a dynamic and flexible model of negative binomially distributed claim numbers with trends and seasonal variations of the parameters. For illustration purposes, we fit the model to a fire insurance portfolio and show that it allows the modeling of cluster occurrences in a seasonal pattern while preserving overdispersion, which is frequently observed in claim count data. We illustrate its use in forecasting and Value-at-Risk and expected shortfall computations of the aggregate insurance risk. Finally, we provide a multivariate extension of the model, where simultaneous cluster arrivals in different components are generated by a nonstationary common subordinator. Journal: North American Actuarial Journal Pages: 135-162 Issue: 2 Volume: 25 Year: 2021 Month: 4 X-DOI: 10.1080/10920277.2019.1703752 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1703752 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:2:p:135-162 Template-Type: ReDIF-Article 1.0 Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Title: Reply to Hans U. Gerber and Elias S. W. Shiu on Their Discussion on Our Paper Entitled "Agricultural Insurance Ratemaking: Development of a New Premium Principle" Journal: North American Actuarial Journal Pages: 466-467 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1795554 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1795554 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:466-467 Template-Type: ReDIF-Article 1.0 Author-Name: Julia Eisenberg Author-X-Name-First: Julia Author-X-Name-Last: Eisenberg Author-Name: Zbigniew Palmowski Author-X-Name-First: Zbigniew Author-X-Name-Last: Palmowski Title: Optimal Dividends Paid in a Foreign Currency for a Lévy Insurance Risk Model Abstract: This article considers an optimal dividend distribution problem for an insurance company where the dividends are paid in a foreign currency. In the absence of dividend payments, our risk process follows a spectrally negative Lévy process. We assume that the exchange rate is described by a an exponentially Lévy process, possibly containing the same risk sources like the surplus of the insurance company under consideration. The control mechanism chooses the amount of dividend payments. The objective is to maximize the expected dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. Via the corresponding Hamilton–Jacobi–Bellman equation we find the necessary and sufficient conditions for optimality of a single dividend barrier strategy. A number of numerical examples illustrate the theoretical analysis. Journal: North American Actuarial Journal Pages: 417-437 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1805633 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1805633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:417-437 Template-Type: ReDIF-Article 1.0 Author-Name: Hong Beng Lim Author-X-Name-First: Hong Beng Author-X-Name-Last: Lim Author-Name: Nariankadu D. Shyamalkumar Author-X-Name-First: Nariankadu D. Author-X-Name-Last: Shyamalkumar Title: A Semiparametric Method for Assessing Life Expectancy Evaluations Abstract: In the life settlements industry, life expectancy (LE) providers are firms that conduct health underwriting toward predicting the future mortality of an insured. Multiple stakeholders are interested in evaluating the quality of their assessments. There has been some recent interest in better alternatives to the traditional metric for this quality, the A/E ratio: the ratio of actual to expected number of deaths. One such alternative is the implied difference in life expectancies (IDLE) metric proposed by Bauer et al. Its design largely retains the simplicity of the A/E ratio while being informative, unlike the A/E ratio, throughout the life of a policy block. Even though the IDLE is a significant improvement over the A/E ratio, it turns out that the IDLE is sensitive to departures from a key assumption, which motivates our development of a more robust metric. Our proposed methodology for evaluating the quality of the LE assessments involves using a survival regression model for estimating the mortality distribution of the insureds, with the average deviation of the life assessments from those derived using this model serving as a metric. In particular, we show that utilizing a Cox proportional hazards model with covariates derived from the LE assessments results in a robust yet well-performing alternative to both the A/E ratio and the IDLE. Journal: North American Actuarial Journal Pages: 360-394 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1768409 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1768409 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:360-394 Template-Type: ReDIF-Article 1.0 Author-Name: Kai Liu Author-X-Name-First: Kai Author-X-Name-Last: Liu Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: Real-Time Valuation of Large Variable Annuity Portfolios: A Green Mesh Approach Abstract: The valuation of large variable annuity (VA) portfolios is an important problem of interest, not only because of its practical relevance but also because of its theoretical significance. This is prompted by the phenomenon that many existing sophisticated algorithms are typically efficient at valuing a single VA policy but they are not scalable to valuing large VA portfolios consisting of hundreds of thousands of policies. As a result, this sparks a new research direction exploiting machine learning methods (such as data clustering, nearest neighbor kriging, neural network) on providing more efficient algorithms to estimate the market values and sensitivities of large VA portfolios. The idea underlying these approximation methods is to first determine a set of VA policies that is “representative” of the entire large VA portfolio. Then the values from these representative VA policies are used to estimate the respective values of the entire large VA portfolio. A substantial reduction in computation time is possible because we only need to value the representative set of VA policies, which typically is a much smaller subset of the entire large VA portfolio. Ideally the large VA portfolio valuation method should adequately address issues such as (1) the complexity of the proposed algorithm; (2) the cost of finding representative VA policies; (3) the cost of the initial training set, if any; (4) the cost of estimating the entire large VA portfolio from the representative VA policies; (5) the computer memory constraint; and (6) the portability to other large VA portfolio valuation. Most of the existing large VA portfolio valuation methods do not necessary reflect all of these issues, particularly the property of portability, which ensures that we only need to incur the start-up time once and the same representative VA policies can be recycled to valuing other large portfolios of VA policies. Motivated by their limitations and by exploiting the greater uniformity of the randomized low discrepancy sequence and the Taylor expansion, we show that our proposed method, a green mesh method, addresses all of the above issues. The numerical experiment further highlights its simplicity, efficiency, portability, and, more important, its real-time valuation application. Journal: North American Actuarial Journal Pages: 313-333 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2019.1697707 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1697707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:313-333 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Furman Author-X-Name-First: Edward Author-X-Name-Last: Furman Author-Name: Yisub Kye Author-X-Name-First: Yisub Author-X-Name-Last: Kye Author-Name: Jianxi Su Author-X-Name-First: Jianxi Author-X-Name-Last: Su Title: A Reconciliation of the Top-Down and Bottom-Up Approaches to Risk Capital Allocations: Proportional Allocations Revisited Abstract: In the current reality of prudent risk management, the problem of determining aggregate risk capital in financial entities has been intensively studied. As a result, canonical methods have been developed and even embedded in regulatory accords. Though applauded by some and questioned by others, these methods provide a much desired standard benchmark for everyone. The situation is very different when the aggregate risk capital needs to be allocated to the business units (BUs) of a financial entity. That is, there are overwhelmingly many ways to conduct the allocation exercise, and there is arguably no standard method to do so on the horizon. Two overarching approaches to allocate the aggregate risk capital stand out. These are the top-down allocation (TDA) approach that entails that the allocation exercise be imposed by the corporate center, and the bottom-up allocation (BUA) approach that implies that the allocation of the aggregate risk to BUs is informed by these units. Briefly, the TDA starts with the aggregate risk capital that is then replenished among the BUs according to the views of the center, thus limiting the inputs from the BUs. The BUA does start with the BUs but it is, as a rule, too granular and so may lead to missing the wood for the trees. Irrespective of whether the TDA or the BUA is assumed, it is the proportional contribution of the riskiness of a stand-alone BU to the aggregate riskiness of the financial entity that is of central importance, and it is routinely computed nowadays as the quotient of the allocated risk capital due to the BU of interest and the aggregate risk capital due to the financial entity. For instance, in the simplest case when the mathematical expectation plays the role of the risk measure that generates the allocation rule, the desired proportional contribution is just a quotient of two means. Clearly, in general, this quotient of means does not concur with the mean of the quotient random variable that captures the genuine stochastic proportional contribution of the riskiness of the BU of interest. Inspired by this observation, herein we reenvision the way in which the allocation problem is tackled in the state of the art. As a by-product, we unify the TDA and the BUA into one encompassing approach. Journal: North American Actuarial Journal Pages: 395-416 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1774781 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1774781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:395-416 Template-Type: ReDIF-Article 1.0 Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Lysa Porth Author-X-Name-First: Lysa Author-X-Name-Last: Porth Title: Reply to Abylay Zhexembay on the Discussion on Our Paper Entitled "Agricultural Insurance Ratemaking: Development of a New Premium Principle" Journal: North American Actuarial Journal Pages: 472-472 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1795555 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1795555 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:472-472 Template-Type: ReDIF-Article 1.0 Author-Name: Abylay Zhexembay Author-X-Name-First: Abylay Author-X-Name-Last: Zhexembay Title: Abylay Zhexembay's Discussion on “Agricultural Insurance Ratemaking: Development of a New Premium Principle,” by Wenjun Zhu, Ken Seng Tan, and Lysa Porth, Volume 23(4) Journal: North American Actuarial Journal Pages: 468-471 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1793785 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1793785 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:468-471 Template-Type: ReDIF-Article 1.0 Author-Name: Liqun Diao Author-X-Name-First: Liqun Author-X-Name-Last: Diao Author-Name: Yechao Meng Author-X-Name-First: Yechao Author-X-Name-Last: Meng Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Title: A DSA Algorithm for Mortality Forecasting Abstract: Borrowing information from populations with similar structural mortality patterns and trajectories has been well recognized as an useful strategy to the mortality forecasting of a target population. This article presents a flexible framework for the selection of populations from a given candidate pool to assist a target population in mortality forecasting. The defining feature of the framework is the deletion-substitution-addition (DSA) algorithm, which is entirely data driven and versatile to work with any multiple-population model for mortality prediction. In numerical studies, the framework with an extended augmented common factor model is applied to the Human Mortality Database, and the superiority of the proposed framework is evident in mortality forecasting performance. Journal: North American Actuarial Journal Pages: 438-458 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1806884 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1806884 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:438-458 Template-Type: ReDIF-Article 1.0 Author-Name: Rogemar Mamon Author-X-Name-First: Rogemar Author-X-Name-Last: Mamon Author-Name: Heng Xiong Author-X-Name-First: Heng Author-X-Name-Last: Xiong Author-Name: Yixing Zhao Author-X-Name-First: Yixing Author-X-Name-Last: Zhao Title: The Valuation of a Guaranteed Minimum Maturity Benefit under a Regime-Switching Framework Abstract: Global insurance markets have become more sophisticated in recent times in response to the evolving needs of populations that tend to live longer. Policy holders desire the benefits of longevity/mortality protection while taking advantage of investment growth opportunities in equity markets. As a result, insurers incorporate payment guarantees in new insurance products, known as equity-linked contracts, whose values are dependent on prices of risky assets. A guaranteed minimum maturity benefit (GMMB) is now common in many equity-linked contracts. We develop an integrated pricing framework for a GMMB focusing on segregated fund contracts. More specifically, we construct hidden Markov models (HMMs) for a stock index, interest rate, and mortality rate. The dependence between these risk factors is characterized explicitly. We assume that the stock index follows a Markov-modulated geometric Brownian motion and the interest and mortality rates have Markov-modulated affine dynamics. A series of measure changes is employed to obtain a semi-closed-form solution for the GMMB price. A Fourier transform method is applied to numerically approximate the prices more efficiently. Recursive HMM filtering is used in our model calibration. Numerical investigations in our article demonstrate the accuracy of GMMB prices and an extensive analysis is included to systematically examine how risk factors affect the value of a GMMB. Journal: North American Actuarial Journal Pages: 334-359 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2019.1703753 File-URL: http://hdl.handle.net/10.1080/10920277.2019.1703753 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:334-359 Template-Type: ReDIF-Article 1.0 Author-Name: Hans U. Gerber Author-X-Name-First: Hans U. Author-X-Name-Last: Gerber Author-Name: Elias S. W. Shiu Author-X-Name-First: Elias S. W. Author-X-Name-Last: Shiu Title: Hans U. Gerber and Elias S. W. Shiu’s Discussion on “Agricultural Insurance Ratemaking: Development of a New Premium Principle,” by Wenjun Zhu, Ken Seng Tan, and Lysa Porth, Volume 23(4) Journal: North American Actuarial Journal Pages: 459-465 Issue: 3 Volume: 25 Year: 2021 Month: 7 X-DOI: 10.1080/10920277.2020.1793784 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1793784 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:3:p:459-465 Template-Type: ReDIF-Article 1.0 Author-Name: Thorsten Moenig Author-X-Name-First: Thorsten Author-X-Name-Last: Moenig Author-Name: Nan Zhu Author-X-Name-First: Nan Author-X-Name-Last: Zhu Title: The Economics of a Secondary Market for Variable Annuities Abstract: This article demonstrates that a secondary market for U.S. variable annuity policies may be immediately welfare enhancing to all parties involved: the insurer, the original policyholder, and a third-party investor. Our model reflects relevant market frictions—here, the product’s tax benefits—that produce differing valuation perspectives for the three parties. This allows for policy transfers that benefit all parties simultaneously, including the insurance company, irrespective of the level of control that it exerts over this secondary market. We illustrate our insights first with a theoretical two-period model, followed by an empirically motivated numerical analysis. Our numerical results suggest a best-estimate total welfare gain of 2.6% of the initial investment amount under the optimal secondary market structure. Journal: North American Actuarial Journal Pages: 604-630 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1802598 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1802598 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:604-630 Template-Type: ReDIF-Article 1.0 Author-Name: Todd G. Griffith Author-X-Name-First: Todd G. Author-X-Name-Last: Griffith Author-Name: Andre P. Liebenberg Author-X-Name-First: Andre P. Author-X-Name-Last: Liebenberg Title: The Effect of Incidental Reinsurance Assumption on Insurer Performance Abstract: This article empirically examines the profitability and risk implications of the supply of reinsurance by incidental reinsurers to unaffiliated insurers. For a sample of U.S. property–liability insurers that do not specialize in reinsurance, we find that the decision to assume a nontrivial amount of external reinsurance (from unaffiliated insurers) increases firm risk and decreases firm profitability. However, when we examine internal reinsurance assumption (from affiliated insurers) we find no evidence of a negative performance effect. The fact that the negative performance effect is confined to external reinsurance assumption suggests that asymmetric information is driving the increased risk and decreased profitability. Further analysis shows that reinsurers are able to mitigate the negative impact of information asymmetries by engaging in long-term contracting and by focusing their reinsurance assumption in fewer lines of business. Journal: North American Actuarial Journal Pages: 503-523 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1758152 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1758152 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:503-523 Template-Type: ReDIF-Article 1.0 Author-Name: Sébastien Jessup Author-X-Name-First: Sébastien Author-X-Name-Last: Jessup Author-Name: Jean-Philippe Boucher Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Boucher Author-Name: Mathieu Pigeon Author-X-Name-First: Mathieu Author-X-Name-Last: Pigeon Title: On Fitting Dependent Nonhomogeneous Loss Models to Unearned Premium Risk Abstract: Unearned premium or, more particularly, the risk associated to it, has only recently received regulatory attention. Losses linked to unearned premium, or unearned losses, occur after the evaluation date for policies written before the evaluation date. Given that an inadequate acquisition pattern of premium and approximate modeling of premium liability can lead to an inaccurate reserve around unearned premium risk, an individual nonhomogeneous loss model including cross-coverage dependence is proposed to provide an alternative method of evaluating this risk. Claim occurrence is analyzed in terms of both claim seasonality and multiple coverage frequency. Homogeneous and heterogeneous distributions are fitted to marginals. Copulas are fitted to pairs of coverages using rank-based methods and a tail function. This approach is used on a recent Ontario auto database. Journal: North American Actuarial Journal Pages: 524-542 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1776623 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1776623 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:524-542 Template-Type: ReDIF-Article 1.0 Author-Name: Maochao Xu Author-X-Name-First: Maochao Author-X-Name-Last: Xu Author-Name: Yiying Zhang Author-X-Name-First: Yiying Author-X-Name-Last: Zhang Title: Data Breach CAT Bonds: Modeling and Pricing Abstract: Data breaches cause millions of dollars in financial losses each year. The insurance industry has been exploring the ways to transfer such extreme risk. In this work, we investigate data breach catastrophe (CAT) bonds via developing a multiperiod pricing model. It is found that the nonstationary extreme value model can capture the statistical pattern of the monthly maximum of data breach size very well and, in particular, a positive time trend is discovered. For the financial risks, data-driven time series approaches are proposed to model the complex patterns exhibited by the financial data, which are different from those in the literature. Simulation studies are performed to determine the bond prices and cash flows. Our results show that the data breach CAT bond can be an attractive financial product and an effective instrument for transferring the extreme data breach risk. Journal: North American Actuarial Journal Pages: 543-561 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2021.1886948 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1886948 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:543-561 Template-Type: ReDIF-Article 1.0 Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: Jiandong Ren's Discussion on “Size-Biased Risk Measures of Compound Sums,” by Michel Denuit, January 2020 Journal: North American Actuarial Journal Pages: 639-642 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2021.1914666 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1914666 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:639-642 Template-Type: ReDIF-Article 1.0 Author-Name: Tatjana Miljkovic Author-X-Name-First: Tatjana Author-X-Name-Last: Miljkovic Author-Name: Bettina Grün Author-X-Name-First: Bettina Author-X-Name-Last: Grün Title: Using Model Averaging to Determine Suitable Risk Measure Estimates Abstract: Recent research in loss modeling resulted in a growing number of classes of statistical models as well as additional models being proposed within each class. Empirical results indicate that a range of models within or between model classes perform similarly well, as measured by goodness-of-fit or information criteria, when fitted to the same data set. This leads to model uncertainty and makes model selection a challenging task. This problem is particularly virulent if the resulting risk measures vary greatly between and within the model classes. We propose an approach to estimate risk measures that accounts for model selection uncertainty based on model averaging. We exemplify the application of the approach considering the class of composite models. This application considers 196 different left-truncated composite models previously used in the literature for loss modeling and arrives at point estimates for the risk measures that take model uncertainty into account. A simulation study highlights the benefits of this approach. The data set on Norwegian fire losses is used to illustrate the proposed methodology. Journal: North American Actuarial Journal Pages: 562-579 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2021.1911668 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1911668 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:562-579 Template-Type: ReDIF-Article 1.0 Author-Name: Hong Sun Author-X-Name-First: Hong Author-X-Name-Last: Sun Author-Name: Maochao Xu Author-X-Name-First: Maochao Author-X-Name-Last: Xu Author-Name: Peng Zhao Author-X-Name-First: Peng Author-X-Name-Last: Zhao Title: Modeling Malicious Hacking Data Breach Risks Abstract: Malicious hacking data breaches cause millions of dollars in financial losses each year, and more companies are seeking cyber insurance coverage. The lack of suitable statistical approaches for scoring breach risks is an obstacle in the insurance industry. We propose a novel frequency–severity model to analyze hacking breach risks at the individual company level, which would be valuable for underwriting purposes. We find that breach frequency can be modeled by a hurdle Poisson model, which is different from the negative binomial model used in the literature. The breach severity shows a heavy tail that can be captured by a nonparametric- generalized Pareto distribution model. We further discover a positive nonlinear dependence between frequency and severity, which our model also accommodates. Both the in-sample and out-of-sample studies show that the proposed frequency–severity model that accommodates nonlinear dependence has satisfactory performance and is superior to the other models, including the independence frequency–severity and Tweedie models. Journal: North American Actuarial Journal Pages: 484-502 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1752255 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1752255 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:484-502 Template-Type: ReDIF-Article 1.0 Author-Name: Kwangmin Jung Author-X-Name-First: Kwangmin Author-X-Name-Last: Jung Title: Extreme Data Breach Losses: An Alternative Approach to Estimating Probable Maximum Loss for Data Breach Risk Abstract: This study proposes a measure of the data breach risk’s probable maximum loss, which stands for the worst data breach loss likely to occur, using an alternative approach to estimating the potential loss degree of an extreme event with one of the largest private databases for data breach risk. We determine stationarity, the presence of autoregressive feature, and the Fréchet type of generalized extreme value distribution (GEV) as the best fit for data breach loss maxima series and check robustness of the model with a public dataset. We find that the predicted data breach loss likely to occur in the next five years is substantially larger than the loss estimated by the recent literature with a Pareto model. In particular, the comparison between the estimates from the recent data (after 2014) and those for the old data (before 2014) shows a significant increase with a break in the loss severity. We design a three-layer reinsurance scheme based on the probable maximum loss estimates with public–private partnership. Our findings are important for risk managers, actuaries, and policymakers concerned about the enormous cost of the next extreme cyber event. Journal: North American Actuarial Journal Pages: 580-603 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2021.1919145 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1919145 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:580-603 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Reply to Edward Furman, Yisub Kye, and Jianxi Su on Their Discussion on the Paper Titled “Size-Biased Risk Measures of Compound Sums” Journal: North American Actuarial Journal Pages: 637-638 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1848300 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1848300 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:637-638 Template-Type: ReDIF-Article 1.0 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Author-Name: Ryan Martin Author-X-Name-First: Ryan Author-X-Name-Last: Martin Title: Valid Model-Free Prediction of Future Insurance Claims Abstract: Bias resulting from model misspecification is a concern when predicting insurance claims. Indeed, this bias puts the insurer at risk of making invalid or unreliable predictions. A method that could provide provably valid predictions uniformly across a large class of possible distributions would effectively eliminate the risk of model misspecification bias. Conformal prediction is one such method that can meet this need, and here we tailor that approach to the typical insurance application and show that the predictions are not only valid but also efficient across a wide range of settings. Journal: North American Actuarial Journal Pages: 473-483 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1802599 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1802599 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:473-483 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Reply to Jiandong Ren on Their Discussion on the Paper Titled “Size-Biased Risk Measures of Compound Sums” Journal: North American Actuarial Journal Pages: 643-643 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2021.1925823 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1925823 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:643-643 Template-Type: ReDIF-Article 1.0 Author-Name: Edward Furman Author-X-Name-First: Edward Author-X-Name-Last: Furman Author-Name: Yisub Kye Author-X-Name-First: Yisub Author-X-Name-Last: Kye Author-Name: Jianxi Su Author-X-Name-First: Jianxi Author-X-Name-Last: Su Title: Discussion on “Size-Biased Risk Measures of Compound Sums,” by Michel Denuit, January 2020 Journal: North American Actuarial Journal Pages: 631-636 Issue: 4 Volume: 25 Year: 2021 Month: 11 X-DOI: 10.1080/10920277.2020.1831934 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1831934 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:25:y:2021:i:4:p:631-636 Template-Type: ReDIF-Article 1.0 Author-Name: Yaming Yang Author-X-Name-First: Yaming Author-X-Name-Last: Yang Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: On a Family of Log-Gamma-Generated Archimedean Copulas Abstract: Modeling dependence structure among various risks, especially the measure of tail dependence and the aggregation of risks, is crucial for risk management. In this article, we present an extension to the traditional one-parameter Archimedean copulas by integrating the log-gamma-generated (LGG) margins. This class of novel multivariate distribution can better capture the tail dependence. The distortion effect on the classic one-parameter Archimedean copulas is well exhibited and the analytical expression of the sum of bivariate margins is proposed. The model provides a flexible way to capture tail risks and aggregate portfolio losses. Sufficient conditions for constructing a legitimate d-dimensional LGG Archimedean copula as well as the simulation framework are also proposed. Furthermore, two applications of this model are presented using concrete insurance datasets. Journal: North American Actuarial Journal Pages: 123-142 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1856687 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1856687 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:123-142 Template-Type: ReDIF-Article 1.0 Author-Name: Jing Ai Author-X-Name-First: Jing Author-X-Name-Last: Ai Author-Name: Jennifer Russomanno Author-X-Name-First: Jennifer Author-X-Name-Last: Russomanno Author-Name: Skyla Guigou Author-X-Name-First: Skyla Author-X-Name-Last: Guigou Author-Name: Rachel Allan Author-X-Name-First: Rachel Author-X-Name-Last: Allan Title: A Systematic Review and Qualitative Assessment of Fraud Detection Methodologies in Health Care Abstract: Health care fraud is a costly, challenging problem in health insurance. This study provides a systematic evaluation and synthesis of the methodologies and data samples used in current peer-reviewed studies from different academic fields on characterizing health care fraud. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was used to guide reviewing the literature. In addition, a qualitative case study approach was employed to assess the studies included in the review in order to independently confirm the conclusions of the systematic review. Out of the 450 articles that were identified by the search criteria, 27 studies were deemed as relevant and included in the analysis. Using 24 variables designed from the literature to synthesize the fraud detection methodologies, the systematic review showed an inability to compare studies quantitatively because few studies reported the accuracy of their detection methods or the overall rate of fraud. The qualitative assessment independently confirmed that prior studies are highly diverse, with the only common characteristic being widespread use of data mining methods. Applying a previously validated approach that has not been taken by prior health care fraud reviews, our qualitative method showed high validity in terms of reviewers’ agreement on the classification of fraud detection methods (r = 93%). Two limitations of this study are that the strength of the evidence is reliant on the quality and number of studies previously performed on the topic, and our systematic review and qualitative results were limited to the text of the final studies as published in peer-reviewed journals. The main gaps we identified are the need to validate existing methods, lack of proof of intent to commit fraud, absence of a fraud rate estimate in the studies analyzed, and inability to use prior evidence to select the best fraud detection method(s). Additional research designed to address these gaps would be of value to researchers, policymakers, and health care practitioners who aim to select the best fraud detection methods for their specific area of practice. Journal: North American Actuarial Journal Pages: 1-26 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2021.1895843 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1895843 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:1-26 Template-Type: ReDIF-Article 1.0 Author-Name: Di Wang Author-X-Name-First: Di Author-X-Name-Last: Wang Author-Name: Wai-Sum Chan Author-X-Name-First: Wai-Sum Author-X-Name-Last: Chan Title: Backcasting Mortality in England and Wales, 1600–1840 Abstract: There have been significant developments in using extrapolative stochastic models for mortality forecasting (forward projection) in the literature. However, little attention has been devoted to mortality backcasting (backward projection). This article proposes a simple mortality backcasting framework that can be used in practice. Research and analysis of English demography in the 17th and 18th centuries have suffered from a lack of mortality data. We attempt to alleviate this problem by developing a technique that runs backward in time and produces estimates of mortality data before the time at which such data became available. After confirming the time reversibility of the mortality data, we compare the backcasting performance of some commonly used stochastic mortality models for the England and Wales data. The original Lee–Carter model is selected for backcasting purpose of this dataset. Finally, we examine the longevity of British artists between the 17th and the 20th centuries using the backcasted population mortality as benchmarks. The results show that artists living in Britain from 1600 to the mid 1800s had life expectancies similar to those of the general population, with a marked increase in longevity after the Industrial Revolution. Journal: North American Actuarial Journal Pages: 102-122 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1853574 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1853574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:102-122 Template-Type: ReDIF-Article 1.0 Author-Name: Patrice Gaillardetz Author-X-Name-First: Patrice Author-X-Name-Last: Gaillardetz Author-Name: Emmanuel Osei Mireku Author-X-Name-First: Emmanuel Author-X-Name-Last: Osei Mireku Title: Worst-Case Valuation of Equity-Linked Products Using Risk-Minimizing Strategies Abstract: The impact of model risk when hedging equity-linked products and other investment guarantees is significant. We propose a model to determine the worst-case value of an equity-linked product through partial hedging. Risk control strategies based on conditional Value at Risk measures are used. The model integrates both mortality and financial risk associated with these products to find the worst-case value. We adopt robust optimization techniques to compute an optimal hedging strategy. To demonstrate versatility of the framework, numerical examples of point-to-point equity-indexed annuities are presented in multinomial lattice dynamics. We compare robustness of the model to super-replicating and quadratic hedging strategies by computing their capital requirements. Journal: North American Actuarial Journal Pages: 64-81 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1826975 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1826975 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:64-81 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Christian Y. Robert Author-X-Name-First: Christian Y. Author-X-Name-Last: Robert Title: Collaborative Insurance with Stop-Loss Protection and Team Partitioning Abstract: Denuit (2019, 2020a) demonstrated that conditional mean risk sharing introduced by Denuit and Dhaene (2012) is the appropriate theoretical tool to share losses in collaborative peer-to-peer insurance schemes. Denuit and Robert (2020a, 2020b, 2021) studied this risk sharing mechanism and established several attractive properties including linear approximations when total losses or the number of participants get large. It is also shown there that the conditional expectation defining the conditional mean risk sharing is asymptotically increasing in the total loss (under mild technical assumptions). This ensures that the risk exchange is Pareto-optimal and that all participants have an interest to keep total losses as small as possible. In this article, we design a flexible system where entry prices can be made attractive compared to the premium of a regular, commercial insurance contract and participants are awarded cash-backs in case of favorable experience while being protected by a stop-loss treaty in the opposite case. Members can also be grouped according to some meaningful criteria, resulting in a hierarchical decomposition of the community. The particular case where realized losses are allocated in proportion to the pure premiums is studied. Journal: North American Actuarial Journal Pages: 143-160 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1855199 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1855199 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:143-160 Template-Type: ReDIF-Article 1.0 Author-Name: Carolyn W. Chang Author-X-Name-First: Carolyn W. Author-X-Name-Last: Chang Author-Name: Jack S. K. Chang Author-X-Name-First: Jack S. K. Author-X-Name-Last: Chang Author-Name: Min-Teh Yu Author-X-Name-First: Min-Teh Author-X-Name-Last: Yu Title: Pricing Hurricane Bonds Using a Physically Based Option Pricing Approach Abstract: Hurricane bonds are unique in that they are structured with a dual exercise condition: a physically based condition that the underlying hurricane makes landfall at a prespecified location, and a standard moneyness condition that they end in the money. As the time of landfall is uncertain, their maturities are also uniquely random. This research thus proposes a modeling methodology to solve this option-pricing problem—that is, to price hurricane bonds at the nexus of atmospheric science and finance by integrating hurricane risk modeling and option pricing modeling. We resolve this dual exercise/random maturity issue by implementing a coupled hurricane generator to simulate hurricane synthetic tracks, intensity, radius, two-dimensional wind fields, and hurricane-index value evolution along the tracks. We price the increasingly popular parametric and parametric-index hurricane bonds by Monte Carlo simulations, as the underlying hurricane indices are untraded and thus replication pricing is not viable. Journal: North American Actuarial Journal Pages: 27-42 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1824798 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1824798 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:27-42 Template-Type: ReDIF-Article 1.0 Author-Name: Han Li Author-X-Name-First: Han Author-X-Name-Last: Li Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Title: Joint Extremes in Temperature and Mortality: A Bivariate POT Approach Abstract: This article contributes to insurance risk management by modeling extreme climate risk and extreme mortality risk in an integrated manner via extreme value theory (EVT). We conduct an empirical study using monthly temperature and death data in the United States and find that the joint extremes in cold weather and old-age death counts exhibit the strongest level of dependence. Based on the estimated bivariate generalized Pareto distribution, we quantify the extremal dependence between death counts and temperature indexes. Methodologically, we employ the cutting-edge multivariate peaks over threshold (POT) approach, which is readily applicable to a wide range of topics in extreme risk management. Journal: North American Actuarial Journal Pages: 43-63 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1823236 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1823236 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:43-63 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-François Bégin Author-X-Name-First: Jean-François Author-X-Name-Last: Bégin Author-Name: Mathieu Boudreault Author-X-Name-First: Mathieu Author-X-Name-Last: Boudreault Title: Do Jumps Matter in the Long Term? A Tale of Two Horizons Abstract: Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. Because the resulting liabilities are very long-lived and the short-term performance of the assets backing these liabilities may trigger important losses, it is thus a desired feature of an ESG to replicate equity returns over such horizons. In light of this horizon duality, we investigate the relevance of jumps in ESGs to replicate dynamics over different horizons and compare their performance to popular models in actuarial science. We show that jump-diffusion models cannot replicate higher moments if estimated with the maximum likelihood. Using a generalized method of moments–based approach, however, we find that simple jump-diffusion models have an excellent fit overall (moments and the entire distribution) at different timescales. We also investigate three typical applications: the value of $1 accumulated with no intermediate monitoring, a solvency analysis with frequent monitoring, and a dynamic portfolio problem. We find that jumps have long-lasting effects that are difficult to replicate otherwise, so, yes, jumps do matter in the long term. Journal: North American Actuarial Journal Pages: 82-101 Issue: 1 Volume: 26 Year: 2022 Month: 1 X-DOI: 10.1080/10920277.2020.1837636 File-URL: http://hdl.handle.net/10.1080/10920277.2020.1837636 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:1:p:82-101 Template-Type: ReDIF-Article 1.0 Author-Name: Yawen Hwang Author-X-Name-First: Yawen Author-X-Name-Last: Hwang Author-Name: Linus Fang-Shu Chan Author-X-Name-First: Linus Fang-Shu Author-X-Name-Last: Chan Author-Name: Chenghsien Jason Tsai Author-X-Name-First: Chenghsien Jason Author-X-Name-Last: Tsai Title: On Voluntary Terminations of Life Insurance: Differentiating Surrender Propensity From Lapse Propensity Across Product Types Abstract: Understanding the causes of voluntary terminations is important to the service quality, profitability, and risk management of the life insurer. This article extends the literature on the determinants of the termination propensities in four aspects. First, we decompose voluntary terminations into surrender and lapse and build models accordingly. This decomposition is important because the motives, causes, and consequences of lapse and surrender are distinct. Second, we construct models for the surrender and lapse propensities by product type. Without such construction, one would overlook the diverse motivations of buying different types of product and distinct behaviors of terminating product holding. Third, we introduce new explanatory variables (commission ratio and occupation of the insured) in modeling the propensities and these variables are found to be significant. Fourth, this is the first article on the determinants of voluntary terminations for the market of Taiwan with implications for other regions having significant Chinese people presence. Journal: North American Actuarial Journal Pages: 252-282 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1973507 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1973507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:252-282 Template-Type: ReDIF-Article 1.0 Author-Name: Hong Beng Lim Author-X-Name-First: Hong Beng Author-X-Name-Last: Lim Author-Name: Nariankadu D. Shyamalkumar Author-X-Name-First: Nariankadu D. Author-X-Name-Last: Shyamalkumar Title: Evaluating Medical Underwriters in Life Settlements: Problem of Unreported Deaths Abstract: The valuation of policies in the life settlement market hinges upon life expectancy assessments provided by medical underwriters. Because accurate assessments are essential to the market functioning well, determining so is of interest to various stakeholders, including regulatory bodies. As a third party to settlement transactions, these underwriters, and hence their auditors, have to rely on public sources in compiling mortality data on underwritten insureds. Such acquired data are known to contain a significant proportion of unreported deaths. Accurate accounting for their presence is crucial to a fair evaluation of an underwriter’s methodology. However, existing methods for doing so either rely solely on actuarial opinion or are based on assumptions untenable in the life settlement context. Toward developing a practical data-driven methodology for consistently estimating mortality in the presence of unreported deaths, we propose the IBNR (incurred but not reported) rate model. This adaptation of the cure rate model accommodates the heterogeneity in the rates of both mortality and unreported deaths seen in practice. Our methodology thus facilitates an accurate and objective evaluation of an underwriter. Journal: North American Actuarial Journal Pages: 298-322 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1927109 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1927109 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:298-322 Template-Type: ReDIF-Article 1.0 Author-Name: Yinzhi Wang Author-X-Name-First: Yinzhi Author-X-Name-Last: Wang Author-Name: Erik Bølviken Author-X-Name-First: Erik Author-X-Name-Last: Bølviken Title: How Much Is Optimal Reinsurance Degraded by Error? Abstract: Estimation error reduces reinsurance optimality under a fitted model to suboptimality under the true one. A mathematical formulation of this issue of degradation is offered and examined through asymptotics as the sample size n of the historical observations becoming infinite. Assuming economic or distortion pricing of reinsurance it is shown that the rate of degradation is either O(1/n) or O(1n) depending on smoothness properties of the risk measure employed. Examples are conditional Value at Risk criteria, which tend to be O(1/n), and Value at Risk, which is O(1/n). A numerical study investigates the issue for smaller n and suggests a need for developing more robust optimal reinsurance techniques that can with stand model errors better. Journal: North American Actuarial Journal Pages: 283-297 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1956974 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1956974 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:283-297 Template-Type: ReDIF-Article 1.0 Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: Analysis of Prescription Drug Utilization with Beta Regression Models Abstract: The health care sector in the United States is complex and is also a large sector that generates about 20% of the country’s gross domestic product. Health care analytics has been used by researchers and practitioners to better understand the industry. In this article, we examine and demonstrate the use of Beta regression models to study the utilization of brand name drugs in the United States to understand the variability of brand name drug utilization across different areas. The models are fitted to public datasets obtained from the Medicare & Medicaid Services and the Internal Revenue Service. Integrated nested Laplace approximation (INLA) is used to perform the inference. The numerical results show that Beta regression models can fit the brand name drug claim rates well and including spatial dependence improves the performance of the Beta regression models. Such models can be used to reflect the effect of prescription drug utilization when updating an insured’s health risk in a risk scoring model. Journal: North American Actuarial Journal Pages: 205-226 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1890127 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1890127 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:205-226 Template-Type: ReDIF-Article 1.0 Author-Name: Séverine Arnold Author-X-Name-First: Séverine Author-X-Name-Last: Arnold Author-Name: Viktoriya Glushko Author-X-Name-First: Viktoriya Author-X-Name-Last: Glushko Title: Short- and Long-Term Dynamics of Cause-Specific Mortality Rates Using Cointegration Analysis Abstract: This article applies cointegration analysis and vector error correction models to model the short- and long-run relationships between cause-specific mortality rates. We work with the data from five developed countries (the United States, Japan, France, England and Wales, and Australia) and split the mortality rates into five main causes of death (infectious and parasitic, cancer, circulatory diseases, respiratory diseases, and external causes). We successively adopt short- and long-term perspectives, and analyze how each cause-specific mortality rate impacts and reacts to the shocks received from the rest of the causes. We observe that the cause-specific mortality rates are closely linked to each other, apart from the external causes that show an entirely independent behavior and hence could be considered as truly exogenous. We summarize our findings with the aim to help practitioners set more informed assumptions concerning the future development of mortality. Journal: North American Actuarial Journal Pages: 161-183 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1874421 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1874421 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:161-183 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Gutterman Author-X-Name-First: Sam Author-X-Name-Last: Gutterman Title: Alcohol and Mortality: An Actuarial Issue Abstract: Despite some favorable global trends in the prevalence of heavy episodic drinking, alcohol-related mortality and morbidity since 2010, and the prevalence of youth drinking in certain developed countries, there has been limited progress in reducing total per-capita alcohol consumption. The burden of disease attributable to alcohol remains high, particularly at pre-retirement ages, and is increasing in some countries and for some causes of death. This article describes the status and trends in alcohol consumption, both worldwide and in the United States. It also describes the adverse consequences of heavy and binge drinking, which are significant to the individual, family and friends, and society. Although the overall effect on mortality of moderate alcohol drinking compared with no drinking at all has generally been viewed to be somewhat favorable due to the effect of certain cardiovascular risks, this view is not shared by all—the arguments involved are examined in this article. The recognition and need for active management of the adverse effects of heavy and binge alcohol consumption, remain essential to favorable health and longevity. Possible public interventions are also described. Actuaries involved in assessing mortality trends and product design need to assess trends in drivers and consequences of historical, current, and expected future alcohol-attributable mortality and morbidity patterns on a regular basis. Journal: North American Actuarial Journal Pages: 184-204 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1946660 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1946660 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:184-204 Template-Type: ReDIF-Article 1.0 Author-Name: Peter A. Forsyth Author-X-Name-First: Peter A. Author-X-Name-Last: Forsyth Title: A Stochastic Control Approach to Defined Contribution Plan Decumulation: “The Nastiest, Hardest Problem in Finance” Abstract: We pose the decumulation strategy for a defined contribution (DC) pension plan as a problem in optimal stochastic control. The controls are the withdrawal amounts and the asset allocation strategy. We impose maximum and minimum constraints on the withdrawal amounts, and impose no-shorting no-leverage constraints on the asset allocation strategy. Our objective function measures reward as the expected total withdrawals over the decumulation horizon, and risk is measured by expected shortfall (ES) at the end of the decumulation period. We solve the stochastic control problem numerically, based on a parametric model of market stochastic processes. We find that, compared to a fixed constant withdrawal strategy, with minimum withdrawal set to the constant withdrawal amount the optimal strategy has a significantly higher expected average withdrawal, at the cost of a very small increase in ES risk. Tests on bootstrapped resampled historical market data indicate that this strategy is robust to parametric model misspecification. Journal: North American Actuarial Journal Pages: 227-251 Issue: 2 Volume: 26 Year: 2022 Month: 4 X-DOI: 10.1080/10920277.2021.1878043 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1878043 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:227-251 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1943451_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Pamela M. Chiroque-Solano Author-X-Name-First: Pamela M. Author-X-Name-Last: Chiroque-Solano Author-Name: Fernando Antônio da S. Moura Author-X-Name-First: Fernando Antônio da S. Author-X-Name-Last: Moura Title: A Heavy-Tailed and Overdispersed Collective Risk Model Abstract: Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, a hierarchical model for collective risk with heavy tails of the claims distributions that also takes into account overdispersion of the number of claims is proposed. In particular, the distribution of the logarithm of the aggregate value of claims is assumed to follow a Student t distribution. Additionally, to incorporate possible overdispersion, the number of claims is modeled as having a negative binomial distribution. Bayesian decision theory is invoked to calculate the fair premium based on the modified absolute deviation utility. An application to a health insurance data set is presented together with some diagnostic measures to identify excess variability. The variability measures are analyzed using the marginal posterior predictive distribution of the premiums according to some competitive models. Finally, a simulation study is carried out to assess the predictive capability of the model and the adequacy of the Bayesian estimation procedure. Journal: North American Actuarial Journal Pages: 323-335 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.1943451 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1943451 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:323-335 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1953536_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Xin Che Author-X-Name-First: Xin Author-X-Name-Last: Che Author-Name: Andre Liebenberg Author-X-Name-First: Andre Author-X-Name-Last: Liebenberg Author-Name: Jianren Xu Author-X-Name-First: Jianren Author-X-Name-Last: Xu Title: Usage-Based Insurance—Impact on Insurers and Potential Implications for InsurTech Abstract: Insurers are increasingly embracing the InsurTech ecosystem. The most important InsurTech-related trend in automobile insurance is usage-based insurance (UBI), which enables insurers to access and incorporate drivers’ behavioral risk factors in actuarial pricing. Using a difference-in-difference research design with firm fixed effects, we provide evidence that UBI improves private passenger auto liability (PPAL) insurers’ underwriting performance by reducing their loss ratio. However, the improvement in underwriting performance is only significant among early UBI adopters, highlighting the early-mover advantage in InsurTech. Also, UBI produces benefits only when it matures. Our findings are robust to analyses that address potential reverse causality and self-selection bias. Additional tests show that early UBI adopters experience a significant increase in their market share, implying UBI’s advantage to attract low-risk drivers from other insurers. The overall performance effect of UBI programs for early adopters is a 1% increase in ROA and a 3% increase in ROE. The policy implications of our findings from the perspective of insurers should be of interest to firms’ management, actuaries, investors, and rating agencies. Journal: North American Actuarial Journal Pages: 428-455 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.1953536 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1953536 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:428-455 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1914665_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Gary Venter Author-X-Name-First: Gary Author-X-Name-Last: Venter Author-Name: Şule Şahin Author-X-Name-First: Şule Author-X-Name-Last: Şahin Title: Semiparametric Regression for Dual Population Mortality Abstract: Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at each point. Rather than shrinking these toward zero, nearby parameters are better shrunk toward each other. Semiparametric regression is a statistical discipline for building curves across parameter classes using shrinkage methodology. It is similar to but more parsimonious than cubic splines. We introduce it in the context of Bayesian shrinkage and apply it to joint mortality modeling for related populations. Bayesian shrinkage of slope changes of linear splines is an approach to semiparametric modeling that evolved in the actuarial literature. It has some theoretical and practical advantages, like closed-form curves, direct and transparent determination of degree of shrinkage and of placing knots for the splines, and quantifying goodness of fit. It is also relatively easy to apply to the many nonlinear models that arise in actuarial work. We find that it compares well to a more complex state-of-the-art statistical spline shrinkage approach on a popular example from that literature. Journal: North American Actuarial Journal Pages: 403-427 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.1914665 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1914665 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:403-427 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2022497_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Jared Cummings Author-X-Name-First: Jared Author-X-Name-Last: Cummings Author-Name: Brian Hartman Author-X-Name-First: Brian Author-X-Name-Last: Hartman Title: Using Machine Learning to Better Model Long-Term Care Insurance Claims Abstract: Long-term care insurance (LTCI) should be an essential part of a family financial plan. It could protect assets from the expensive and relatively common risk of needing disability assistance, and LTCI purchase rates are lower than expected. Though there are multiple reasons for this trend, it is partially due to the difficultly insurers have in operating profitably as LTCI providers. If LTCI providers were better able to forecast claim rates, they would have less difficulty maintaining profitability. In this article, we develop several models to improve upon those used by insurers to forecast claim rates. We find that standard logistic regression is outperformed by tree-based and neural network models. More modest improvements can be found by using a neighbor-based model. Of all of our tested models, the random forest models were the consistent top performers. Additionally, simple sampling techniques influence the performance of each of the models. This is especially true for the deep neural network, which improves drastically under oversampling. The effects of the sampling vary depending on the size of the available data. To better understand this relationship, we thoroughly examine three states with various amounts of available data as case studies. Journal: North American Actuarial Journal Pages: 470-483 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.2022497 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2022497 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:470-483 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1948430_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Ha Nguyen Author-X-Name-First: Ha Author-X-Name-Last: Nguyen Author-Name: Ning Wang Author-X-Name-First: Ning Author-X-Name-Last: Wang Title: Dynamic Fund Protection for Property Markets Abstract: This article aims to investigate, from an academic perspective, a potential application of dynamic fund protection to protect a mortgagor of a property against the downside risk due to falling property price. The valuation of the dynamic fund protection is discussed through modeling the property price and interest rate, which may be considered to be two key factors having a material impact on the mortgagor. Specifically, a mean-reverting process is used to describe the property price and the Heath-Jarrow-Morton theory is used to model the interest rate. The valuation is done via the use of a forward measure approach. The numerical solution to the pricing partial differential equation is obtained via applying the finite difference method. Numerical results with some model parameters being estimated from the data on an Australian residential property index and Australian zero-coupon yields and forward rates are provided. The implications of the numerical results for the potential implementation of the dynamic fund protection are discussed. Journal: North American Actuarial Journal Pages: 383-402 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.1948430 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1948430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:383-402 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2000876_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Marjorie Rosenberg Author-X-Name-First: Marjorie Author-X-Name-Last: Rosenberg Author-Name: Fanghao Zhong Author-X-Name-First: Fanghao Author-X-Name-Last: Zhong Title: Using Clusters Based on Social Determinants to Identify the Top 5% Utilizers of Health Care Abstract: This article extends prior work that used only social determinants to create clusters that are labeled using an external measure of average total expenditures. In this article we show that these clusters can identify a reasonable percentage of the top 5% utilizers of health care and compare two methods of clustering (PAM and k-means). We include two independent cohorts to show the consistency of the use of clusters across cohorts. We find that the three clusters with the highest average total expenditure (labeled from the intial studies) identify approximately 40% of those who are among the top 5% utilizers and from 25% to over 50% of the expenditures of the top 5% utilizers for each of the three cohorts. By identifying characteristics of individuals who are consistently in the top 5%, third-party payors and other stakeholders have a better opportunity to prospectively apply effective interventions. Social determinants such whether the individual is not working, on food stamps, or homeless are more frequent in those top 5% utilizers compared to the overall population. Journal: North American Actuarial Journal Pages: 456-469 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.2000876 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2000876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:456-469 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1966805_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Yichun Chi Author-X-Name-First: Yichun Author-X-Name-Last: Chi Author-Name: Zuo Quan Xu Author-X-Name-First: Zuo Quan Author-X-Name-Last: Xu Author-Name: Sheng Chao Zhuang Author-X-Name-First: Sheng Chao Author-X-Name-Last: Zhuang Title: Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk Abstract: In this article, we examine the effect of background risk on portfolio selection and optimal reinsurance design under the criterion of maximizing the probability of reaching a goal. Following the literature, we adopt dependence uncertainty to model the dependence ambiguity between financial risk (or insurable risk) and background risk. Because the goal-reaching objective function is nonconcave, these two problems bring highly unconventional and challenging issues for which classical optimization techniques often fail. Using a quantile formulation method, we derive the optimal solutions explicitly. The results show that the presence of background risk does not alter the shape of the solution but instead changes the parameter value of the solution. Finally, numerical examples are given to illustrate the results and verify the robustness of our solutions. Journal: North American Actuarial Journal Pages: 351-382 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.1966805 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1966805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:351-382 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1956975_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220823T191300 git hash: 39867e6e2f Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: Tail Moments of Compound Distributions Abstract: In this article, we study the moment transform of both univariate and multivariate compound sums. We first derive simple explicit formulas for the first and second moment transforms when the (loss) frequency distribution is in the so-called (a,b,0) class. Then we show that the derived formulas can be used to efficiently compute risk measures such as the tail conditional expectation (TCE), the tail variance (TV), and higher tail moments. The results generalize those in Denuit (North American Actuarial Journal, 24 (4):512–32, 2020). Journal: North American Actuarial Journal Pages: 336-350 Issue: 3 Volume: 26 Year: 2022 Month: 8 X-DOI: 10.1080/10920277.2021.1956975 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1956975 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:3:p:336-350 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2026229_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: G. P. Clemente Author-X-Name-First: G. P. Author-X-Name-Last: Clemente Author-Name: N. Savelli Author-X-Name-First: N. Author-X-Name-Last: Savelli Author-Name: G. A. Spedicato Author-X-Name-First: G. A. Author-X-Name-Last: Spedicato Author-Name: D. Zappa Author-X-Name-First: D. Author-X-Name-Last: Zappa Title: Modeling General Practitioners’ Total Drug Costs through GAMLSS and Collective Risk Models Abstract: Monitoring general practitioner prescribing costs is an important topic in order to efficiently allocate National Health Insurance resources. Using generalized additive models for location, scale, and shape with random effects, we investigate how second-order variables, related to patients, contribute to estimating the frequency, severity, and hence the total amount of costs. The total cost of prescriptions associated with a general practitioner is then derived following a collective risk theory approach by aggregating cumulants of patient cost distributions. By means of the fourth-order Cornish-Fisher expansion series of quantiles of the aggregate cost distribution of general practitioners, we construct a confidence interval for each doctor, which is used to select a subset of doctors that should be monitored to identify potential inefficiencies. A case study is developed by using structured data regarding the number and cost of prescriptions of about 900,000 patients linked to corresponding general practitioners. The prescription costs considered are only those paid fully by the national health coverage. Journal: North American Actuarial Journal Pages: 610-625 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2022.2026229 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2026229 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:610-625 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2003209_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Title: Sample Size Determination for Credibility Estimation Abstract: The credibility estimator has been successfully and widely applied by practitioners in the insurance industry for decades. However, an important issue remains unresolved: What sample size should the actuary choose when he or she applies the credibility estimator? In particular, is the size of a given claims dataset large enough for the credibility estimator to be accurate? This article aims to address this issue by first suggesting a sample size criterion for the credibility estimator and then proposing a sample size based on that. The proposed sample size is easy to apply, and it guarantees provable accuracy for credibility estimation. Journal: North American Actuarial Journal Pages: 485-495 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2021.2003209 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2003209 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:485-495 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2013896_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Tsz Chai Fung Author-X-Name-First: Tsz Chai Author-X-Name-Last: Fung Author-Name: Andrei L. Badescu Author-X-Name-First: Andrei L. Author-X-Name-Last: Badescu Author-Name: X. Sheldon Lin Author-X-Name-First: X. Sheldon Author-X-Name-Last: Lin Title: Fitting Censored and Truncated Regression Data Using the Mixture of Experts Models Abstract: The logit-weighted reduced mixture of experts model (LRMoE) is a flexible yet analytically tractable non-linear regression model. Though it has shown usefulness in modeling insurance loss frequencies and severities, model calibration becomes challenging when censored and truncated data are involved, which is common in actuarial practice. In this article, we present an extended expectation–conditional maximization (ECM) algorithm that efficiently fits the LRMoE to random censored and random truncated regression data. The effectiveness of the proposed algorithm is empirically examined through a simulation study. Using real automobile insurance data sets, the usefulness and importance of the proposed algorithm are demonstrated through two actuarial applications: individual claim reserving and deductible ratemaking. Journal: North American Actuarial Journal Pages: 496-520 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2021.2013896 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2013896 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:496-520 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2018614_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Le Chang Author-X-Name-First: Le Author-X-Name-Last: Chang Author-Name: Yanlin Shi Author-X-Name-First: Yanlin Author-X-Name-Last: Shi Title: Age-Coherent Mortality Modeling and Forecasting Using a Constrained Sparse Vector-Autoregressive Model Abstract: Accurate forecasts and analyses of mortality rates are essential to many practical issues, such as population projections and the design of pension schemes. Recent studies have considered a spatial–temporal autoregressive (STAR) model, in which the mortality rates of each age depend on their own historical values (temporality) and the neighboring cohort ages (spatiality). Despite the realization of age coherence and improved forecasting accuracy over the famous Lee-Carter (LC) model, the assumption of STAR that only the effects of the same and the neighboring cohorts exist can be too restrictive. In this study, we adopt a data-driven principle, as in a sparse vector autoregressive (SVAR) model, to improve the flexibility of the parametric structure of STAR and develop a constrained SVAR (CSVAR) model. To solve its objective function consisting of non-standard L2 and L1 penalties subject to constraints, we develop a new algorithm and prove the existence of the desirable age-coherence in CSVAR. Using empirical data from the United Kingdom, France, Italy, Spain, and Australia, we show that CSVAR consistently outperforms the LC, SVAR, and STAR models with respect to forecasting accuracy. The estimates and forecasts of the CSVAR model also demonstrate important demographic differences between these five countries. Journal: North American Actuarial Journal Pages: 591-609 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2021.2018614 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2018614 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:591-609 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2022499_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Francis Duval Author-X-Name-First: Francis Author-X-Name-Last: Duval Author-Name: Jean-Philippe Boucher Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Boucher Author-Name: Mathieu Pigeon Author-X-Name-First: Mathieu Author-X-Name-Last: Pigeon Title: How Much Telematics Information Do Insurers Need for Claim Classification? Abstract: It has been shown several times in the literature that telematics data collected in motor insurance help to better understand an insured’s driving risk. Insurers who use these data reap several benefits, such as a better estimate of the pure premium, more segmented pricing, and less adverse selection. The flip side of the coin is that collected telematics information is often sensitive and can therefore compromise policyholders’ privacy. Moreover, due to their large volume, this type of data is costly to store and hard to manipulate. These factors, combined with the fact that insurance regulators tend to issue more and more recommendations regarding the collection and use of telematics data, make it important for an insurer to determine the right amount of telematics information to collect. In addition to traditional contract information such as the age and gender of the insured, we have access to a telematics dataset where information is summarized by trip. We first derive several features of interest from these trip summaries before building a claim classification model using both traditional and telematics features. By comparing a few classification algorithms, we find that logistic regression with lasso penalty is the most suitable for our problem. Using this model, we develop a method to determine how much information about policyholders’ driving should be kept by an insurer. Using real data from a North American insurance company, we find that telematics data become redundant after about 3 months or 4000 km of observation, at least from a claim classification perspective. Journal: North American Actuarial Journal Pages: 570-590 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2021.2022499 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2022499 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:570-590 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2036197_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Daniel Abramson Author-X-Name-First: Daniel Author-X-Name-Last: Abramson Title: A Nonproportional Premium Rating Method for Construction Risks Abstract: Correct pricing of nonproportional (primary or excess of loss) insurance for construction risks must consider not only how the insured property values build up over time, but also how the probable maximum loss (PML) changes. Conventional pricing methods for static property risks cannot be employed for construction risks, since the latter are characterized by PML patterns that change over time, as well as evolving loss exposures and perils arising from the various phases of the construction project. A further complication arises when delay in startup (DSU) is covered, because a DSU loss is triggered by a property damage loss and both losses contribute jointly to the erosion of an excess layer. This article describes a pricing method with analysis of specific cases of interest, including guidelines for creating practical excess of loss rating models. Journal: North American Actuarial Journal Pages: 626-645 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2022.2036197 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2036197 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:626-645 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2014891_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Guohui Guan Author-X-Name-First: Guohui Author-X-Name-Last: Guan Author-Name: Xiang Hu Author-X-Name-First: Xiang Author-X-Name-Last: Hu Title: Time-Consistent Investment and Reinsurance Strategies for Mean–Variance Insurers in N-Agent and Mean-Field Games Abstract: In this study, we investigate the competition among insurers under the mean–variance criterion. The optimization problems are formulated for finite and infinite insurers. The surplus processes of the insurers are characterized by jump-diffusion processes with common and idiosyncratic insurance risks. The insurers can purchase a reinsurance business to divide the insurance risk. In the financial market, the insurers decide the proportion of their fund to be retained as cash and to be invested in a stock characterized by a jump-diffusion process with common and idiosyncratic financial risks. The insurers compete with each other and are concerned with the relative performance. By the extended Hamilton-Jacobi-Bellman equation, the explicit forms of the n-agent equilibrium and mean-field equilibrium (MFE) are obtained in the n-agent case and mean-field case, respectively. Our results show that the MFE of the reinsurance strategy is composed of two parts, one part associated with the individual preference and the other associated with the common insurance shock. Meanwhile, the MFE of the investment strategy is composed of three parts: the individual preference, common market risks, and common shocks. Numerical examples are presented at the end of this article to demonstrate the effects of different parameters on the MFE. The results reveal that the insurers become convergent in a competitive environment. Journal: North American Actuarial Journal Pages: 537-569 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2021.2014891 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2014891 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:537-569 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1916537_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Dean Buckner Author-X-Name-First: Dean Author-X-Name-Last: Buckner Author-Name: Kevin Dowd Author-X-Name-First: Kevin Author-X-Name-Last: Dowd Title: Discounting the Discounted Projection Approach Abstract: U.K. equity release actuaries are using a flawed approach to value the no-negative equity guarantees in their equity release mortgages. The approach they use, the discounted projection approach, incorrectly uses projected future house prices as the underlying prices in their put option pricing equations. The correct approach uses forward house prices. The discounted projection approach entails significant undervaluations of no-negative equity guarantees and overvaluations of equity release mortgages and can produce valuations that violate rational pricing principles. The discounted projection approach is also inconsistent with both actuarial and accounting standards. Our results have significant ramifications for equity release industry practice and prudential regulation. Journal: North American Actuarial Journal Pages: 521-536 Issue: 4 Volume: 26 Year: 2022 Month: 11 X-DOI: 10.1080/10920277.2021.1916537 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1916537 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:521-536 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_12254408_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Howell Tong Author-X-Name-First: Howell Author-X-Name-Last: Tong Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: On Pricing Derivatives Under GARCH Models: A Dynamic Gerber-Shiu Approach Abstract: This paper proposes a method for pricing derivatives under the generalized autoregressive conditional heteroskedasticity (GARCH) assumption for underlying assets in the context of a "dynamic" version of Gerber and Shiu's (1994) option-pricing model. Instead of adopting the notion of a local risk-neutral valuation relationship (LRNVR), introduced by Duan (1995), the authors here employ the concept of conditional Esscher transforms introduced by Bühlmann et al. (1996) to identify a martingale measure under the incomplete market setting. One advantage of this model is that it provides a unified and convenient approach to deal with different parametric models for the innovation of the GARCH stock-price process. Under the conditional normality assumption for stock innovation, our pricing result is consistent with that of Duan (1995). In line with the celebrated Gerber-Shiu option pricing model, the pricing result can be justified within the dynamic framework of utility maximization problems, which makes the economic intuition of the pricing result more appealing. In fact, the use of the Esscher transform for option valuation can also be justified by the minimization of the relative entropy between the statistical probability and the risk-neutralized pricing probability. Numerical results for comparing the model with the Black-Scholes optionpricing model are also presented. Journal: North American Actuarial Journal Pages: 17-31 Issue: 3 Volume: 8 Year: 2004 Month: 7 X-DOI: 10.1080/10920277.2004.12254408 File-URL: http://hdl.handle.net/10.1080/10920277.2004.12254408 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:8:y:2004:i:3:p:17-31 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2050260_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario Marino Author-X-Name-First: Mario Author-X-Name-Last: Marino Author-Name: Susanna Levantesi Author-X-Name-First: Susanna Author-X-Name-Last: Levantesi Author-Name: Andrea Nigri Author-X-Name-First: Andrea Author-X-Name-Last: Nigri Title: A Neural Approach to Improve the Lee-Carter Mortality Density Forecasts Abstract: Several countries worldwide are experiencing a continuous increase in life expectancy, extending the challenges of life actuaries and demographers in forecasting mortality. Although several stochastic mortality models have been proposed in the literature, mortality forecasting research remains a crucial task. Recently, various research works have encouraged the use of deep learning models to extrapolate suitable patterns within mortality data. Such learning models allow achieving accurate point predictions, though uncertainty measures are also necessary to support both model estimate reliability and risk evaluation. As a new advance in mortality forecasting, we formalize the deep neural network integration within the Lee-Carter framework, as a first bridge between the deep learning and the mortality density forecasts. We test our model proposal in a numerical application considering three representative countries worldwide and for both genders, scrutinizing two different fitting periods. Exploiting the meaning of both biological reasonableness and plausibility of forecasts, as well as performance metrics, our findings confirm the suitability of deep learning models to improve the predictive capacity of the Lee-Carter model, providing more reliable mortality boundaries in the long run. Journal: North American Actuarial Journal Pages: 148-165 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2022.2050260 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2050260 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:148-165 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2069124_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gaurav Khemka Author-X-Name-First: Gaurav Author-X-Name-Last: Khemka Author-Name: David Pitt Author-X-Name-First: David Author-X-Name-Last: Pitt Author-Name: Jinhui Zhang Author-X-Name-First: Jinhui Author-X-Name-Last: Zhang Title: On Fitting Probability Distribution to Univariate Grouped Actuarial Data with Both Group Mean and Relative Frequencies Abstract: Many publicly available datasets relevant to actuarial work contain data grouped in various ways. For example, operational loss data are often reported in a grouped format that includes group boundaries, loss frequency, and average or total amount of loss for each group. The process of fitting a parametric distribution to grouped data becomes more complex but potentially more accurate when additional information, such as group means, is incorporated in the estimation process. This article compares the relative performance of three methods of inference using distributions suitable for actuarial applications, particularly those that are right-skewed, heavy-tailed, and left-truncated. We compare the traditional maximum likelihood method, which only considers the group limits and frequency of observations in each group, to two research innovations: a modified maximum likelihood method and a modified generalized method of moments approach, both of which incorporate additional group mean information in the estimation process. We perform a simulation study where the proposed methods outperform the traditional maximum likelihood method and the maximum entropy when the true underlying distribution is both known and unknown. Further, we apply the methods to three actuarial datasets: operational loss data, pension fund data, and car insurance claims data. Here we compare the performance of the three methods along with the maximum entropy distribution (under the traditional maximum likelihood and the modified maximum likelihood methods) and find that for all three datasets the proposed methods outperform the traditional maximum likelihood method. We conclude that there is merit in considering the proposed methods while fitting a parametric distribution to grouped data. Journal: North American Actuarial Journal Pages: 185-205 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2022.2069124 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2069124 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:185-205 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2068611_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yang Miao Author-X-Name-First: Yang Author-X-Name-Last: Miao Author-Name: Kristina P. Sendova Author-X-Name-First: Kristina P. Author-X-Name-Last: Sendova Author-Name: Bruce L. Jones Author-X-Name-First: Bruce L. Author-X-Name-Last: Jones Title: On a Risk Model With Dual Seasonalities Abstract: We consider a risk model where both the premium income and the claim process have seasonal fluctuations. We obtain the probability of ruin based on the simulation approach presented in Morales. We also discuss the conditions that must be satisfied for this approach to work. We give both a numerical example that is based on a simulation study and an example using a real-life auto insurance data set. Various properties of this risk model are also discussed and compared with the existing literature. Journal: North American Actuarial Journal Pages: 166-184 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2022.2068611 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2068611 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:166-184 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1951296_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Edward W. (Jed) Frees Author-X-Name-First: Edward W. (Jed) Author-X-Name-Last: Frees Author-Name: Fei Huang Author-X-Name-First: Fei Author-X-Name-Last: Huang Title: The Discriminating (Pricing) Actuary Abstract: The insurance industry is built on risk classification, grouping insureds into homogeneous classes. Through actions such as underwriting, pricing, and so forth, it differentiates, or discriminates, among insureds. Actuaries have responsibility for pricing insurance risk transfers and are intimately involved in other aspects of company actions and so have a keen interest in whether or not discrimination is appropriate from both company and societal viewpoints. This article reviews social and economic principles that can be used to assess the appropriateness of insurance discrimination. Discrimination issues vary by the line of insurance business and by the country and legal jurisdiction. This article examines social and economic principles from the vantage of a specific line of business and jurisdiction; these vantage points provide insights into principles. To sharpen understanding of the social and economic principles, this article also describes discrimination considerations for prohibitions based on diagnosis of COVID-19, the pandemic that swept the globe in 2020. Insurance discrimination issues have been an important topic for the insurance industry for decades and are evolving in part due to insurers’ extensive use of Big Data; that is, the increasing capacity and computational abilities of computers, availability of new and innovative sources of data, and advanced algorithms that can detect patterns in insurance activities that were previously unknown. On the one hand, the fundamental issues of insurance discrimination have not changed with Big Data; one can think of credit-based insurance scoring and price optimization as simply forerunners of this movement. On the other hand, issues regarding privacy and use of algorithmic proxies take on increased importance as insurers’ extensive use of data and computational abilities evolve. Journal: North American Actuarial Journal Pages: 2-24 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2021.1951296 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1951296 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:2-24 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2169533_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Society of Actuaries and North American Actuarial Journal Announce New Editor Journal: North American Actuarial Journal Pages: 1-1 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2023.2169533 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2169533 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:1-1 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2022498_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tzuling Lin Author-X-Name-First: Tzuling Author-X-Name-Last: Lin Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Author-Name: Hung-Wen Cheng Author-X-Name-First: Hung-Wen Author-X-Name-Last: Cheng Title: Asset Liability Management of Longevity and Interest Rate Risks: Using Survival–Mortality Bonds Abstract: In this article, we propose to attach a mortality index to a conventional bond, called a survival–mortality (SM) bond. Its cash flow pattern is like a conventional bond but it can be separated into a survival (S) part and a mortality (M) part; the cash flow pattern in the former is like an annuity or a longevity bond and that in the latter is like a mortality–catastrophe bond. We further propose to split it into S, M, and SM zero-coupon STRIPS (Separate Trading Registered Interest and Principal Securities). We apply these S, M, and SM issues to hedging longevity risk and interest rate risk of 1-year and multiple-year annuity exposures for the asset liability management of an annuity provider by adopting mortality, interest, mortality–interest duration, and convexity matching strategies. Numerical illustrations show that using SM STRIPS rather than S STRIPS can be sufficient to hedge the risks embedded in 1-year annuity exposures, whereas for multiple-year annuity exposures using S issues is more effective to reduce longevity risk and interest rate risk than using SM issues. We can infer that mortality-linked bonds play an essential role in asset liability management; the proposed survival–mortality bonds will be a feasible way to develop an efficient market for longevity risk. Journal: North American Actuarial Journal Pages: 74-95 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2021.2022498 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2022498 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:74-95 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1977144_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Cuixia Chen Author-X-Name-First: Cuixia Author-X-Name-Last: Chen Author-Name: Yijia Lin Author-X-Name-First: Yijia Author-X-Name-Last: Lin Author-Name: Ming Zhou Author-X-Name-First: Ming Author-X-Name-Last: Zhou Title: Risk-Seeking Behavior and Its Implications for the Optimal Decision Making of Annuity Insurers Abstract: This study investigates risk-seeking and optimal decisions of annuity providers. On the basis of a sample of U.S. life and annuity (L/A) insurers between 1997 and 2016, the results show clear performance-dependent risk attitudes. Specifically, insurers with returns below aspiration levels take more risks, whereas those with returns above reference levels decrease their risk-seeking, which supports the basic propositions of the cumulative prospect theory (CPT). Given initial evidence of mixed risk preferences in the L/A insurance industry, we derive an annuity insurer’s optimal investment and business strategies in a CPT decision-making framework. We show that changing risk preferences considerably affect an annuity provider’s decisions. We further illustrate how risk management changes an annuity insurer’s optimal strategies. Our results suggest that risk management lowers downside risk and allows a loss-averse decision maker to assume more risk and achieve a higher level of utility. Journal: North American Actuarial Journal Pages: 25-46 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2021.1977144 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1977144 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:25-46 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2041040_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tianxiang Shi Author-X-Name-First: Tianxiang Author-X-Name-Last: Shi Author-Name: Xuesong You Author-X-Name-First: Xuesong Author-X-Name-Last: You Title: Multiemployer Defined Benefit Pension Plans: Employer Withdrawals and Financial Vulnerability Abstract: Multiemployer defined benefit pension plans are facing severe funding challenges. The Pension Protection Act of 2006 requires that a multiemployer pension plan with an actuarial funded percentage of less than 80% must take corrective actions to improve its financial health. We use a regression discontinuity design to examine the effect of funding rule requirements on employer withdrawals from multiemployer pension plans. We find that multiemployer pension plans subject to funding rule requirements are about 14 percentage points more likely to experience employer withdrawals in a 1-year period compared to plans not required to take any corrective actions. We also find that plans with ex ante employer withdrawal experiences are more vulnerable to financial shocks such as the 2008 financial crisis. Our study provides important policy implications for regulators concerning best practices to build pension plan resilience to insolvency events. Journal: North American Actuarial Journal Pages: 121-147 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2022.2041040 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2041040 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:121-147 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2006068_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrew Hunt Author-X-Name-First: Andrew Author-X-Name-Last: Hunt Author-Name: Andrés M. Villegas Author-X-Name-First: Andrés M. Author-X-Name-Last: Villegas Title: Mortality Improvement Rates: Modeling, Parameter Uncertainty, and Robustness Abstract: Rather than looking at mortality rates directly, a number of recent academic studies have looked at modeling rates of improvement in mortality when making mortality projections. Although relatively new in the academic literature, the use of mortality improvement rates has a long-standing tradition in actuarial practice when allowing for improvements in mortality from standard mortality tables. However, mortality improvement rates are difficult to estimate robustly, and models of them are subject to high levels of parameter uncertainty, because they are derived by dividing one uncertain quantity by another. Despite this, the studies of mortality improvement rates to date have not investigated parameter uncertainty due to the ad hoc methods used to fit the models to historical data. In this study, we adapt the Poisson model for the numbers of deaths at each age and year proposed in Brouhns, Denuit, and Vermunt to model mortality improvement rates. This enables models of improvement rates to be fitted using standard maximum likelihood techniques and allows parameter uncertainty to be investigated using a standard bootstrapping approach. We illustrate the proposed modeling approach using data for the England and Wales population. The methods used in this article are available in the R package iMoMo. Journal: North American Actuarial Journal Pages: 47-73 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2021.2006068 File-URL: http://hdl.handle.net/10.1080/10920277.2021.2006068 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:47-73 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2036198_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Colin M. Ramsay Author-X-Name-First: Colin M. Author-X-Name-Last: Ramsay Author-Name: Victor I. Oguledo Author-X-Name-First: Victor I. Author-X-Name-Last: Oguledo Title: Doubly Enhanced Medicaid Partnership Annuities (DEMPANs): A New Tool for Providing Long Term Care to Retired U.S. Seniors in the Medicaid Penumbra Abstract: A major problem facing many U.S. retirees is accessing and paying for long term care. The 2019 National Association of Insurance Commissioners (NAIC) guide on long-term care insurance estimates that, of the individuals living in the United States who reach age 65, about 70% are expected to need some form of long-term care at least once in their lifetime and about 35% are expected to enter a nursing home at least once in their lifetime. Although Medicare covers most of a U.S. retiree’s medical care, Medicare does not ordinarily pay for long-term care. U.S. retirees often can access long-term care services via the Medicaid program, which is a means-tested program geared to lower income Americans. But, to quickly qualify for Medicaid, many retirees take drastic steps, such as transferring their assets to family members. When access to long-term care is not urgent and long-term planning is an option, most U.S. states have developed so-called Partnership for Long-Term Care (PLTC) Program insurance policies that provide access to Medicaid services while sheltering some or all of a retiree’s assets. In this article, we propose a hybrid annuity product called a doubly enhanced Medicaid partnership annuity (DEMPAN) that combines an annuity with a long-term care rider that is integrated within the framework of a qualified partnership policy. (Outside the United States, bundled retirement products similar to DEMPANs are often called life-care annuities.) To analyze our DEMPANs, we use a multistate model of long-term care with health states that are based on a retiree’s ability to perform activities of daily living (ADLs) and instrumental activities of daily living (IADLs) and cognitive ability. A significant contribution of this article is to explicitly model how the quality of long-term care a retiree receives affects the retiree’s health state transition probabilities used in the multistate model. As higher quality of care usually comes at a higher cost but with better health outcomes, we provide an example that explores an expected discounted utility maximizing retiree’s optimal choice of DEMPAN. Our example showed that it may be optimal for retirees who purchase DEMPANs to simply buy average quality long-term care. We hope DEMPANs fill a gap in the long-term care market by providing an important tool for elder care planning for those in the Medicaid penumbra (i.e., in the middle- and lower-middle-income classes). Retirees who purchase DEMPANs have the benefits of an annuity, private long-term care, Medicaid assistance with paying their long-term care bills, and some degree of asset protection from Medicaid estate recovery. Journal: North American Actuarial Journal Pages: 96-120 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2022.2036198 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2036198 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:96-120 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2078373_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: R. Guy Thomas Author-X-Name-First: R. Guy Author-X-Name-Last: Thomas Title: Discussion on “The Discriminating (Pricing) Actuary,” by Edward W. (Jed) Frees and Fei Huang Journal: North American Actuarial Journal Pages: 206-207 Issue: 1 Volume: 27 Year: 2023 Month: 1 X-DOI: 10.1080/10920277.2022.2078373 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2078373 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:1:p:206-207 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2078374_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Maximilian Bär Author-X-Name-First: Maximilian Author-X-Name-Last: Bär Author-Name: Nadine Gatzert Author-X-Name-First: Nadine Author-X-Name-Last: Gatzert Title: Products and Strategies for the Decumulation of Wealth during Retirement: Insights from the Literature Abstract: The question how individuals should (optimally) annuitize their wealth remains of high relevance in light of longevity risk and volatile capital markets. In this article, we first present traditional and innovative products and strategies for the decumulation of wealth during retirement, based on a review of 72 selected academic articles in peer-reviewed journals. We further identify relevant factors that generally influence the conception of these products from the retirees’ perspectives, and derive implications for product developers, before concluding with avenues of future research. Our results indicate that innovative suggestions often comprise tontine-like structures, exploit actuarial and accounting smoothing in various ways, defer annuitization to higher ages, or combine it with long-term care options, for instance. Key areas of future research in this field include the consideration of both insurer and retiree perspectives in the analysis of products, using behavioral considerations when evaluating the retirees’ perspective, and taking into account the impact of costs or expenses. While recent articles increasingly consider these aspects, manifold opportunities for future research remain. Journal: North American Actuarial Journal Pages: 322-340 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2078374 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2078374 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:322-340 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2071741_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Author-Name: Ponmalar Ratnam Author-X-Name-First: Ponmalar Author-X-Name-Last: Ratnam Title: Smoothed Quantiles for Measuring Discrete Risks Abstract: Many risk measures can be defined through the quantile function of the underlying loss variable (e.g., a class of distortion risk measures). When the loss variable is discrete or mixed, however, the definition of risk measures has to be broadened, which makes statistical inference trickier. To facilitate a straightforward transition from the risk measurement literature of continuous loss variables to that of discrete, in this article we study smoothing of quantiles for discrete variables. Smoothed quantiles are defined using the theory of fractional or imaginary order statistics, which was originated by Stigler (1977). To prove consistency and asymptotic normality of sample estimators of smoothed quantiles, we utilize the results of Wang and Hutson (2011) and generalize them to vectors of smoothed quantiles. Further, we thoroughly investigate extensions of this methodology to discrete populations with infinite support (e.g., Poisson and zero-inflated Poisson distributions). Furthermore, large- and small-sample properties of the newly designed estimators are investigated theoretically and through Monte Carlo simulations. Finally, applications of smoothed quantiles to risk measurement (e.g., estimation of distortion risk measures such as Value at Risk, conditional tail expectation, and proportional hazards transform) are discussed and illustrated using automobile accident data. Comparisons between the classical (and linearly interpolated) quantiles and smoothed quantiles are performed as well. Journal: North American Actuarial Journal Pages: 253-277 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2071741 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2071741 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:253-277 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2099426_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tsz Chai Fung Author-X-Name-First: Tsz Chai Author-X-Name-Last: Fung Author-Name: George Tzougas Author-X-Name-First: George Author-X-Name-Last: Tzougas Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Mixture Composite Regression Models with Multi-type Feature Selection Abstract: The aim of this article is to present a mixture composite regression model for claim severity modeling. Claim severity modeling poses several challenges such as multimodality, tail-heaviness, and systematic effects in data. We tackle this modeling problem by studying a mixture composite regression model for simultaneous modeling of attritional and large claims and for considering systematic effects in both the mixture components as well as the mixing probabilities. For model fitting, we present a group-fused regularization approach that allows us to select the explanatory variables that significantly impact the mixing probabilities and the different mixture components, respectively. We develop an asymptotic theory for this regularized estimation approach, and fitting is performed using a novel generalized expectation-maximization algorithm. We exemplify our approach on a real motor insurance dataset. Journal: North American Actuarial Journal Pages: 396-428 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2099426 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2099426 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:396-428 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2201565_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Patrick L. Brockett Author-X-Name-First: Patrick L. Author-X-Name-Last: Brockett Title: In Memoriam: Ken Seng Tan and His Contributions to Actuarial Science, Finance, and Agricultural Insurance Journal: North American Actuarial Journal Pages: 209-210 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2023.2201565 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2201565 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:209-210 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2082986_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Boheng Su Author-X-Name-First: Boheng Author-X-Name-Last: Su Author-Name: Sharon Tennyson Author-X-Name-First: Sharon Author-X-Name-Last: Tennyson Title: Price Subsidies and the Demand for Automobile Insurance Abstract: This article tests for regulation-induced adverse selection in the Massachusetts automobile insurance market during the 1990–2004 period of fix-and-establish rate regulation. We demonstrate the application of the test for adverse selection in Finkelstein and Poterba (Journal of Risk and Insurance 81 (4):709–34, 2014) to a regulated insurance market using group-level panel data on purchase amounts and loss costs. Differences between rates that incorporate state-mandated restrictions and those based on actuarial estimates provide a proxy for the unused observables needed to implement the test. Consistent with regulation-induced adverse selection, proxy values indicating higher unpriced risk are statistically significant and positively related to both insurance purchases and loss costs. Journal: North American Actuarial Journal Pages: 341-354 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2082986 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2082986 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:341-354 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2073453_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Shang Wu Author-X-Name-First: Shang Author-X-Name-Last: Wu Author-Name: Hazel Bateman Author-X-Name-First: Hazel Author-X-Name-Last: Bateman Author-Name: Ralph Stevens Author-X-Name-First: Ralph Author-X-Name-Last: Stevens Title: Optimal Portfolio Choice with Health-Contingent Income Products: The Value of Life Care Annuities Abstract: We study optimal retirement portfolio choice and welfare when individuals can choose between stocks, bonds, and either a life-contingent (life) annuity or a health-contingent (life care) annuity. We develop a life-cycle model of annuitization, consumption, and investment decisions for a single retired individual who faces stochastic capital market returns, uncertain health status, differential mortality risks, and uncertain out-of-pocket health care expenditure, including at end of life. Using the calibrated model, we find that life care annuities are more attractive than life annuities and would enhance annuity demand by 12 percentage points. Life care annuities allow individuals to reduce precautionary savings and consume more throughout retirement, with individuals willing to pay a loading of up to 21% for access to the product. Journal: North American Actuarial Journal Pages: 278-302 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2073453 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2073453 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:278-302 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1993927_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ian Duncan Author-X-Name-First: Ian Author-X-Name-Last: Duncan Author-Name: Andrew Mackenzie Author-X-Name-First: Andrew Author-X-Name-Last: Mackenzie Author-Name: Elise Bonfiglio Author-X-Name-First: Elise Author-X-Name-Last: Bonfiglio Author-Name: Thomas Wrigley Author-X-Name-First: Thomas Author-X-Name-Last: Wrigley Author-Name: Xiyue Liao Author-X-Name-First: Xiyue Author-X-Name-Last: Liao Title: Shared Savings Model Risk in the MSSP Program Abstract: The Centers for Medicare and Medicaid Services (CMS) introduced the Medicare Shared Savings Program (MSSP) for accountable care organizations (ACOs) as part of the Affordable Care Act. Participating ACOs accept risk for the financial outcomes of their assigned populations and share in gains (and, depending on the ACO model, losses) when these are generated. Gains and losses are calculated by comparing actual costs of the ACO population against a benchmark cost based on the historical performance of members in the ACO. Participating ACOs are at risk of model error. Because of stochastic variance in cost distributions and the imperfect operation of the risk-adjustment process, there is a nontrivial probability that an ACO may experience a false positive (gains are calculated where no gains were actually generated) or false negative (a loss is calculated by the model when no losses were actually generated). Using a sample of Medicare fee-for-service data, we model outcomes for typical ACOs and for ACOs consisting of chronic patients. For a typical ACO, the probability of model error resulting in a false positive or false negative outcome is between 5% and 8%. Chronic populations with higher variance have higher probabilities of model error, between 26% and 28% for a diabetes population, and about 23% for a cancer population. In the case of an ACO that generates gains through increased efficiency, model error can result in the ACO failing to realize gains, or even (in a minority of cases) require a reimbursement to the payer. From the perspective of the payer with a number of ACOs, the average overpayment or recovery will be minor. The percentage overpayment (recovery) increases as the prevalence of chronic patients increases. For a population of cancer patients a payer can expect to pay (or recover) between 1.0% and 2.0% of claims, while for a diabetes population the range is 1.5–2.5%. For an individual ACO the loss or gain is more significant because the ACO gains or loses the full amount, with a relatively high probability. While this study has focused on the Medicare Shared Savings Program, the MSSP is just an example of a class of gainsharing models that is increasingly prevalent in value-based contracts. Payers and providers who negotiate value-based contracts need to be aware of and account for model risk in their contracts, particularly as the sizes of populations under management become smaller. Journal: North American Actuarial Journal Pages: 242-252 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2021.1993927 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1993927 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:242-252 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_1978850_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: George Tzougas Author-X-Name-First: George Author-X-Name-Last: Tzougas Author-Name: Alice Pignatelli di Cerchiara Author-X-Name-First: Alice Pignatelli Author-X-Name-Last: di Cerchiara Title: Bivariate Mixed Poisson Regression Models with Varying Dispersion Abstract: The main purpose of this article is to present a new class of bivariate mixed Poisson regression models with varying dispersion that offers sufficient flexibility for accommodating overdispersion and accounting for the positive correlation between the number of claims from third-party liability bodily injury and property damage. Maximum likelihood estimation for this family of models is achieved through an expectation-maximization algorithm that is shown to have a satisfactory performance when three members of this family, namely, the bivariate negative binomial, bivariate Poisson–inverse Gaussian, and bivariate Poisson–Lognormal distributions with regression specifications on every parameter are fitted on two-dimensional motor insurance data from a European motor insurer. The a posteriori, or bonus-malus, premium rates that are determined by these models are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. Finally, we present an extension of the proposed approach with varying dispersion by developing a bivariate Normal copula-based mixed Poisson regression model with varying dispersion and dependence parameters. This approach allows us to consider the influence of individual and coverage-specific risk factors on the mean, dispersion, and copula parameters when modeling different types of claims from different types of coverage. For expository purposes, the Normal copula paired with negative binomial distributions for marginals and regressors on the mean, dispersion, and copula parameters is fitted on a simulated dataset via maximum likelihood. Journal: North American Actuarial Journal Pages: 211-241 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2021.1978850 File-URL: http://hdl.handle.net/10.1080/10920277.2021.1978850 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:211-241 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2077220_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jiang Cheng Author-X-Name-First: Jiang Author-X-Name-Last: Cheng Author-Name: Frank Y. Feng Author-X-Name-First: Frank Y. Author-X-Name-Last: Feng Author-Name: Xudong Zeng Author-X-Name-First: Xudong Author-X-Name-Last: Zeng Title: Pay-As-You-Drive Insurance: Modeling and Implications Abstract: Pay-as-you-drive (PAYD) insurance is an exciting innovation. We develop a dynamic model to study PAYD insurance from the policyholder’s utility maximization perspective. We demonstrate that PAYD insurance does benefit the policyholder by reducing premium paid and increasing the total utility derived from auto usage and wealth. PAYD insurance may also improve overall social welfare by incentivizing customers to drive less. We illustrate that PAYD insurance is more efficient than fuel tax in reducing mileage due to the concavity relation of premium and driving distance. Finally, we derive a cut-off value of mileage below which policyholders who drive with traditional insurance should switch to a PAYD policy. Our research proposes a reliable theoretical framework, and confirms that PAYD insurance benefits both individual customers and society as a whole. Journal: North American Actuarial Journal Pages: 303-321 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2077220 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2077220 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:303-321 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2087679_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fabio Baione Author-X-Name-First: Fabio Author-X-Name-Last: Baione Author-Name: Davide Biancalana Author-X-Name-First: Davide Author-X-Name-Last: Biancalana Author-Name: Paolo De Angelis Author-X-Name-First: Paolo Author-X-Name-Last: De Angelis Title: A Two-Part Beta Regression Approach for Modeling Surrenders and Withdrawals in a Life Insurance Portfolio Abstract: Beta regression is a flexible tool in modeling proportions and rates, but is rarely applied in th actuarial field. In this article, we propose its application in the context of policyholder behavior and particularly to model surrenders and withdrawals. Surrender implies the expiration of the contract and denotes the payment of the surrender value, which is contractually defined. Withdrawal does not imply the termination of the contract and denotes the payment of a cash amount, left to the discretion of the policyholder, within the limits of the surrender value. Moreover, the Actuarial Standard of Practice 52 states that, for surrender and withdrawal estimation, the actuary should take into account several risk factors that could influence the phenomenon. To this aim, we introduce a two-part Beta regression model, where the first part consists in the estimate of the number of surrenders and withdrawals by means of a multinomial regression, as an extension of the logistic regression model frequently used in the empirical literature just to estimate surrender. Then, considering the uncertainty on the amount withdrawn, we express it as a proportion of surrender value; in this way, it assumes values continuously in the interval (0,1) and it is compliant with a Beta distribution. Therefore, in the second part, we propose the adoption of a Beta regression approach to model the proportion withdrawn of the surrender value. Our final goal is to apply our model on a real-life insurance portfolio providing the estimates of the number of surrenders and withdrawals as well as the corresponding cash amount for each risk class considered. Journal: North American Actuarial Journal Pages: 380-395 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2087679 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2087679 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:380-395 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2086141_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Douglas Bujakowski Author-X-Name-First: Douglas Author-X-Name-Last: Bujakowski Author-Name: Shinichi Kamiya Author-X-Name-First: Shinichi Author-X-Name-Last: Kamiya Title: Estimating Spillover Effects in Property and Casualty Insurance Consumption Abstract: The determinants of insurance consumption have been extensively studied, yet spatial correlations are rarely considered within this framework. In this article, we discuss several channels through which spatial dependence may arise and test for spatial dependence using six years (2009–2014) of province, city, and firm-level data from China. Results suggest that spatial spillover effects are large and have the potential to seriously bias marginal effect estimates if neglected. Specifically, when regions experience similar changes in determinants, marginal effect estimates in spatial models are nearly 1.5 times that implied by aspatial models. Additionally, we investigate the sources of the spatial dependence and find that cross-border spillovers occur within and between firms. Journal: North American Actuarial Journal Pages: 355-379 Issue: 2 Volume: 27 Year: 2023 Month: 4 X-DOI: 10.1080/10920277.2022.2086141 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2086141 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:2:p:355-379 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2034507_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Martin Eling Author-X-Name-First: Martin Author-X-Name-Last: Eling Author-Name: Mauro Elvedi Author-X-Name-First: Mauro Author-X-Name-Last: Elvedi Author-Name: Greg Falco Author-X-Name-First: Greg Author-X-Name-Last: Falco Title: The Economic Impact of Extreme Cyber Risk Scenarios Abstract: Numerous industry studies discuss the economic effects of potentially extreme cyber incidents, with considerable variation in the applied methodology and estimated costs. We implement a dynamic inoperability input–output model that allows a consistent analysis and comparison of the economic impacts resulting from six widely discussed cyber risk scenarios. Our model accounts for the frequently omitted qualitative context of the scenarios to be considered as part of the economic projection. Overall, our loss estimations remain in an insurable range from US$0.7 to 35 billion. To our knowledge, this is the first effort to develop a standardized evaluation framework that allows for a consistent assessment of cyber risk scenarios, thereby enabling comparability. Journal: North American Actuarial Journal Pages: 429-443 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2034507 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2034507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:429-443 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2112233_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Pengcheng Zhang Author-X-Name-First: Pengcheng Author-X-Name-Last: Zhang Author-Name: Enrique Calderín-Ojeda Author-X-Name-First: Enrique Author-X-Name-Last: Calderín-Ojeda Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Author-Name: Xueyuan Wu Author-X-Name-First: Xueyuan Author-X-Name-Last: Wu Title: Bayesian Multivariate Mixed Poisson Models with Copula-Based Mixture Abstract: It is common practice to use multivariate count modeling in actuarial literature when dealing with claim counts from insurance policies with multiple covers. One possible way to construct such a model is to implement copula directly on discrete margins. However, likelihood inference under this construction involves the computation of multidimensional rectangle probabilities, which could be computationally expensive, especially in the elliptical copula case. Another potential approach is based on the multivariate mixed Poisson model. The crucial work under this method is to find an appropriate multivariate continuous distribution for mixing parameters. By virtue of the copula, this issue could be easily addressed. Under such a framework, the Markov chain Monte Carlo (MCMC) method is a feasible strategy for inference. The usefulness of our model is then illustrated through a real-life example. The empirical analysis demonstrates the superiority of adopting a copula-based mixture over other types of mixtures. Finally, we demonstrate how those fitted models can be applied to the insurance ratemaking problem in a Bayesian context. Journal: North American Actuarial Journal Pages: 560-578 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2112233 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2112233 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:560-578 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2110123_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Atefeh Kanani Dizaji Author-X-Name-First: Atefeh Kanani Author-X-Name-Last: Dizaji Author-Name: Amir T. Payandeh Najafabadi Author-X-Name-First: Amir T. Author-X-Name-Last: Payandeh Najafabadi Title: Updating Bonus–Malus Indexing Mechanism to Adjust Long-Term Health Insurance Premiums Abstract: Economic shocks, high inflation, longevity, and new emerging technologies make the long-term health care insurance challenging for insurers. To overcome this problem, an indexing mechanism has been employed to update predicted premiums based on the new information in hand. Such indexing mechanisms have thus far failed to consider the available policyholder’s risk experience at its updating time. This article employs the well-known bonus–malus system to introduce a bonus–malus indexing mechanism that takes into account the policyholder’s risk experience in its updating mechanism. More precisely, it uses the bonus–malus system’s idea to update the premium of each policyholder based upon her or his risk experience as well as updated inflation. The theoretical foundation of this approach has been developed and its practical implementation is shown through a simulation study. Journal: North American Actuarial Journal Pages: 546-559 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2110123 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2110123 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:546-559 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2108453_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Title: A Model Stacking Approach for Forecasting Mortality Abstract: This article adopts a machine learning method called stacked generalization for forecasting mortality. The main idea is to combine the forecasts from different projection models or algorithms in a certain way in order to increase the prediction accuracy. In particular, the article considers not just the traditionally used mortality projection models, such as the Lee–Carter and CBD models and their extensions, but also some learning algorithms called feedforward and recurrent neural networks that are starting to gain attention in the actuarial literature. For blending the different forecasts, the article examines a number of choices, including simple averaging, weighted averaging, linear regression, and neural network. Using U.S. mortality data, it is found that the proposed stacking approach often outperforms the cases where a projection model or algorithm is applied individually, and that neural networks tend to generate better results than many of the traditional models. Journal: North American Actuarial Journal Pages: 530-545 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2108453 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2108453 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:530-545 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2100425_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jean-François Bégin Author-X-Name-First: Jean-François Author-X-Name-Last: Bégin Title: Ensemble Economic Scenario Generators: Unity Makes Strength Abstract: Over the last 40 years, various frameworks have been proposed to model economic and financial variables relevant to actuaries. These models are helpful, but searching for a unique model that gives optimal forecasting performance can be frustrating and ultimately futile. This study therefore investigates whether we can create better, more reliable economic scenario generators by combining them. We first consider eight prominent economic scenario generators and apply Bayesian estimation techniques to them, thus allowing us to account for parameter uncertainty. We then rely on predictive distribution stacking to obtain optimal model weights that prescribe how the models should be averaged. The weights are constructed in a leave-future-out fashion to build truly out-of-sample forecasts. An extensive empirical study based on three economies—the United States, Canada, and the United Kingdom—and data from 1992 to 2021 is performed. We find that the optimal weights change over time and differ from one economy to another. The out-of-sample behavior of the ensemble model compares favorably to the other eight models: the ensemble model’s performance is substantially better than that of the worse models and comparable to that of the better models. Creating ensembles is thus beneficial from an out-of-sample perspective because it allows for robust and reasonable forecasts. Journal: North American Actuarial Journal Pages: 444-471 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2100425 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2100425 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:444-471 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2123360_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Patricia Born Author-X-Name-First: Patricia Author-X-Name-Last: Born Author-Name: J. Bradley Karl Author-X-Name-First: J. Author-X-Name-Last: Bradley Karl Author-Name: Robert Klein Author-X-Name-First: Robert Author-X-Name-Last: Klein Title: An Empirical Assessment of Regulatory Lag in Insurance Rate Filings Abstract: In this article, we evaluate factors that help to explain an important source of variation in insurers' rate filing experiences across states and over time for personal automobile insurance. Using a new source of data from personal auto insurance rate filings for all U.S. insurers, we examine factors associated with regulatory lag. The timeliness of the disposition of insurers' rate filings is important, as significant delays can undermine the usefulness of the actuarial analysis required for justifying rate changes and may result in rate inadequacy pending the approval of rate increases. While there is a considerable literature on the effect of rate regulation regimes on insurance market outcomes, this is the first article that evaluates factors associated with regulatory lag. We use a principal components approach to explore the relative influence of various factors on the timeliness of filing approval. These factors are associated with (1) industry interest, resources, and influence, (2) demand conditions, complexity, and saliency, (3) the goals of political elites, and (4) the goals and resources of regulators as important drivers of insurers' rate filing experience. We find that state rate filing statutes account for some of the variation in regulatory lag and identify other significant factors that explain the variation in the timeliness of rate approvals across states and over time. Journal: North American Actuarial Journal Pages: 602-617 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2123360 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2123360 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:602-617 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2106576_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jingshu Luo Author-X-Name-First: Jingshu Author-X-Name-Last: Luo Author-Name: Martin F. Grace Author-X-Name-First: Martin F. Author-X-Name-Last: Grace Title: Does Public Health Insurance Expansion Influence Medical Liability Insurance Prices? The Case of the ACA’s Optional Medicaid Expansion Abstract: Medical liability insurance covers physicians’ liability, and its price could affect physicians’ practice. In this article, we use a unique county-level dataset to study how medical liability insurance prices of three specialties, internal medicine, general surgery, and obstetrics–gynecology (OB-GYN), changed after the Affordable Care Act (ACA) elective Medicaid expansion provision. The Medicaid expansion has largely increased the demand for health care services and potentially exposed physicians to higher medical liability risks. With higher expected losses, insurers could react by increasing medical malpractice insurance prices. We first study all counties in states that elected to expand Medicaid and compare them to counties in nonexpansion states. Then we narrow our analysis to consider differential effects in bordering counties with different Medicaid expansion statuses over the period 2010–2018. In both samples, we find significantly higher medical liability insurance prices 2 years after the expansion (on average) in expansion states in comparison to nonexpansion states, and the difference is larger for physicians practicing internal medicine (6–8% at 2 years after expansion) and general surgery (12–16% at 2 years after expansion) but less so for OB-GYN. Our OB-GYN results are likely because significant numbers of births were already covered under Medicaid and were not affected by the expansion. Our finding suggests that the expansion of health insurance increases liability costs to medical practitioners. Journal: North American Actuarial Journal Pages: 508-529 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2106576 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2106576 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:508-529 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2102040_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Thiago Pedra Signorelli Author-X-Name-First: Thiago Pedra Author-X-Name-Last: Signorelli Author-Name: Carlos Heitor Campani Author-X-Name-First: Carlos Heitor Author-X-Name-Last: Campani Author-Name: César da Rocha Neves Author-X-Name-First: César da Rocha Author-X-Name-Last: Neves Title: Extrapolating Long-Run Yield Curves: An Innovative and Consistent Approach Abstract: This article proposes a method to build term structures that are consistent with market data and that provide interest rates for which the volatility, on average, decreases as maturities increase. The method is designed for continuous repetitive use and is consistent with work by Diebold and Li, providing reasonable extrapolated rates, with an appropriate level of volatility over time. The Svensson model is adopted, and its parameters are estimated by the combination of a genetic algorithm and a quasi-Newton nonlinear optimization method. We innovate with a new objective function that focuses on both parts of the estimated curves (interpolated and extrapolated). For this purpose, a stability component is added. The new objective function aims to solve the problem of estimating long-term rates not observable in the market, for which the estimates are usually artificially stable or excessively volatile. The results show that the estimation method is able to bring the volatility of extrapolated rates to levels consistent with those observed for the longest liquid rate. Estimation errors are small enough and there is no statistical evidence that they are biased. The method is useful for the insurance market, since it provides interest rates that do not lead to artificially stable or excessively volatile technical provisions. Journal: North American Actuarial Journal Pages: 472-492 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2102040 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2102040 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:472-492 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2123361_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peng Shi Author-X-Name-First: Peng Author-X-Name-Last: Shi Author-Name: Kun Shi Author-X-Name-First: Kun Author-X-Name-Last: Shi Title: Non-Life Insurance Risk Classification Using Categorical Embedding Abstract: This article presents several actuarial applications of categorical embedding in the context of non-life insurance risk classification. In non-life insurance, many rating factors are naturally categorical, and often the categorical variables have a large number of levels. The high cardinality of categorical rating variables presents challenges in the implementation of traditional actuarial methods. Categorical embedding that is proposed in the machine learning literature for handling categorical variables has recently received attention in actuarial studies. The method is inspired by the neural network language models for learning text data and maps a categorical variable into a real-valued representation in the Euclidean space. Using a property insurance claims we demonstrate the use of categorical embedding in three applications. The first shows how embeddings are used to construct rating classes and calculate rating relativities for a single insurance risk. The second concerns predictive modeling for multivariate insurance risks and emphasizes the effects of dependence on tail risks. The third focuses on pricing new products where transfer learning is used to gather knowledge from existing products. Journal: North American Actuarial Journal Pages: 579-601 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2123361 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2123361 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:579-601 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2099425_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Patrick Brockett Author-X-Name-First: Patrick Author-X-Name-Last: Brockett Author-Name: Linda Golden Author-X-Name-First: Linda Author-X-Name-Last: Golden Author-Name: Pengyu Wei Author-X-Name-First: Pengyu Author-X-Name-Last: Wei Author-Name: Charles Yang Author-X-Name-First: Charles Author-X-Name-Last: Yang Title: Medicare Advantage, Medical Loss Ratio, Service Efficiency, and Efficiently Positive Health Outcomes Abstract: Within the context of Medicare’s enunciated triple aims of better health, better care, and lower costs, we examine the effectiveness of medical loss ratio (MLR) on health outcomes of Medicare Advantage insurers. We simultaneously examine the effect of an efficiency measure for the insurer performance: medical service utilization efficiency (an assessment of how efficiently an insurer provides medical services). This research is based upon collection and integration of several data sources: health outcome data, financial data, and medical service utilization data. The assessment procedure employs a two-stage analytical approach: efficiency analysis followed by regressions. We quantify insurer efficiency using data envelopment analysis (DEA), which determines the relative efficiency of an insurer when the inputs and outputs can both be multivariate. We then run regressions with the dependent variables being functional health outcomes (“improving or maintaining mental health,” “improving or maintaining physical health,” and “improving or maintaining physical and mental health”) and health improvement efficiency (how cost-efficient the insurer is in improving functional health outcomes). Independent variables include MLR, medical service utilization efficiency, and a rich set of control variables. We find that neither MLR nor medical service utilization efficiency provides a good regulatory and evaluation indicator for stimulating/producing functional health outcomes. On the other hand, they do both significantly relate to health improvement efficiency, and hence are both reasonable regulatory and monitoring indicators for efficiently producing positive health outcomes. Our results suggest that to enhance health improvement efficiency, medical service utilization efficiency should be incorporated as a cost-efficient regulatory and monitoring indicator when evaluating Medical Advantage insurers. Journal: North American Actuarial Journal Pages: 493-507 Issue: 3 Volume: 27 Year: 2023 Month: 7 X-DOI: 10.1080/10920277.2022.2099425 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2099425 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:3:p:493-507 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2161578_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gee Y. Lee Author-X-Name-First: Gee Y. Author-X-Name-Last: Lee Title: Multivariate Insurance Portfolio Risk Retention Using the Method of Multipliers Abstract: For an insurance company insuring multiple risks, capital allocation is an important practical problem. In the capital allocation problem, the insurance company must determine the amount of capital to assign to each policy or, equivalently, the amount of premium to be collected from each policy. Doing this relates to the problem of determining the risk retention parameters for each policy within the portfolio. In this article, the insurance risk retention problem of determining the optimal retention parameters is explored in a multivariate context. Given an underlying claims distribution and premium constraint, we are interested in finding the optimal amount of risk to retain or, equivalently, which level of risk retention parameters should be chosen by an insurance company. The risk retention parameter may be deductible (d), upper limit (u), or coinsurance (c). We present a numerical approach to solving the risk retention problem using the method of multipliers and illustrate how it can be implemented. In a case study, the minimum amount of premium to be collected is used as a constraint to the optimization and the upper limit is optimized for each policyholder. A Bayesian approach is taken for estimation of the parameters in a simple model involving regional effects and individual policyholder effects for the Wisconsin Local Government Property Insurance Fund (LGPIF) data, where the parameter estimation is performed in the R computing environment using the Stan library. Journal: North American Actuarial Journal Pages: 787-805 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2161578 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2161578 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:787-805 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2126373_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: James M. Carson Author-X-Name-First: James M. Author-X-Name-Last: Carson Author-Name: Evan M. Eastman Author-X-Name-First: Evan M. Author-X-Name-Last: Eastman Author-Name: David L. Eckles Author-X-Name-First: David L. Author-X-Name-Last: Eckles Author-Name: Joshua D. Frederick Author-X-Name-First: Joshua D. Author-X-Name-Last: Frederick Title: Are Internal Capital Markets Ex Post Efficient? Abstract: Internal capital markets enable conglomerates to allocate capital to segments throughout the enterprise. Prior literature provides evidence that internal capital markets efficiently allocate capital based predominantly on group member prior performance, consistent with the “winner picking” hypothesis. However, existing research has not examined the critical question of how these “winners” perform subsequent to receiving internal capital—that is, do winners keep winning? We extend the literature by providing empirical evidence on whether or not internal capital markets are ex post efficient. We find, in contrast to mean reversion, that winners continue their relatively high performance. Our study contributes to the literature examining the efficiency of internal capital markets and the conglomerate discount, as well as the literature specifically examining capital allocation in financial firms. Journal: North American Actuarial Journal Pages: 630-655 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2126373 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2126373 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:630-655 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2167833_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Martin Bladt Author-X-Name-First: Martin Author-X-Name-Last: Bladt Title: A Tractable Class of Multivariate Phase-Type Distributions for Loss Modeling Abstract: Phase-type (PH) distributions are a popular tool for the analysis of univariate risks in numerous actuarial applications. Their multivariate counterparts (MPH∗), however, have not seen such a proliferation because of a lack of explicit formulas and complicated estimation procedures. A simple construction of multivariate phase-type distributions––mPH––is proposed for the parametric description of multivariate risks, leading to models of considerable probabilistic flexibility and statistical tractability. The main idea is to start different Markov processes at the same state and allow them to evolve independently thereafter, leading to dependent absorption times. By dimension augmentation arguments, this construction can be cast under the umbrella of MPH∗ class but enjoys explicit formulas that the general specification lacks, including common measures of dependence. Moreover, it is shown that the class is still rich enough to be dense on the set of multivariate risks supported on the positive orthant, and it is the smallest known subclass to have this property. In particular, the latter result provides a new short proof of the denseness of the MPH∗ class. In practice, this means that the mPH class allows for the modeling of bivariate risks with any given correlation or copula. We derive an expectation-maximization algorithm for its statistical estimation and illustrate it on bivariate insurance data. Extensions to more general settings are outlined. Journal: North American Actuarial Journal Pages: 710-730 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2023.2167833 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2167833 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:710-730 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2167832_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Liqun Diao Author-X-Name-First: Liqun Author-X-Name-Last: Diao Author-Name: Yechao Meng Author-X-Name-First: Yechao Author-X-Name-Last: Meng Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Author-Name: Tony Wirjanto Author-X-Name-First: Tony Author-X-Name-Last: Wirjanto Title: Enhancing Mortality Forecasting through Bivariate Model–Based Ensemble Abstract: We propose a bivariate model–based ensemble (BMBE) method to borrow information from the mortality data of a given pool of auxiliary populations to enhance the mortality forecasting of a target population. The BMBE method establishes a cascade of bivariate mortality models between the target population and each auxiliary population as the base learners. Then it aggregates prediction results from all of the base learners by means of an averaging strategy. Augmented common factor–type and CBD-type bivariate models are applied as the base learners as illustrative examples in the empirical studies with the Human Mortality Database. Empirical results presented in this article confirm the effectiveness of the proposed BMBE method in enhancing mortality prediction. For completeness, we also conduct a synthetic study to illustrate a particular setting for the superior performance of the BMBE method. Journal: North American Actuarial Journal Pages: 751-770 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2023.2167832 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2167832 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:751-770 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2102041_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sabyasachi Ghosh Author-X-Name-First: Sabyasachi Author-X-Name-Last: Ghosh Author-Name: Ian Smith Author-X-Name-First: Ian Author-X-Name-Last: Smith Author-Name: James Davidson Author-X-Name-First: James Author-X-Name-Last: Davidson Author-Name: Tao Fan Author-X-Name-First: Tao Author-X-Name-Last: Fan Author-Name: Ninfa Candela Author-X-Name-First: Ninfa Author-X-Name-Last: Candela Author-Name: Cynthia Tsang Author-X-Name-First: Cynthia Author-X-Name-Last: Tsang Author-Name: Troy Koch Author-X-Name-First: Troy Author-X-Name-Last: Koch Author-Name: Jason Fehr Author-X-Name-First: Jason Author-X-Name-Last: Fehr Title: Payer-Addressable Burden of Crohn’s Disease in Members Treated with Biologics in the United States: Actuarial Analysis Findings from RAINBOW Abstract: Payer-addressable burden (PAB) reflects how real-world disease-associated costs impact the per member per month (PMPM) budget of a health plan, and can help to delineate drivers of PMPM costs and inform cost-management strategies for diseases with a high cost burden, such as Crohn’s disease (CD). We aimed to evaluate the U.S. PAB of CD managed with biologics. Weighted mean costs per member with CD in the commercial health plan population between 2017 and 2019 were evaluated from a health plan actuarial perspective. In addition to the overall population of members with CD treated with adalimumab, infliximab, vedolizumab, or ustekinumab, the subpopulations of members who were naive to biologic therapies at treatment initiation and/or treatment-adherent members were also analyzed. Members treated with vedolizumab contributed the lowest PMPM costs. A similar number of members were treated with vedolizumab and ustekinumab, yet PMPM costs associated with ustekinumab were more than double those of vedolizumab. Biologic naivety and treatment adherence drove lower CD-related PMPM costs. The analyses we present here highlight that treatments and patient subgroups with lower PMPM costs are important focus areas for payers in terms of identifying strategies to manage the budget for CD in a U.S. plan population.Video AbstractRead the transcriptWatch the video on Vimeo© 2022 The Author(s). Published with license by Taylor & Francis Group, LLC Journal: North American Actuarial Journal Pages: 619-629 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2102041 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2102041 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:619-629 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2141781_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bettina Grün Author-X-Name-First: Bettina Author-X-Name-Last: Grün Author-Name: Tatjana Miljkovic Author-X-Name-First: Tatjana Author-X-Name-Last: Miljkovic Title: The Automated Bias-Corrected and Accelerated Bootstrap Confidence Intervals for Risk Measures Abstract: Different approaches to determining two-sided interval estimators for risk measures such as Value-at-Risk (VaR) and conditional tail expectation (CTE) when modeling loss data exist in the actuarial literature. Two contrasting methods can be distinguished: a nonparametric one not relying on distributional assumptions or a fully parametric one relying on standard asymptotic theory to apply. We complement these approaches and take advantage of currently available computer power to propose the bias-corrected and accelerated (BCA) confidence intervals for VaR and CTE. The BCA confidence intervals allow the use of a parametric model but do not require standard asymptotic theory to apply. We outline the details to determine interval estimators for these three different approaches using general computational tools as well as with analytical formulas when assuming the truncated Lognormal distribution as a parametric model for insurance loss data. An extensive simulation study is performed to assess the performance of the proposed BCA method in comparison to the two alternative methods. A real dataset of left-truncated insurance losses is employed to illustrate the implementation of the BCA-VaR and BCA-CTE interval estimators in practice when using the truncated Lognormal distribution for modeling the loss data. Journal: North American Actuarial Journal Pages: 731-750 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2141781 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2141781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:731-750 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2137201_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sahadeb Upretee Author-X-Name-First: Sahadeb Author-X-Name-Last: Upretee Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Title: Computing and Estimating Distortion Risk Measures: How to Handle Analytically Intractable Cases? Abstract: In insurance data analytics and actuarial practice, distortion risk measures are used to capture the riskiness of the distribution tail. Point and interval estimates of the risk measures are then employed to price extreme events, to develop reserves, to design risk transfer strategies, and to allocate capital. Often the computation of those estimates relies on Monte Carlo simulations, which, depending upon the complexity of the problem, can be very costly in terms of required expertise and computational time. In this article, we study analytic and numerical evaluation of distortion risk measures, with the expectation that the proposed formulas or inequalities will reduce the computational burden. Specifically, we consider several distortion risk measures––value-at-risk (VaR), conditional tail expectation (cte), proportional hazards transform (pht), Wang transform (wt), and Gini shortfall (gs)––and evaluate them when the loss severity variable follows shifted exponential, Pareto I, and shifted lognormal distributions (all chosen to have the same support), which exhibit common distributional shapes of insurance losses. For these choices of risk measures and loss models, only the VaR and cte measures always possess explicit formulas. For pht, wt, and gs, there are cases when the analytic treatment of the measure is not feasible. In the latter situations, conditions under which the measure is finite are studied rigorously. In particular, we prove several theorems that specify two-sided bounds for the analytically intractable cases. The quality of the bounds is further investigated by comparing them with numerically evaluated risk measures. Finally, a simulation study involving application of those bounds in statistical estimation of the risk measures is also provided. Journal: North American Actuarial Journal Pages: 689-709 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2137201 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2137201 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:689-709 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2123362_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David McCarthy Author-X-Name-First: David Author-X-Name-Last: McCarthy Title: Why Changes in PBGC and FDIC Premiums Should Not Fully Reflect Changes in Underlying Risk (With Some Application to Long-Term Private Insurance Contracts) Abstract: The degree of risk adjustment in both FDIC and PBGC premiums appears to be much smaller than actuarially fair. We explore why this is using a stylized theoretical model of multiperiod insurance contracts in the presence of moral hazard where the risk status of insureds changes over the life of the contract. If insureds value stable premiums and there is moral hazard, we show that the optimal multiperiod insurance contract for full insurance allocates greater premiums to higher risk states, and lower premiums to lower risk states, but the optimal allocation of premiums across risk states will usually not be actuarially fair. The degree of risk adjustment rises with the extent of moral hazard and falls as risk aversion rises. We extend our analysis to examine optimal risk classification in private insurance in the presence of moral hazard, with similar results. We also discuss practical considerations that further reduce the desirability and feasibility of actuarially fair risk adjustments in premiums for the FDIC and PBGC, and show how our model extends prior work on social insurance with moral hazard. Journal: North American Actuarial Journal Pages: 656-674 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2123362 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2123362 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:656-674 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2123364_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Title: Conformal Prediction Credibility Intervals Abstract: In the predictive modeling context, the credibility estimator is a point predictor; it is easy to calculate and avoids the model misspecification risk asymptotically, but it provides no quantification of inferential uncertainty. A Bayesian prediction interval quantifies uncertainty of prediction, but it often requires expensive computation and is subject to model misspecification risk even asymptotically. Is there a way to get the best of both worlds? Based on a powerful machine learning strategy called conformal prediction, this article proposes a method that converts the credibility estimator into a conformal prediction credibility interval. This conformal prediction credibility interval contains the credibility estimator, has computational simplicity, and guarantees finite-sample validity at a pre-assigned coverage level. Journal: North American Actuarial Journal Pages: 675-688 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2022.2123364 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2123364 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:675-688 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2167835_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Thorsten Moenig Author-X-Name-First: Thorsten Author-X-Name-Last: Moenig Author-Name: Chenxin Xu Author-X-Name-First: Chenxin Author-X-Name-Last: Xu Title: Valuing Lifetime Withdrawal Guarantees in RILAs Abstract: In recent years, registered index-linked annuities (RILAs) have reinvigorated the equity-linked annuities market in the United States. Now insurers are beginning to add lifetime withdrawal guarantees (GLWBs) to these products. GLWBs have been well studied in the context of traditional variable annuities, where they are infamous for the risk exposure they create on insurers’ balance sheets. In this study, we present a simple pricing model for GLWBs embedded in RILA policies and offer an extensive numerical illustration that quantifies their pricing and risk exposure for various RILA contracts. We find that a GLWB rider—unlike for fixed index annuities—exposes RILA carriers to considerable long-term financial risks, comparable to a variable annuity account with a heavily reduced equity exposure (∼40%). Journal: North American Actuarial Journal Pages: 771-786 Issue: 4 Volume: 27 Year: 2023 Month: 10 X-DOI: 10.1080/10920277.2023.2167835 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2167835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:27:y:2023:i:4:p:771-786 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2176323_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Suikai Gao Author-X-Name-First: Suikai Author-X-Name-Last: Gao Author-Name: Guillaume Bagnarosa Author-X-Name-First: Guillaume Author-X-Name-Last: Bagnarosa Author-Name: Gareth W. Peters Author-X-Name-First: Gareth W. Author-X-Name-Last: Peters Author-Name: Matthew Ames Author-X-Name-First: Matthew Author-X-Name-Last: Ames Author-Name: Tomoko Matsui Author-X-Name-First: Tomoko Author-X-Name-Last: Matsui Title: A Dynamic Stochastic Integrated Climate–Economic Spatiotemporal Model for Agricultural Insurance Products Abstract: We propose a new methodology for area yield distribution modeling. We explore a variety of new hybrid data emulators for spatialtemporal statistical modeling of agricultural crop yields. The regression models explored leverage from a combination of model-generated and observed features incorporating climate/weather variables relating to temperature and precipitation over space and time and agricultural variables for farms such as crop allocations, crop types, land use, and crop rotation. This provides the modeling framework to achieve a hierarchical decomposition of the yield distribution at multiple spatial scales over time, allowing us to study both county- and individual farm-level information with suitably selected weighting functions that take into account farm size and crop type. A core component of our model framework is the climate model component that involves a spatialtemporal local approximate seasonal autoregressive integrated moving average Gaussian process (La-SARIMA-GP) model that is suitable for accurately studying local monthly temperatures and rainfalls. Upon construction of the crop yield model, we demonstrate that for practitioners, there is a clear incentive to consider such a model because it accommodates apportioning of the county yield information to the farms level. This is of significance for both individual and index-based agricultural crop insurance product design and for farm risk management. We demonstrate an application of our model in the insurance context of crop insurance risk pooling and insurance policy rating where we investigate the impact of different temporal and spatial interpolation methods on insurance loss ratios using a rating game. Journal: North American Actuarial Journal Pages: 27-56 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2176323 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2176323 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:27-56 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2162924_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Jinggong Zhang Author-X-Name-First: Jinggong Author-X-Name-Last: Zhang Title: Flexible Weather Index Insurance Design with Penalized Splines Abstract: In this article, we propose a flexible framework for the design of weather index insurance (WII) based on penalized spline methods. The aim is to find the indemnity function that optimally characterizes the intricate relationship between agricultural production losses and weather variables and thus effectively improves policyholders’ utilities. We use B-spline functions to define the feasible set of the optimization problem and a penalty function to avoid the “overfitting” issue. The proposed design framework is applied to an empirical study in which we use precipitation and vapor pressure deficit (VPD) to construct an index insurance contract for corn producers in Illinois. Numerical evidence shows that the resulting optimal insurance contract effectively enhances policyholder’s utility, even in the absence of the government’s premium subsidy. In addition, the performance of our proposed index insurance is robust to a variety of key factors, and the general payment structure is highly interpretable for marketing purposes. All of these merits indicate its potential to increase efficiency of the agricultural insurance market and thus enhance social welfare. Journal: North American Actuarial Journal Pages: 1-26 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2022.2162924 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2162924 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:1-26 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2185260_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Yanlin Shi Author-X-Name-First: Yanlin Author-X-Name-Last: Shi Title: Coherent Mortality Forecasting with a Model Averaging Approach: Evidence from Global Populations Abstract: Accurate forecasts and analyses of mortality rates are essential to many economic and finance practices, such as the designing of pension schemes. Recent studies have proposed advanced mortality models with age coherent forecasts, such that long-term predictions will not diverge infinitely among ages. Despite their effectiveness, individual models are inevitably misspecified in the empirical analysis, which reduces the reliableness. In this article, we propose a model averaging approach (MAA) that allows for age-specific weights and asymptotically achieves age coherence. Relevant technical details are also provided. The proposed method balances both the in-sample fitting and out-of-sample forecasting, with a uniquely designed smoothness penalty to resolve the potential overfitting and thus avoid abrupt changes in the long-term mortality forecasting. Using a large empirical dataset of 10 countries including 0 to 100 ages and spanning 1950 to 2018, the outstanding forecasting performance of MAA is presented. This robustly holds in various sensitivity analyses and is supported by simulation evidence. A case study is further conducted to discuss the improved forecasting efficiency of MAA, as well as its usefulness in economic and finance applications such as the annuity pricing. The proposed MAA approach is therefore a useful tool in forecasting mortality data for other practices. Journal: North American Actuarial Journal Pages: 218-235 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2185260 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2185260 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:218-235 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2159839_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Emmanuel Hamel Author-X-Name-First: Emmanuel Author-X-Name-Last: Hamel Author-Name: Yvonne Chueh Author-X-Name-First: Yvonne Author-X-Name-Last: Chueh Author-Name: Donald Davendra Author-X-Name-First: Donald Author-X-Name-Last: Davendra Title: Economic Representative Scenarios for Variable Annuity Dynamic Hedging of GMMB and GMDB Abstract: Variable annuities introduce significant risk for the insurers. To control this risk, insurers generally use dynamic hedging models. In practice, calculations for dynamic hedging models for variable annuities are computationally intensive since they require many nested stochastic scenario projections with outer and inner loops. In this article, we study the relationship between the hedging errors and the descriptive statistics of economic scenarios. Then, using the relationships between the hedging errors and the descriptive statistics of the economics scenarios, we present two novel scenario selection algorithms to determine economic representative scenarios (ERS) to run for dynamic risk hedging models. We do this for guaranteed minimum maturity benefit (GMMB) and guaranteed minimum death benefit (GMDB). We also benchmark these new algorithms against a control variate algorithm and Monte Carlo simulations. One of the two proposed novel scenario selection algorithms, the adapted Clara algorithm gives a lower mean absolute deviation of the conditional tail expectation (CTE) than the control variate method and Monte Carlo simulations for the same number of scenarios. Also, 500 representative scenarios selected by the adapted Clara algorithm generate a mean absolute deviation of the CTE95 of the hedging errors approximately equivalent to 1000 (or more in some cases) Monte Carlo simulations for 5 years GMMB and GMDB. Journal: North American Actuarial Journal Pages: 73-103 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2022.2159839 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2159839 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:73-103 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2182792_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Wenjun Zhu Author-X-Name-First: Wenjun Author-X-Name-Last: Zhu Title: A Deep Factor Model for Crop Yield Forecasting and Insurance Ratemaking Abstract: Effective agricultural insurance and risk management programs rely on accurate crop yield forecasting. In this article, a novel deep factor model for crop yield forecasting and crop insurance ratemaking is proposed. This framework first utilizes a deep autoencoder to extract a latent factor, called the production index, that integrates salient spatial temporal patterns in the original yield data. Then, a concatenated deep learning model is constructed to enhance the modeling of the production index and the reconstruction of crop yields. Convolutional neural networks are employed to capture the high-dimensional and highly nonlinear structure within the crop yield data, as well as its interactions with weather and economic variables. The proposed deep factor framework is applied to the county-level data in the state of Iowa. Empirical results show that the newly proposed deep factor model significantly improves the prediction accuracy, especially in the test set. Based on a retain–cede crop insurance rating game between a private insurer and the government, we show that the proposed deep factor model provides economically and statistically significant improvement over the current Risk Management Agency ratemaking methodology. Journal: North American Actuarial Journal Pages: 57-72 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2182792 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2182792 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:57-72 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2167834_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Andrés M. Villegas Author-X-Name-First: Andrés M. Author-X-Name-Last: Villegas Author-Name: Madhavi Bajekal Author-X-Name-First: Madhavi Author-X-Name-Last: Bajekal Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Author-Name: Luke Zhou Author-X-Name-First: Luke Author-X-Name-Last: Zhou Title: Key Drivers of Long-Term Rates of Mortality Improvements in the United States: Period, Cohort, and Cause of Death Analysis, 1959–2016 Abstract: The main objective of this article is to identify significant mortality drivers in the U.S. population that have a high likelihood of being linked to the historical improvement or deterioration of mortality over the 1959 to 2016 period. To achieve this objective, we integrate cause of death modeling with epidemiological evidence to explain the underlying drivers. In particular, we analyze cause of death data for six broad groups of causes including circulatory diseases, neoplasms, respiratory diseases, digestive system diseases, external causes, and other causes. We also identify and analyze some key causes that serve as markers of trends in behavioral risk factors that could drive mortality change. These risk factors are AIDS and tuberculosis, alcohol abuse, dementia and Alzheimer’s disease, diabetes and obesity, drug dependency, homicide, hypertensive disease, self-harm, and smoking. We analyze these different groupings of causes of death using life expectancy decomposition techniques and formal age–period–cohort decomposition of both mortality rates and mortality improvement rates. We find that the story of mortality evolution in the United States in the second half of the 20th century, which continued into the first decade of the 21st century, has been mainly a story of mortality improvements from circulatory diseases. Nevertheless, despite the clear dominance of circulatory diseases as a leading cause of death and as the main contributor to mortality improvements between 1959 and 2016, the decline in mortality has been more complex. The trajectories of other major causes have ebbed and flowed, and the patterns of behavioral risk factors that contribute to overall mortality change have seen changes between generations. Journal: North American Actuarial Journal Pages: 187-217 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2167834 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2167834 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:187-217 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2176324_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Thorsten Moenig Author-X-Name-First: Thorsten Author-X-Name-Last: Moenig Author-Name: Bobby Samuelson Author-X-Name-First: Bobby Author-X-Name-Last: Samuelson Title: A Comparison of Index-Linked Annuities Abstract: In recent years, index-linked annuities (ILAs) have gained considerable popularity in the U.S. retirement savings market, reflected by rapidly increasing sales and new product developments. These products offer investors some equity exposure while also providing financial protection against downside risk. The products differ primarily based on how much the investor could potentially lose (and gain) year over year. A second (and related) differential is that some products are considered “fixed annuities” (due to their principal protection) and, as such, they face fewer regulations, among other benefits, compared to “variable annuities.” We describe the most common types of ILAs, discuss their differences, and compare them from the perspective of a typical investor by numerically solving dynamic optimization problems. When calibrating the model to current market conditions, we find that the newly introduced fixed index-linked annuity is the preferred product for investors with moderate to high levels of risk aversion, particularly if carriers can convert the lighter regulatory framework into moderately higher cap rates. On the other hand, investors who are only mildly risk averse or even risk-loving would generally prefer a traditional mutual fund investment or a registered index-linked annuity with a buffer feature. Our insights should prove useful for actuaries working on product development as well as for insurance agents and retirement planners. Journal: North American Actuarial Journal Pages: 104-125 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2176324 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2176324 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:104-125 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2161577_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Xiyue Liao Author-X-Name-First: Xiyue Author-X-Name-Last: Liao Author-Name: Ian Duncan Author-X-Name-First: Ian Author-X-Name-Last: Duncan Author-Name: Samuel O’Neill Author-X-Name-First: Samuel Author-X-Name-Last: O’Neill Title: Alternative Predictive Models for Medicare Patient Cost Abstract: As health care expenditures increase, patient cost mitigation becomes more essential. Cost mitigation through intervention programs such as accountable care organizations relies on the ability to accurately predict patient risk, which is notoriously difficult because of highly skewed data. We examine the Medicare Limited dataset (a 5% sample of Medicare claims) that includes demographics, costs, and health conditions. We first consider the Centers for Medicare and Medicaid Services (CMS) currently used Hierarchical Condition Category (HCC) linear model and then implement more complex two-part generalized additive and random forest models to predict patient costs in a future year based on current-year data. We find that the latter models more accurately predict the entire distribution of Medicare patient costs and can better support the existing cost mitigation frameworks. The two-part lognormal generalized additive model is chosen as the optimal model for its robust performance and reasonable interpretability when the data have extreme values. Journal: North American Actuarial Journal Pages: 126-138 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2022.2161577 File-URL: http://hdl.handle.net/10.1080/10920277.2022.2161577 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:126-138 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2177676_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Brian Hartman Author-X-Name-First: Brian Author-X-Name-Last: Hartman Author-Name: Courtney Larson Author-X-Name-First: Courtney Author-X-Name-Last: Larson Author-Name: Christopher Kunkel Author-X-Name-First: Christopher Author-X-Name-Last: Kunkel Author-Name: Cason Wight Author-X-Name-First: Cason Author-X-Name-Last: Wight Author-Name: Richard L. Warr Author-X-Name-First: Richard L. Author-X-Name-Last: Warr Title: A Two-Part Model of the Individual Costs of Chronic Kidney Disease Abstract: Chronic kidney disease (CKD) affects many lives and has a large impact on health systems around the world. To better understand and predict costs for insurance plan people with CKD in the United States, we built a new model of their individual costs. Our model is the first to explicitly model both the CKD stage transition process and the distribution of costs given those stages. Additionally, it incorporates numerous covariates and comorbidities. We applied the models to two large and rich datasets, one commercial insurance and the other Medicare fee-for-service, totaling about 40 million beneficiary months. We found that the XGBoost models best predict both stage transitions and costs. If XGBoost models are unavailable, a multivariate logistic regression model with regularization to predict stage and a logit-gamma model of the costs given the stage best predicted the people’s health care costs in the next month. Journal: North American Actuarial Journal Pages: 139-186 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2177676 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2177676 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:139-186 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2183869_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Chudamani Poudyal Author-X-Name-First: Chudamani Author-X-Name-Last: Poudyal Author-Name: Qian Zhao Author-X-Name-First: Qian Author-X-Name-Last: Zhao Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Title: Method of Winsorized Moments for Robust Fitting of Truncated and Censored Lognormal Distributions Abstract: When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (1) models should be designed to accommodate deductibles, policy limits, and coinsurance factors; (2) parameters should be estimated robustly to control the influence of outliers on model predictions; and (3) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this article provides a framework for addressing all of these aspects simultaneously. Using payment per payment and payment per loss variables, we construct the adaptive version of method of winsorized moments (MWM) estimators for the parameters of truncated and censored lognormal distribution. Further, the asymptotic distributional properties of this approach are derived and compared with those of the maximum likelihood estimator (MLE) and method of trimmed moments (MTM) estimators, the latter being a primary competitor to MWM. Moreover, the theoretical results are validated with extensive simulation studies and risk measure robustness analysis. Finally, practical performance of these methods is illustrated using the well-studied dataset of 1500 U.S. indemnity losses. Journal: North American Actuarial Journal Pages: 236-260 Issue: 1 Volume: 28 Year: 2024 Month: 1 X-DOI: 10.1080/10920277.2023.2183869 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2183869 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:1:p:236-260 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2197475_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Oscar Espinosa Author-X-Name-First: Oscar Author-X-Name-Last: Espinosa Author-Name: Valeria Bejarano Author-X-Name-First: Valeria Author-X-Name-Last: Bejarano Author-Name: Jeferson Ramos Author-X-Name-First: Jeferson Author-X-Name-Last: Ramos Title: Predictability and Financial Sufficiency of Health Insurance in Colombia: An Actuarial Analysis With a Bayesian Approach Abstract: Every year, the Colombian government provides a prospective premium, known as the capitation payment unit (CPU), for each affiliated person (according to sex, region, and age) to each health insurance company, in order to manage the corresponding risk in health. This article studies the prediction capacity for the health expenditure for the more than 20 million affiliates to the contributory regime of health, as well as the CPU’s financial sufficiency, using an actuarial approach. Using the pure risk premium method and generalized linear models, both classic and Bayesian, the CPU is estimated; these results are compared to actual expenditure by an index of forecasting ability. It is concluded that the use of historical information about expenditure on health, as well as the Bayesian inference, among the other methodological innovations developed, provides an advantage for obtaining more accurate prospective values. These technical recommendations seek to support an improvement in the public budget allocation of more than 6 billion dollars per year to the Colombian health system. Journal: North American Actuarial Journal Pages: 320-336 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2197475 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2197475 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:320-336 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2190528_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Xi Xin Author-X-Name-First: Xi Author-X-Name-Last: Xin Author-Name: Fei Huang Author-X-Name-First: Fei Author-X-Name-Last: Huang Title: Antidiscrimination Insurance Pricing: Regulations, Fairness Criteria, and Models Abstract: On the issue of insurance discrimination, a grey area in regulation has resulted from the growing use of big data analytics by insurance companies: direct discrimination is prohibited, but indirect discrimination using proxies or more complex and opaque algorithms is not clearly specified or assessed. This phenomenon has recently attracted the attention of insurance regulators all over the world. Meanwhile, various fairness criteria have been proposed and flourished in the machine learning literature with the rapid growth of artificial intelligence (AI) in the past decade and have mostly focused on classification decisions. In this article, we introduce some fairness criteria that are potentially applicable to insurance pricing as a regression problem to the actuarial field, match them with different levels of potential and existing antidiscrimination regulations, and implement them into a series of existing and newly proposed antidiscrimination insurance pricing models, using both generalized linear models (GLMs) and Extreme Gradient Boosting (XGBoost). Our empirical analysis compares the outcome of different models via the fairness–accuracy trade-off and shows their impact on adverse selection and solidarity. Journal: North American Actuarial Journal Pages: 285-319 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2190528 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2190528 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:285-319 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2186430_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Guohui Guan Author-X-Name-First: Guohui Author-X-Name-Last: Guan Author-Name: Lin He Author-X-Name-First: Lin Author-X-Name-Last: He Author-Name: Zongxia Liang Author-X-Name-First: Zongxia Author-X-Name-Last: Liang Author-Name: Yang Liu Author-X-Name-First: Yang Author-X-Name-Last: Liu Author-Name: Litian Zhang Author-X-Name-First: Litian Author-X-Name-Last: Zhang Title: Robust Dividend, Financing, and Reinsurance Strategies Under Model Uncertainty with Proportional Transaction Costs Abstract: This article studies the robust dividend, financing, and reinsurance strategies for an ambiguity aversion insurer (AAI) under model uncertainty. The AAI controls its liquid reserves by purchasing proportional reinsurance, paying dividends, and issuing new equity. We consider model uncertainty and suppose that the AAI is ambiguous about the liquid reserves process, which is described by a class of equivalent probability measures. The objective of the AAI is to maximize the expected present value of the dividend payouts minus the discounted costs of issuing new equity before bankruptcy under the worst-case scenario. A detailed proof of the verification theorem is shown for the robust singular-regular problem. We obtain the explicit solutions of the robust strategies, which are classified into three cases. Numerical results are also presented to show the impacts of the ambiguity aversion coefficient, and the transaction cost factor. Journal: North American Actuarial Journal Pages: 261-284 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2186430 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2186430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:261-284 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2213295_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Tim J. Boonen Author-X-Name-First: Tim J. Author-X-Name-Last: Boonen Author-Name: Wenjun Jiang Author-X-Name-First: Wenjun Author-X-Name-Last: Jiang Title: Bowley Insurance with Expected Utility Maximization of the Policyholders Abstract: This article studies the Bowley solution for a sequential game within the expected utility framework. We assume that the policyholders are expected utility maximizers and there exists a representative policyholder who faces a fixed loss with given probability and no loss otherwise. This policyholder selects the optimal indemnity function in response to the pricing kernel set by the insurer. Knowing the policyholder’s choice of indemnity function, the insurer adjusts the pricing kernel to maximize its expected net profit. This pricing kernel is of our central interest in this article, and in our setting the pricing kernel can be evaluated via the safety loading factor in an expected value premium principle. For a wide class of utility functions, we show that the optimal safety loading factor increases with respect to both the policyholder’s risk aversion level and the probability of zero loss. We also show that the insurance contract corresponding to the Bowley solution is Pareto dominated in the sense that both parties’ interests can be further improved, which shows the inefficiency of the Bowley solution. Some numerical examples are presented to illustrate the main results, and it is shown that both the policyholder and insurer can strictly benefit from the Bowley solution. Journal: North American Actuarial Journal Pages: 407-425 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2213295 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2213295 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:407-425 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2216764_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Yiqing Chen Author-X-Name-First: Yiqing Author-X-Name-Last: Chen Author-Name: Jiajun Liu Author-X-Name-First: Jiajun Author-X-Name-Last: Liu Title: An Asymptotic Result on Catastrophe Insurance Losses Abstract: Consider an insurer who both sells catastrophe insurance policies and makes risky investments. Suppose that insurance claims arrive according to a Poisson process and the price of the investment portfolio evolves according to a general stochastic process independent of the insurance claims. In the focus of catastrophe risk management are catastrophe insurance losses. For the case of heavy-tailed claims, we derive a simple asymptotic formula for the tail probability of the present value of future claims. The transparent expression of our formula explicitly reflects the different roles of the various underlying risks in driving catastrophic losses. Our work is distinguished from most other works in this strand of research in that we carry out the asymptotic study over the whole class of subexponential distributions. Thus, our work allows both very heavy-tailed distributions such as Pareto-type distributions and moderately heavy-tailed distributions such as Lognormal and Weibull distributions. Journal: North American Actuarial Journal Pages: 426-437 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2216764 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2216764 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:426-437 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2202707_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Roxane Turcotte Author-X-Name-First: Roxane Author-X-Name-Last: Turcotte Author-Name: Jean-Philippe Boucher Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Boucher Title: GAMLSS for Longitudinal Multivariate Claim Count Models Abstract: By generalizing traditional regression frameworks, generalized additive models for location, scale, and shape (GAMLSSs) allow parametric or semiparametric modeling of one or more parameters of distributions that are not members of the linear exponential family. Consequently, these GAMLSS approaches offer an interesting theoretical framework to allow the use of several potentially helpful distributions in actuarial science. GAMLSS theory is coupled with longitudinal approaches for counting data because these approaches are essential to predictive pricing models. Indeed, they are mainly known for modeling the dependence between the number of claims from the contracts of the same insured over time. Considering that the models’ cross-sectional counterparts have been successfully applied in actuarial work and the importance of longitudinal models, we show that the proposed approach allows one to quickly implement multivariate longitudinal models with nonparametric terms for ratemaking. This semiparametric modeling is illustrated using a dataset from a major insurance company in Canada. An analysis is then conducted on the improvement of predictive power that the use of historical data and nonparametric terms in the modeling allows. In addition, we found that the weight of past experience in bonus–malus predictive premiums analysis is reduced in comparison with a parametric model and that this method could help for continuous covariate segmentation. Our approach differs from previous studies because it does not use any simplifying assumptions as to the value of the a priori explanatory variables and because we have carried out a predictive pricing integrating nonparametric terms within the framework of the GAMLSS in an explicit way, which makes it possible to reproduce the same type of study using other distributions. Journal: North American Actuarial Journal Pages: 337-360 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2202707 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2202707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:337-360 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2218465_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Hua Chen Author-X-Name-First: Hua Author-X-Name-Last: Chen Author-Name: Jin Gao Author-X-Name-First: Jin Author-X-Name-Last: Gao Author-Name: Wei Zhu Author-X-Name-First: Wei Author-X-Name-Last: Zhu Title: A Unified Framework for Insurance Demand and Mortality Immunization Abstract: This article explores an individual’s optimal insurance choice and an insurer’s optimal product mix consisting of whole life insurance and deferred life annuities in a market equilibrium framework. On the demand side, the insured decides an optimal insurance choice by maximizing lifetime expected utility. On the supply side, an insurer chooses an optimal product mix by minimizing the conditional value-at-risk (CVaR) in its lines of business. By varying the loading for each insurance product, we match demand and supply of these products to clear the market. Our results suggest that market equilibria may occur when life insurance loading is relatively high and annuity loading is relatively low. This calls for attention from insurance regulators and life insurers to review insurance/annuity underwriting and pricing. Journal: North American Actuarial Journal Pages: 469-490 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2218465 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2218465 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:469-490 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2208192_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Qin Shang Author-X-Name-First: Qin Author-X-Name-Last: Shang Author-Name: Xueyang Wang Author-X-Name-First: Xueyang Author-X-Name-Last: Wang Author-Name: Xuezhi Qin Author-X-Name-First: Xuezhi Author-X-Name-Last: Qin Author-Name: Xiaohui Zhao Author-X-Name-First: Xiaohui Author-X-Name-Last: Zhao Title: Pricing of Joint Life Long-Term Care Insurance Based on a Multistate Markov Model Abstract: This study considers elderly couples as the research object and proposes a new mode of joint life long-term care insurance. Based on the data from the China Health and Retirement Longitudinal, the study is used to define six health states and to establish an ordered logistic model to derive a health-state transition probability matrix for elderly couples in China. On the basis of the estimated annual transfer probability matrix, a Markov model is selected for the calculation of premiums of joint life long-term care insurance. In addition, the study analyzes the impacts of initial health status, age, residential area, and care status on state transition probabilities and joint life long-term care insurance (LTCI) premiums. Journal: North American Actuarial Journal Pages: 361-372 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2208192 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2208192 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:361-372 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2214603_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Leon Chen Author-X-Name-First: Leon Author-X-Name-Last: Chen Author-Name: Steven W. Pottier Author-X-Name-First: Steven W. Author-X-Name-Last: Pottier Title: Event Studies for Publicly Traded Insurers: An Investigation of the Bad-Model Problem Abstract: The potential that abnormal returns are due to a misspecified expected (normal) return model is well known in the event study literature. Prior research shows that this “bad-model problem” is serious in long-run studies, and can also be problematic in short-run studies for firms grouped by certain characteristics. We investigate the bad-model problem for a large sample of insurance firms over an 18-year period, based on nine different expected return models and short- and long-run event windows. Using 1000 samples of randomly selected firms and dates, we find that the different normal return models make little difference in the statistical or economic significance of abnormal returns for short event windows (up to 3 days). However, for longer event windows, such as 1 month and 13 months, statistically and economically significant abnormal returns are more common. Further, we find that characteristic-based benchmark models generally perform better than models that require an estimation period. We also examine a sample of insurers that experienced a financial strength rating downgrade, and find significant differences between characteristic-based benchmark models and other normal return models for the 13-month event window. We recommend that abnormal returns from actual events be evaluated for their qualitative significance in relation to random samples with random event dates. Our results support the need to exercise caution in interpreting the findings of event studies. Journal: North American Actuarial Journal Pages: 438-468 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2214603 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2214603 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:438-468 Template-Type: ReDIF-Article 1.0 # input file: UAAJ_A_2211648_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Hirbod Assa Author-X-Name-First: Hirbod Author-X-Name-Last: Assa Author-Name: Liyuan Lin Author-X-Name-First: Liyuan Author-X-Name-Last: Lin Author-Name: Ruodu Wang Author-X-Name-First: Ruodu Author-X-Name-Last: Wang Title: Calibrating Distribution Models from PELVE Abstract: The Value at Risk (VaR) and the expected shortfall (ES) are the two most popular risk measures in banking and insurance regulation. To bridge between the two regulatory risk measures, the probability equivalent level of VaR-ES (PELVE) was recently proposed to convert a level of VaR to that of ES. It is straightforward to compute the value of PELVE for a given distribution model. In this article, we study the converse problem of PELVE calibration; that is, to find a distribution model that yields a given PELVE, which may be obtained either from data or from expert opinion. We discuss separately the cases when one-point, two-point, n-point, and curve constraints are given. In the most complicated case of a curve constraint, we convert the calibration problem to that of an advanced differential equation. We apply the model calibration techniques to estimation and simulation for datasets used in insurance. We further study some technical properties of PELVE by offering a few new results on monotonicity and convergence. Journal: North American Actuarial Journal Pages: 373-406 Issue: 2 Volume: 28 Year: 2024 Month: 4 X-DOI: 10.1080/10920277.2023.2211648 File-URL: http://hdl.handle.net/10.1080/10920277.2023.2211648 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:373-406