Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413959_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vladimir V. Kalashnikov Author-X-Name-First: Vladimir V. Author-X-Name-Last: Kalashnikov Title: Two-sided bounds of ruin probabilities Abstract: A new method for obtaining two-sided bounds of ruin probabilities is proposed. This is based on the analysis of so-called geometric sums which are sums of i.i.d.r.v.'s and the number of summands is a r.v. also having a geometric distribution. The method uses probabilistic arguents only and does not use analytic relations such as Spitzer identity. It is shown that some well known bounds can be proved with the help of the developed method. Numerical examples are considered. Journal: Scandinavian Actuarial Journal Pages: 1-18 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413959 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413959 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:1-18 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413965_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Christian Hipp Author-X-Name-First: Christian Author-X-Name-Last: Hipp Title: The delta-method for actuarial statistics Abstract: Asymptotic normality of nonparametric estimators is derived using the delta-method and Pollard's Central Limit Theorem for the empirical process indexed by a class of functions. The results are applied to estimation problems in actuarial mathematics. Journal: Scandinavian Actuarial Journal Pages: 79-94 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413965 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413965 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:79-94 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413964_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ajit Chaturvedi Author-X-Name-First: Ajit Author-X-Name-Last: Chaturvedi Author-Name: Rahul Gupta Author-X-Name-First: Rahul Author-X-Name-Last: Gupta Title: On multi-stage procedures for estimating the largest mean of NOrmal populations having unequal and unknown variances Abstract: The problem of constructing confidence interval for the largest of k normal means considered by Saxena and Tong (1969) and Tong (1970, 1973) is extended by considering the case when the populations have unequal and unknown variances. Several multi-stage estimation procedures (like, two-stage, three-stage and accelerated sequential procedures) are developed to deal with the estimation problem. Nice asymptotic properties of these estimation procedures are studied and their relative advantages and disadvantages are discussed. Journal: Scandinavian Actuarial Journal Pages: 64-78 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413964 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413964 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:64-78 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413963_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ole Hesselager Author-X-Name-First: Ole Author-X-Name-Last: Hesselager Title: A recursive procedure for calculation of some mixed compound poisson distributions Abstract: We derive a simple recursive procedure for calculation of mixed compound Poisson distributions, when the logarithm of the mixing density can be written as the ratio of two polynomials. Journal: Scandinavian Actuarial Journal Pages: 54-63 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413963 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413963 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:54-63 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413962_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Title: Addendum to Hattendorff's Theorem and Thiele's Differential Equation Generalized, SAJ 1992, 2–14 Abstract: A. Purpose of this note Any specific application of the theory in Section 3 of the paper would demand that the statewise reserves Vj be precisely defined. There is some latitude at this point, however, and it turns out that Theorem 3 as stated may require that an appropriate definition be used. Paragraph B of the present note adds rigour on the issue. Paragraph C offers some guidance as to how to construct and compute the reserves in nontrivial cases. Some technical lemmas are placed in the final Paragraph D. Journal: Scandinavian Actuarial Journal Pages: 50-53 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413962 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413962 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:50-53 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413961_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Author-Name: Christian Max Møller Author-X-Name-First: Christian Max Author-X-Name-Last: Møller Title: Thiele's differential equation with stochastic interest of diffusion type Abstract: The classical Thiele's differential equation for the prospective reserve of an insurance policy has been generalized to models with counting process driven payments and deterministic interest. Here the result is extended to situations with diffusion driven stochastic interest. The technique of proof consists in identifying the null part of the martingale associated with the initial present value of the payments. The presentation centers on life insurance, but the theory can be adapted to more general stochastic payment streams. Journal: Scandinavian Actuarial Journal Pages: 37-49 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413961 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413961 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:37-49 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413960_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren Asmussen Author-X-Name-First: Søren Author-X-Name-Last: Asmussen Author-Name: Mogens Bladt Author-X-Name-First: Mogens Author-X-Name-Last: Bladt Title: Phase-type distributions and risk processes with state-dependent premiums Abstract: Consider a risk reserve process with initial reserve u, Poisson arrivals, premium rule p(r) depending on the current reserve r and claim size distribution which is phase-type in the sense of Neuts. It is shown that the ruin probabilities ψ(u) can be expressed as the solution of a finite set of differential equations, and similar results are obtained for the case where the process evolves in a Markovian environment (e.g., a numerical example of a stochastic interest rate is presented). Further, an explicit formula for ψ(u) is presented for the case where p(r) is a two-step function. By duality, the results apply also to the stationary distribution of storage processes with the same input and release rate p(r) at content r. Journal: Scandinavian Actuarial Journal Pages: 19-36 Issue: 1 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413960 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413960 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:1:p:19-36 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413966_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Vanneste Author-X-Name-First: M. Author-X-Name-Last: Vanneste Author-Name: M. Goovaerts Author-X-Name-First: M. Author-X-Name-Last: Goovaerts Author-Name: F. De Vylder Author-X-Name-First: F. Author-X-Name-Last: De Vylder Author-Name: R. Kaas Author-X-Name-First: R. Author-X-Name-Last: Kaas Title: A stochastic approach to catastrophic risks Abstract: Road transportation of dangerous materials as well as pollution are considered as being catastrophic risks. In case the normal insurance models are applied to catastrophic risks, one of the basic assumptions, namely that the average surplus is a linear quantity in time, is certainly not satisfied. In more realistic situations, an average movement of the surplus is linear up to a certain time, where a drastic decrease in the surplus occurs, namely at the moment when the claims are paid out, then afterwards the surplus will show a linear trend again. In the present contribution we describe the stochastic approach to this kind of situations, based on the same ideas as used in ‘A stochastic approach to insurance cycles’ by Goovaerts et al. ( 1992). The consequences for the probability of ruin at a specific point in time are also investigated as well as their relation to solvency margins. Journal: Scandinavian Actuarial Journal Pages: 99-108 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413966 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413966 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:99-108 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413967_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: F. De Vylder Author-X-Name-First: F. Author-X-Name-Last: De Vylder Author-Name: E. Marceau Author-X-Name-First: E. Author-X-Name-Last: Marceau Title: Classical numerical ruin probabilities Abstract: Finite and infinite-time classical ruin probabilities can be approximated in Gerber's elementary binomial risk model. In order to obtain good results, rather fine discretizations may be necessary and then the computing times may be much too long. Here we show how rather rough discretizations provide approximations of excellent quality when a new claimsize distribution (with one negative probability mass!!!) is adopted and when a new security loading is introduced. Journal: Scandinavian Actuarial Journal Pages: 109-123 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413967 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413967 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:109-123 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413968_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vsevolod Malinovskii Author-X-Name-First: Vsevolod Author-X-Name-Last: Malinovskii Title: Approximations and upper bounds on probabilities of large deviations in the problem of ruin within finite time Abstract: In the framework of Andersen's risk model, a new asymptotic expression and upper bounds on probabilities of ruin after time t(u) ≫ and before time 0 < t(u) ≪ , as the initial risk reserve u increases to infinity, are suggested. This result complements the classical normal-type approximation for the probability of ruin within finite time and is designed as its large deviations counterpart. The main technical device of the paper (see Section 3), which is of independent interest, are the upper bounds and the asymptotic expressions for the probabilities of large deviations of the stopped random walks, developed under low moment conditions. Journal: Scandinavian Actuarial Journal Pages: 124-147 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413968 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413968 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:124-147 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413969_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Author-Name: Alfredo Egídio Dos Reis Author-X-Name-First: Alfredo Author-X-Name-Last: Egídio Dos Reis Title: On the distribution of the duration of negative surplus Abstract: In the classical risk model we allow the surplus process to continue if the surplus falls below zero. We consider the distributions of the duration of a single period of negative surplus and of the total duration of negative surplus. We derive explicit results where possible and show how to approximate these distributions through the use of a discrete time risk model. Journal: Scandinavian Actuarial Journal Pages: 148-164 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413969 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413969 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:148-164 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413970_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Title: Transient results for a high demand CCRC model Abstract: This paper examines the transient behavior of a stochastic model for high demand continuing care retirement community (CCRC) populations. The CCRC under consideration provides a number of independent living units each of which houses one resident at a time and a skilled nursing facility (SNF) for those who require care. A time-homogeneous Markov process is used to model the care requirements of the CCRC residents. Under the model, the “state” of the population is described by the number of permanent transfers and the number of temporary transfers to the SNF. The paper examines how one can obtain information about the distribution of the state of the CCRC population at a given future time. Journal: Scandinavian Actuarial Journal Pages: 165-182 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413970 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413970 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:165-182 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413972_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Matti Ruohonen Author-X-Name-First: Matti Author-X-Name-Last: Ruohonen Title: Book Review Journal: Scandinavian Actuarial Journal Pages: 187-188 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413972 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413972 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:187-188 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413971_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: A. Boyd Author-X-Name-First: A. Author-X-Name-Last: Boyd Author-Name: J. Perlman Author-X-Name-First: J. Author-X-Name-Last: Perlman Title: A reaction to compound generalized recursions Abstract: Kling & Goovaerts ( 1993) have given a three-step recursive algorithm for the evaluation of terms in compound generalized distributions. This note corrects an error in the second step of their treatment of the compound generalized Poisson and negative binomial distributions. Journal: Scandinavian Actuarial Journal Pages: 183-186 Issue: 2 Volume: 1996 Year: 1996 X-DOI: 10.1080/03461238.1996.10413971 File-URL: http://hdl.handle.net/10.1080/03461238.1996.10413971 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1996:y:1996:i:2:p:183-186 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413979_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Holger Rootzén Author-X-Name-First: Holger Author-X-Name-Last: Rootzén Author-Name: Nader Tajvidi Author-X-Name-First: Nader Author-X-Name-Last: Tajvidi Title: Extreme value statistics and wind storm losses: A case study Abstract: Statistical extreme value theory provides a flexible and theoretically well motivated approach to the study of large losses in insurance. We give a brief review of the modem version of this theory and a “step by step” example of how to use it in large claims insurance. The discussion is based on a detailed investigation of a wind storm insurance problem. New results include a simulation study of estimators in the peaks over thresholds method with Generalised Pareto excesses, a discussion of Pareto and lognormal modelling and of methods to detect trends. Further results concern the use of meteorological information in the wind storm insurance and, of course, the results of the study of the wind storm claims. Journal: Scandinavian Actuarial Journal Pages: 70-94 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413979 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413979 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:70-94 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413977_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: Estimation of the Lundberg coefficient for a Markov modulated risk model Abstract: For a Cox risk model with a piecewise constant intensity some random variables with an exponential tail are constructed and an estimation procedure for the Lundberg exponent (adjustment coefficient) is proposed. It is shown that in the case of a Markov modulated risk model the estimator is strongly consistent. Journal: Scandinavian Actuarial Journal Pages: 48-57 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413977 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413977 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:48-57 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413978_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Philippe Picard Author-X-Name-First: Philippe Author-X-Name-Last: Picard Author-Name: Claude Lefèvre Author-X-Name-First: Claude Author-X-Name-Last: Lefèvre Title: The probability of ruin in finite time with discrete claim size distribution Abstract: The ruin time T is considered as the time of first crossing between a compound Poisson trajectory and an upper increasing boundary. Under the assumption that the claim sizes are integer-valued, we show that the distribution of T can be expressed in terms of generalized Appell polynomials. Using the algebraic properties of these polynomials elegant expressions are obtained for P(T > x). Journal: Scandinavian Actuarial Journal Pages: 58-69 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413978 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413978 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:58-69 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413980_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Erhard Kremer Author-X-Name-First: Erhard Author-X-Name-Last: Kremer Title: Credibility in evolutionary models revisited Abstract: A most general result on credibility estimation in stationary models is given. In principle it is a modification of the well-known Levinson predictor. Journal: Scandinavian Actuarial Journal Pages: 95-96 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413980 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413980 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:95-96 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413974_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: A. De Schepper Author-X-Name-First: A. Author-X-Name-Last: De Schepper Author-Name: M. J. Goovaerts Author-X-Name-First: M. J. Author-X-Name-Last: Goovaerts Author-Name: R. Kaas Author-X-Name-First: R. Author-X-Name-Last: Kaas Title: A recursive scheme for perpetuities with random positive interest rates. Part I. Analytical results Abstract: Recently, the authors showed how interest randomness in actuarial functions can· be described by means of Wiener processes using path integrals. This paper wants to present an extension of this kind of models, by investigating the situation of interest rates that cannot become negative. The case of an annuity certain and in particular that of a perpetuity will be dealt with in detail. Journal: Scandinavian Actuarial Journal Pages: 1-10 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413974 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413974 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:1-10 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413976_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Franco Pellerey Author-X-Name-First: Franco Author-X-Name-Last: Pellerey Title: Some new conditions for the increasing convex comparison of risks Abstract: The preservation under convolutions and mixing of the increasing convex comparison of risks is considered, and new related results are proved. Some applications of these results in actuarial context are shown. Also, similar properties are shown to be satisfied by the convex and the Laplace comparisons of risks. Journal: Scandinavian Actuarial Journal Pages: 38-47 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413976 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413976 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:38-47 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413975_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jostein Paulsen Author-X-Name-First: Jostein Author-X-Name-Last: Paulsen Title: Present value of some insurance portfolios Abstract: In this paper we introduce some general theorems of Poisson processes and use them to study the first two moments of the present value of an insurance portfolio. We allow for several handling times of claims and also allow the discounting process to be stochastic, in particular we let it follow a geometric Brownian motion and the Cox, Ingersoll, and Ross (LIR) model. We also give a brief discussion of the problem of finding the distribution function of the present value. Examples are given to illuminate the general theory, showing that although sometimes complicated, actual computations are often possible. Journal: Scandinavian Actuarial Journal Pages: 11-37 Issue: 1 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413975 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413975 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:1:p:11-37 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413983_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Author-Name: Xiaodong Lin Author-X-Name-First: Xiaodong Author-X-Name-Last: Lin Title: Upper bounds for the tail of the compound negative binomial distribution Abstract: A general upper bound for the tail of the compound negative binomial distribution is constructed. By establishing a connection with the individual risk mode the upper bound is seen to be a (possibly degenerate) mixture of tails of gamma distributions. The bound is sharp in that it is an equality in the compound Pascal-exponential case. Two important special cases of the bound are derived. The issue of construction of an optimal upper bound is considered. Journal: Scandinavian Actuarial Journal Pages: 138-148 Issue: 2 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413983 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413983 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:138-148 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413982_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jacques Janssen Author-X-Name-First: Jacques Author-X-Name-Last: Janssen Author-Name: Raimondo Manca Author-X-Name-First: Raimondo Author-X-Name-Last: Manca Title: A realistic non-homogeneous stochastic pension fund model on scenario basis Abstract: As far as we know, this paper presents for the first time a general, rigorous and tractable stochastic evolution time model for pension fund called the discrete time non-homogeneous semi-Markov model, or in short, the DTNHSM pension fund model taking into account both economic, financial and demographic evolution factors so that it becomes a real-life model. The most important factors are: seniority, general age dependence, rate of inflation and salary lines. The model starts from a set of m states and each member of the fund is necessarily in one and only one of these states at each time epoch, for example each year. The main probabilistic assumption is that the successive state transitions together with transition time epochs constitute a two-dimensional non-homogeneous Markov additive process on which the state at any time epoch t is defined by the imbedded non-homogeneous semi-Markov process. Let us say that we introduce as other fundamental tool the concept of scenario both with strategic choices of the society and the one of economic scenario for the impact of the future economic environment. Finally let us mention that the problem of the statistical estimation problem of the two-dimensional semi-Markov kernel using internal and external data is solved. Journal: Scandinavian Actuarial Journal Pages: 113-137 Issue: 2 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413982 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413982 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:113-137 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413981_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Richard Watt Author-X-Name-First: Richard Author-X-Name-Last: Watt Title: The optimal trading partner for reciprocal insurance treaties Abstract: This paper assumes a situation in which two risk averse individuals each facing an independent lottery use a traditional bargaining model to arrive at a Pareto superior wealth distribution via a mutual insurance contract. The traditional Borch (1960a) solution is considered, and it is shown that under this type of contract for a general utility function, the characteristics of the optimal trading partner are indeterminate. A second set of possible trades is considered under which some uninsurable group risk is eliminated from the contract and it is shown that, in the new setting, the characteristics of the optimal trading partner can be established. Finally, it is shown that the optimal solution under the new contract is not necessarily Pareto dominated by the traditional (Borch) solution. Journal: Scandinavian Actuarial Journal Pages: 97-112 Issue: 2 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413981 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413981 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:97-112 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413986_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hans J. Zwiesler Author-X-Name-First: Hans J. Author-X-Name-Last: Zwiesler Title: Remarks on “A note on compound generalized distributions” Abstract: 1. INTRODUCTION In [1] the authors derive recursion formulae for computing total claim probabilities for a general class of modified power series distributions. Such formulae provide an important tool for computing total claim size probabilities in risk-theory. As it turns out, two of their recursions (Theorem 3.2 and Theorem 3.4) need modifications. Unfortunately, these modifications have the effect that the recursions break down. In the following, we will state the modified theorems and show how these obstacles can be overcome. Journal: Scandinavian Actuarial Journal Pages: 186-188 Issue: 2 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413986 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413986 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:186-188 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413985_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Credibility using a loss function from Spline theory Abstract: Current formulas in credibility theory often calculate net premium as a weighted sum of the average experience of the policyholder and the average experience of the entire collection of policyholders. Because these formulas are linear, they are easy to use. Another advantage of linear formulas is that the estimate changes a fixed amount per change in claim experience; if an insurer uses such a formula, then the policyholder can predict the change in premium. On the other hand, Venter (1990) points out that in some cases, the loss of accuracy makes a linear formula undesirable. We apply decision theory to develop a credibility formula that minimizes a loss function that is 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. An actuary may balance the sometimes conflicting goals of accuracy and linearity by changing a single parameter in the loss function. Our loss function is similar to one used in spline theory, although in a different context. Journal: Scandinavian Actuarial Journal Pages: 160-185 Issue: 2 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413985 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413985 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:160-185 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413984_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: U. Jensen Author-X-Name-First: U. Author-X-Name-Last: Jensen Title: An optimal stopping problem in risk theory Abstract: In classical risk theory often stationary premium and claim processes are considered. In some cases it is more convenient to model non-stationary processes which describe a movement from environmental conditions, for which the premiums were calculated, to less favorable circumstances. This is done by a Markov-modulated Poisson claim process. Moreover the insurance company is allowed to stop the process at some random time, if the situation seems unfavorable, in order to calculate new premiums. This leads to an optimal stopping problem which is solved explicitly to some extent. Journal: Scandinavian Actuarial Journal Pages: 149-159 Issue: 2 Volume: 1997 Year: 1997 X-DOI: 10.1080/03461238.1997.10413984 File-URL: http://hdl.handle.net/10.1080/03461238.1997.10413984 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:149-159 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413993_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Udo Kamps Author-X-Name-First: Udo Author-X-Name-Last: Kamps Title: On a class of premium principles including the Esscher principle Abstract: A class of premium calculation principles is considered with the premiums obtained as expected values of suitably transformed distribution functions. The Esscher principle is a particular example. It is found that the likelihood ratio ordering of risks is preserved for any of these principles. A renewal theoretic interpretation of a special principle is given, and useful properties as well as a related characterization of the exponential distribution are shown. Journal: Scandinavian Actuarial Journal Pages: 75-80 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413993 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413993 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:75-80 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413994_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bronius Grigelionis Author-X-Name-First: Bronius Author-X-Name-Last: Grigelionis Title: On mixed poisson processes and martingales Abstract: In this paper O. Lundberg's martingale characterization of mixed Poisson processes with finite mean value within birth processes is extended for mixed Poisson processes with arbitrary mixing distributions within general point processes. Some applications of this result are also discussed. Journal: Scandinavian Actuarial Journal Pages: 81-88 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413994 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413994 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:81-88 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413991_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claudia Klüppelberg Author-X-Name-First: Claudia Author-X-Name-Last: Klüppelberg Author-Name: Ulrich Stadtmüller Author-X-Name-First: Ulrich Author-X-Name-Last: Stadtmüller Title: Ruin probabilities in the presence of heavy-tails and interest rates Abstract: We study the infinite time ruin probability for the classical Cramér-Lundberg model, where the company also receives interest on its reserve. We consider the large claims case, where the claim size distribution F has a regularly varying tail. Hence our results apply for instance to Pareto, loggamma, certain Benktander and stable claim size distributions. We prove that for a positive force of interest δ the ruin probability ψδ(u) ∼ κδ(1 - F(u)) as the initial risk reserve u→∞. This is quantitatively different from the non-interest model, where ψ(u) ∼ κ (1 – F(y)) dy. Journal: Scandinavian Actuarial Journal Pages: 49-58 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413991 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413991 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:49-58 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413992_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hansjörg Furrer Author-X-Name-First: Hansjörg Author-X-Name-Last: Furrer Title: Risk processes perturbed by α-stable Lévy motion Abstract: The classical model of collective risk theory is extended in that an α-stable Levy motion is added to the compound Poisson process. The convolution formula for the probability of ruin is derived. We then investigate the asymptotic behaviour of the ruin probability as the initial capital becomes large. Journal: Scandinavian Actuarial Journal Pages: 59-74 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413992 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:59-74 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413995_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Exponential dispersion models and credibility Abstract: The Exponential Dispersion Family is a rich family of distributions, comprised of several distributions, some of which are heavy-tailed and as such could be of significant relevance to actuarial science. The family draws its richness from a dispersion parameter σ2 = 1/λ which is equal to 1 in the case of the Natural Exponential Family. We consider three cases. In the first λ is assumed known, in the second a prior distribution for λ is given, and in the third the prior distribution of λ is not known and is derived by means of the maximum entropy principle, assuming the prior mean of λ can be specified. For these cases, a conjugate prior distribution for the risk parameter is assumed and credibility formulae are derived for the estimation of the fair premium. Journal: Scandinavian Actuarial Journal Pages: 89-96 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413995 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413995 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:89-96 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413989_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Nelson De Pril Author-X-Name-First: Nelson Author-X-Name-Last: De Pril Title: Some results on moments and cumulants Abstract: In the present paper we discuss various results related to moments and cumulants of probability distributions and approximations to probability distributions. As the approximations are not necessarily probability distributions themselves, we shall apply the concept of moments and cumulants to more general functions. Recursions are deduced for moments and cumulants of functions in the form Rk[a, b] as defined by Dhaene & Sundt (1996). We deduce a simple relation between the De Pril transform and the cumulants of a function. This relation is applied to some classes of approximations to probability distributions, in particular the approximations of Hipp and De Pril. Journal: Scandinavian Actuarial Journal Pages: 24-40 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413989 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413989 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:24-40 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413988_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: On approximating distributions by approximating their De Pril transforms Abstract: Dhaene & De Pril (1994) gave some general bounds for errors caused by applying an approximation to the De Pril transform of a probability distribution. In this paper we further analyse such bounds. We prove results for several simple situations and indicate how these results can be combined for more complex situations. As an illustration we apply the results to deduce approximations to the convolution of a finite number of compound distributions whose counting distributions belong to a class consisting of the binomial, Poisson, and negative binomial distributions, and we give error bounds for these approximations. Journal: Scandinavian Actuarial Journal Pages: 1-23 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413988 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413988 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:1-23 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413990_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: A generalisation of the De Pril transform Abstract: The De Pril transform was first introduced for distributions on the non-negative integers with a positive probability in zero and later generalised to functions on the non-negative integers with a positive mass in zero. In the present paper we extend the definition of the De Pril transform to functions on the integers with a downwards bounded support and show that some known properties of the De Pril transform also hold under this extension. Journal: Scandinavian Actuarial Journal Pages: 41-48 Issue: 1 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413990 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413990 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:41-48 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10414000_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: B. Højgaard Author-X-Name-First: B. Author-X-Name-Last: Højgaard Author-Name: M. Taksar Author-X-Name-First: M. Author-X-Name-Last: Taksar Title: Optimal proportional reinsurance policies for diffusion models Abstract: When applying a proportional reinsurance policy π the reserve of the insurance company is governed by a SDE =(aπ(t)u dt + aπ(t)σ dWt where {Wt} is a standard Brownian motion, µ, π, > 0 are constants and 0 ⩽ aπ(t) ⩽ 1 is the control process, where aπ(t) denotes the fraction, that is reinsured at time t. The aim of this paper is to find a policy that maximizes the return function Vπ(x) = where c > 0, τπ is the time of ruin and x refers to the initial reserve. Journal: Scandinavian Actuarial Journal Pages: 166-180 Issue: 2 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10414000 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10414000 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:2:p:166-180 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10414001_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrei Gureev Author-X-Name-First: Andrei Author-X-Name-Last: Gureev Title: Bounds of ruin probabilities Abstract: Upper and lower bounds are obtained for ruin probabilities with safety margin ρ in the case of known expectation, variance and range for the claim severity function. Journal: Scandinavian Actuarial Journal Pages: 181-187 Issue: 2 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10414001 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10414001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:2:p:181-187 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413997_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jens Perch Nielsen Author-X-Name-First: Jens Perch Author-X-Name-Last: Nielsen Title: Marker dependent kernel hazard estimation from local linear estimation Abstract: Marker dependent hazard estimation based on weighted least square local linear and local constant kernel estimation is considered, and the nonparametric marker dependent hazard estimator of Nielsen (1992) and Nielsen & Linton (1995) is identified as a local constant estimator. The method is related to local linear fitting known from regression estimation, e.g. Fan & Gijbels (1996), and density estimation, e.g. Jones (1993). We derive the pointwise asymptotic theory. Through the introduction of a second order stochastic kernel, the bias considerations of the local linear estimator turn out to be simpler than the bias considerations of the local constant estimator. We also consider the marker-only case applied by Fusaro et al. (1993) while investigating onset of AIDS. Journal: Scandinavian Actuarial Journal Pages: 113-124 Issue: 2 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413997 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413997 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:2:p:113-124 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413998_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ole Hesselager Author-X-Name-First: Ole Author-X-Name-Last: Hesselager Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: Exponential and scale mixtures and equilibrium distributions Abstract: In this article we discuss mixed exponential distributions and, more generally, scale mixtures with specific consideration the purpose of insurance modeling. Results are derived for equilibrium distributions (defined via stop-loss transforms) of mixed distributions. Some recursive relations are identified for the stop-loss transforms and moments of mixed exponential distributions. Explicit expressions are obtained for equilibrium gamma distributions with arbitrary shape parameter. Journal: Scandinavian Actuarial Journal Pages: 125-142 Issue: 2 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413998 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413998 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:2:p:125-142 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413996_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Svein-Arne Persson Author-X-Name-First: Svein-Arne Author-X-Name-Last: Persson Title: Stochastic interest rate in life insurance: The principle of equivalence revisited Abstract: Based on financial theory, a valuation model—including stochastic interest rates—for traditional life insurance contracts is derived. The interpretation of the principle of equivalence may be revisited in this framework; single premiums are found as expected present values under a risk adjusted probability measure. Using a specific model of the term structure some new formulas for the market value of various life insurance contracts are derived. A partial differential equation for the market values of the assurances, is deduced, corresponding to the traditional Thiele's differential equation of classical actuarial sciences. This equation contains some interesting new terms. Journal: Scandinavian Actuarial Journal Pages: 97-112 Issue: 2 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413996 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413996 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:2:p:97-112 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10413999_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Shaun Wang Author-X-Name-First: Shaun Author-X-Name-Last: Wang Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Risk-adjusted credibility premiums using distorted probabilities Abstract: Denneberg (1990) and Wang (1996a) propose that one calculate risk-adjusted insurance premiums as the expectation with respect to a distorted probability measure, a non-additive set function. This premium principle is supported by the theories of decision making of Yaari (1987) and of Schmeidler (1989). Denneberg (1994a) presents three conditioning rules for updating non-additive set functions in light of available information. In this work, we show how to apply these three update rules to calculate a risk-adjusted credibility premium and, thereby, combine credibility theory with this relatively new premium principle. Our main result is that, for some pairs of distortion function and update rule, one gets the same risk-adjusted credibility premium by distorting the predictive probability distribution, as required by the theory of Yaari, or by updating the distorted probability, as required by the theory of Schmeidler. Journal: Scandinavian Actuarial Journal Pages: 143-165 Issue: 2 Volume: 1998 Year: 1998 X-DOI: 10.1080/03461238.1998.10413999 File-URL: http://hdl.handle.net/10.1080/03461238.1998.10413999 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1998:y:1998:i:2:p:143-165 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150992_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ann De Schepper Author-X-Name-First: Ann Author-X-Name-Last: De Schepper Author-Name: Bart Heijnen Author-X-Name-First: Bart Author-X-Name-Last: Heijnen Author-Name: Marc Goovaerts Author-X-Name-First: Marc Author-X-Name-Last: Goovaerts Title: A Recursive Scheme for Perpetuities with Random Positive Interest Rates. II: The Impenetrable Wall Abstract: In some former contributions, the authors investigated actuarial quantities with stochastic interest rates. In a first model, the randomness is modelled by means of an ordinary Wiener process, and as a consequence negative interest rates are possible. A second model provides a tool to avoid these negative interest rates, which can be necessary in particular situations. This paper wants to present an alternative solution to the problem of negative interest rates. This new model will be implemented to the case of an annuity certain and of a perpetuity. Journal: Scandinavian Actuarial Journal Pages: 1-14 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131849 File-URL: http://hdl.handle.net/10.1080/03461230050131849 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:1-14 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150993_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Author-Name: Udi Markov Author-X-Name-First: Udi Author-X-Name-Last: Markov Title: On Stochastic Approximation and Credibility Abstract: Stochastic approximation is a powerful tool for sequential estimation of zero points of a function. This methodology is defined and is shown to be related to a broad class of credibility formulae derived for the Exponential Dispersion Family (EDF). We further consider a Location Dispersion Family (LDF) which is rich enough and for which no simple credibility formula exists. For this case, a Generalized Sequential Credibility Formula is suggested and an optimal stepwise gain sequence is derived. Journal: Scandinavian Actuarial Journal Pages: 15-31 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131858 File-URL: http://hdl.handle.net/10.1080/03461230050131858 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:15-31 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150994_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Claude Lefévre Author-X-Name-First: Claude Author-X-Name-Last: Lefévre Author-Name: M'Hamed Mesfioui Author-X-Name-First: M'Hamed Author-X-Name-Last: Mesfioui Title: Stochastic Orderings of Convex-Type for Discrete Bivariate Risks Abstract: New classes of order relations for discrete bivariate random vectors are introduced that essentially compare the expectations of real functions of convex-type of the random vectors. For the actuarial context, attention is focused on the so-called increasing convex orderings between discrete bivariate risks. First, various characterizations and properties of these orderings are derived. Then, they are used for comparing two similar portfolios with dependent risks and for constructing bounds on several multilife insurance premiums. Journal: Scandinavian Actuarial Journal Pages: 32-51 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131867 File-URL: http://hdl.handle.net/10.1080/03461230050131867 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:32-51 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150995_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: Recursions for Distribution Functions and Stop-Loss Transforms Abstract: For any function f on the non-negative integers, we can evaluate the cumulative function o f given by o f ( s )= ~ s x=0 f ( x ) from the values of f by the recursion o f ( s )= o f ( s -1)+ f ( s ). Analogously we can use this procedure t times to evaluate the t -th order cumulative function o t f . As an alternative, in the present paper we shall derive recursions for direct evaluation of o t f when f itself satisfies a certain sort of recursion. We shall also derive recursions for the t -th order tails v t f where v f ( s )= ~ X x=s+1 f ( x ). The recursions can be applied for exact and approximate evaluation of distribution functions and stop-loss transforms of probability distributions. The class of recursions for f includes the classes discussed by Sundt (1992), incorporating the class studied by Panjer's (1981). We discuss in particular convolutions and compound functions. Journal: Scandinavian Actuarial Journal Pages: 52-65 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131876 File-URL: http://hdl.handle.net/10.1080/03461230050131876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:52-65 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150996_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Non-exponential Bounds for Ruin Probability with Interest Effect Included Abstract: In this paper, we consider a discrete time risk model. First we discuss the classical model, both exponential and non-exponential upper bounds for ruin probabilities are obtained by using martingale inequalities. Then similar results are obtained for the model with investment income. Journal: Scandinavian Actuarial Journal Pages: 66-79 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131885 File-URL: http://hdl.handle.net/10.1080/03461230050131885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:66-79 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150997_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: José Garrido Author-X-Name-First: José Author-X-Name-Last: Garrido Title: Two-Sided Bounds for Ruin Probabilities when the Adjustment Coefficient does not Exist Abstract: In this paper, we derive two-sided bounds for the ruin probability in the compound Poisson risk model when the adjustment coefficient of the individual claim size distribution does not exist. These bounds also apply directly to the tails of compound geometric distributions. The upper bound is tighter than that of Dickson (1994). The corresponding lower bound, which holds under the same conditions, is tighter than that of De Vylder and Goovaerts (1984). Even when the adjustment coefficient exists, the upper bound is, in some cases, tighter than Lundberg's bound. These bounds are applicable for any positive distribution function with a finite mean. Examples are given and numerical comparisons with asymptotic formulae for the ruin probability are also considered. Journal: Scandinavian Actuarial Journal Pages: 80-92 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131894 File-URL: http://hdl.handle.net/10.1080/03461230050131894 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:80-92 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150998_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jens Neilsen Author-X-Name-First: Jens Author-X-Name-Last: Neilsen Title: Multivariate Boundary Kernels from Local Linear Estimation Abstract: Lejeune and Sarda (1992) and Jones (1993) introduced the principle of local linear estimation to nonparametric estimation of smooth densities on the positive real axes. This methodology results in the basic kernel smoother with Gasser and Müller (1979) type boundary kernels when estimating close to a boundary. This principle is extended to nonparametric multivariate density estimation with arbitrary boundary regions. Journal: Scandinavian Actuarial Journal Pages: 93-95 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131902 File-URL: http://hdl.handle.net/10.1080/03461230050131902 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:93-95 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10150999_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book Review Journal: Pages: 96-96 Issue: 1 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461230050131911 File-URL: http://hdl.handle.net/10.1080/03461230050131911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:1:p:96-96 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151000_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: F. Etienne De Vylder Author-X-Name-First: F. Etienne Author-X-Name-Last: De Vylder Title: Numerical Finite-Time Ruin Probabilities by the Picard-Lef vre Formula Abstract: Numerical finite-time ruin probabilities in the classical actuarial risk model can most easily be obtained by a remarkable formula due to Picard and Lefèvre (1997), via an obvious extension of the Panjer recursions applied to the numerical evaluation of pseudo-compound distributions. Journal: Scandinavian Actuarial Journal Pages: 97-105 Issue: 2 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461239950132598 File-URL: http://hdl.handle.net/10.1080/03461239950132598 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:2:p:97-105 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151001_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren Asmussen Author-X-Name-First: Søren Author-X-Name-Last: Asmussen Author-Name: Bjarne Højgaard Author-X-Name-First: Bjarne Author-X-Name-Last: Højgaard Title: Approximations for Finite Horizon Ruin Probabilities in the Renewal Model Abstract: In Asmussen (1984), 'corrected diffusion approximations' for finite horizon ruin probabilities in the classical Cramér-Lundberg model is given. In this paper we generalize this method to the renewal model, first introduced by Andersen (1957). We calculate the approximations in case of phase type distributed claims and interarrival times. A comparison with simulated values indicates a good fit in situations of main interest in risk theory. Journal: Scandinavian Actuarial Journal Pages: 106-119 Issue: 2 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461239950132606 File-URL: http://hdl.handle.net/10.1080/03461239950132606 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:2:p:106-119 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151002_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Aleksandras Baltrūnas Author-X-Name-First: Aleksandras Author-X-Name-Last: Baltrūnas Title: Second Order Behaviour of Ruin Probabilities Abstract: The Sparre-Andersen model in the collective risk theory is investigated. Assuming that the claim-size is heavy-tailed, say subexponential, the second order asymptotic behaviour of ruin probabilities is obtained. Journal: Scandinavian Actuarial Journal Pages: 120-133 Issue: 2 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461239950132615 File-URL: http://hdl.handle.net/10.1080/03461239950132615 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:2:p:120-133 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151003_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sixto Insua Author-X-Name-First: Sixto Author-X-Name-Last: Insua Author-Name: Jacinto Martin Author-X-Name-First: Jacinto Author-X-Name-Last: Martin Author-Name: David Insua Author-X-Name-First: David Author-X-Name-Last: Insua Author-Name: Fabrizio Ruggeri Author-X-Name-First: Fabrizio Author-X-Name-Last: Ruggeri Title: Bayesian Forecasting for Accident Proneness Evaluation Abstract: As part of their resource allocation processes, insurance companies have to undertake various evaluation tasks concerning the accident proneness of their insurants. Bayesian methods are specially fit for that task since they allow for the coherent incorporation of all sources of information, including expert opinions and data. We describe three increasingly complex and realistic models for that purpose. For predictive and inference purposes, we have to rely on simulation methods. We illustrate the models with a real case and describe their implementation in a forecasting system developed for an insurance company. Journal: Scandinavian Actuarial Journal Pages: 134-156 Issue: 2 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461239950132624 File-URL: http://hdl.handle.net/10.1080/03461239950132624 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:2:p:134-156 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151004_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Elisa Luciano Author-X-Name-First: Elisa Author-X-Name-Last: Luciano Title: A Note on Loadings and Deductibles: Can a Vicious Circle Arise? Abstract: In a recently reprinted paper Borch wonders whether an increase in insurance loadings, together with the consequent increase in customers' deductibles, may be the start of a vicious circle, in which higher deductibles produce higher loadings and vice versa, ad infinitum. This paper rules out the possibility of a vicious circle, in a model à la Borch. First of all, increases in costs of the type considered by Borch are not necessarily followed by increases in loadings. Second, increases in loadings are not necessarily followed by increases in deductibles, since in equilibrium insurance may be Giffen. Last but not least, loadings do not increase with deductibles, because the only viable equilibrium is a Stackelberg one. Journal: Pages: 157-169 Issue: 2 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461239950132633 File-URL: http://hdl.handle.net/10.1080/03461239950132633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:2:p:157-169 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151005_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Catherine Vermandele Author-X-Name-First: Catherine Author-X-Name-Last: Vermandele Title: Lorenz and Excess Wealth Orders, with Applications in Reinsurance Theory Abstract: The purpose of this paper is to study the stochastic orderings defined by means of pointwise comparison of the Lorenz curves, or of the excess wealth transforms, of two risks. The resulting order relations are presented in an actuarial context and put in relation with classical stochastic orderings, namely the stochastic dominance, the stop-loss order, the convex order and the dispersive order. Several relevant applications in reinsurance theory are provided. Journal: Scandinavian Actuarial Journal Pages: 170-185 Issue: 2 Volume: 1999 Year: 1999 X-DOI: 10.1080/03461239950132642 File-URL: http://hdl.handle.net/10.1080/03461239950132642 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:1999:y:1999:i:2:p:170-185 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151006_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Applied Section in the Scandinavian Actuarial Journal Journal: Pages: 1-1 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066683 File-URL: http://hdl.handle.net/10.1080/034612300750066683 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:1-1 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151007_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Svend Haastrup Author-X-Name-First: Svend Author-X-Name-Last: Haastrup Title: Comparison of Some Bayesian Analyses of Heterogeneity in Group Life Insurance Abstract: Norberg (1989) analyses the heterogeneity in a portfolio of group life insurances using a parametric empirical Bayesian approach. In the present paper the model of Norberg is compared to a parametric fully Bayesian model and to a non-parametric fully Bayesian model. Journal: Scandinavian Actuarial Journal Pages: 2-16 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066692 File-URL: http://hdl.handle.net/10.1080/034612300750066692 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:2-16 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151008_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jacques Carriere Author-X-Name-First: Jacques Author-X-Name-Last: Carriere Title: Bivariate Survival Models for Coupled Lives Abstract: This article presents alternative models for modeling the dependence of the time of deaths of coupled lives and applies these to a data set from a life annuity portfolio. The data indicates a very high positive correlation in the time of deaths between coupled lives. The analysis concludes that a mixed frailty copula model with Gompertz marginals fits the data very well. Another model that fits the data well is based on a generalized Frank copula. Journal: Scandinavian Actuarial Journal Pages: 17-32 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066700 File-URL: http://hdl.handle.net/10.1080/034612300750066700 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:17-32 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151009_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Usabel Author-X-Name-First: M. Author-X-Name-Last: Usabel Title: Insurance Considering a New Stochastic Model for the Discount Factor Abstract: In many empirical situations (e.g.: Libor), the rate of interest will remain fixed at a certain level (random instantaneous rate i i ) for a random period of time ( t i ) until a new random rate should be considered, i i + 1 , that will remain for t i + 1 , waiting time until the next change in the rate of interest. Three models were developed using the approach cited above for random rate of interest and random waiting times between changes in the rate of interest. Using easy integral transforms (Laplace & Fourier) we will be able to calculate the moments of the probability function of the discount factor, V ( t ), and even its c.d.f. The approach will also be extended to the calculation of the expected value (net premium) and variance of a term insurance and we will get its c.d.f., something not very common in actuarial literature due to its complexity, but very useful when the law of large numbers cannot be applied and consequently use normal approximations. Journal: Scandinavian Actuarial Journal Pages: 33-45 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066719 File-URL: http://hdl.handle.net/10.1080/034612300750066719 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:33-45 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151010_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Z. G. Ignatov Author-X-Name-First: Z. G. Author-X-Name-Last: Ignatov Author-Name: V. K. Kaishev Author-X-Name-First: V. K. Author-X-Name-Last: Kaishev Title: Two-Sided Bounds for the Finite Time Probability of Ruin Abstract: Explicit, two-sided bounds are derived for the probability of ruin of an insurance company, whose premium income is represented by an arbitrary, increasing real function, the claims are dependent, integer valued r.v.s and their inter-occurrence times are exponentially, non-identically distributed. It is shown, that the two bounds coincide when the moments of the claims form a Poisson point process. An expression for the survival probability is further derived in this special case, assuming that the claims are integer valued, i.i.d. r.v.s. This expression is compared with a different formula, obtained recently by Picard & Lefevre (1997) in terms of generalized Appell polynomials. The particular case of constant rate premium income and non-zero initial capital is considered. A connection of the survival probability to multivariate B -splines is also established. Journal: Scandinavian Actuarial Journal Pages: 46-62 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066728 File-URL: http://hdl.handle.net/10.1080/034612300750066728 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:46-62 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151011_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: On Evaluation of the Conditional Distribution of the Deficit at the Time of Ruin Abstract: Analytic evaluation of the deficit at the time of ruin is shown to be simplified when the residual equilibrium density function associated with the claim size distribution has a certain property. This result is used to show that the conditional distribution of the deficit is a mixture of Erlangs (gamma with integer shape parameters) if the same is true of the claim size distribution. This unifies and generalizes previous results involving combinations of exponentials and a particular Erlang distribution. Extensions are then discussed. Journal: Scandinavian Actuarial Journal Pages: 63-79 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066737 File-URL: http://hdl.handle.net/10.1080/034612300750066737 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:63-79 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151012_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Torbjörn Andréason Author-X-Name-First: Torbjörn Author-X-Name-Last: Andréason Author-Name: Fredrik Johansson Author-X-Name-First: Fredrik Author-X-Name-Last: Johansson Author-Name: Björn Palmgren Author-X-Name-First: Björn Author-X-Name-Last: Palmgren Title: Measuring and Modelling Technical Risks in Non-Life Insurance Abstract: The aim is to highlight some questions that are of practical interest and that we believe could be fruitful areas for further research. Studies in non-life insurance of claims ratio data, show correlation patterns between risk-years and between different classes of insurance. Empirical studies, some progress in international classification of risks, and more work on models would no doubt be helpful for solvency control and methods for insurers' allocation of capital. In particular, we point out the usefulness of more realistic statistical distributions in this context, which is illustrated by analysis of some Swedish data. Journal: Scandinavian Actuarial Journal Pages: 80-88 Issue: 1 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066746 File-URL: http://hdl.handle.net/10.1080/034612300750066746 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:1:p:80-88 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151013_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: H. Dennis Tolley Author-X-Name-First: H. Dennis Author-X-Name-Last: Tolley Author-Name: Gilbert Fellingham Author-X-Name-First: Gilbert Author-X-Name-Last: Fellingham Title: Likelihood Methods for Combining Tables of Data Abstract: Often times actuaries, health policy planners and managers must draw conclusions from several related sources of data. Particularly for actuaries, there is often a need to construct a table based on the experience of several blocks of business or on several different tables of data. Although sophisticated methods for using the resulting tables of data have been developed, often that table representing the information combined from several sources is constructed in a relatively ad hoc manner. This paper presents a likelihood method of combining tables of data from several sources. The methods are based on techniques dating at least back to the mid 1940's, but have been made more feasible with advances in computational power. The method presented allows for situations where the data sources have aggregated the data at different levels. In this case questions of estimability are examined using the implicit function theorem. The method is illustrated with an example. Journal: Scandinavian Actuarial Journal Pages: 89-101 Issue: 2 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066809 File-URL: http://hdl.handle.net/10.1080/034612300750066809 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:2:p:89-101 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151014_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: José Garrido Author-X-Name-First: José Author-X-Name-Last: Garrido Title: Two-Sided Bounds for Tails of Compound Negative Binomial Distributions in the Exponential and Heavy-Tailed Cases Abstract: This paper derives two-sided bounds for tails of compound negative binomial distributions, both in the exponential and heavy-tailed cases. Two approaches are employed to derive the two-sided bounds in the case of exponential tails. One is the convolution technique, as in Willmot & Lin (1997). The other is based on an identity of compound negative binomial distributions; they can be represented as a compound Poisson distribution with a compound logarithmic distribution as the underlying claims distribution. This connection between the compound negative binomial, Poisson and logarithmic distributions results in two-sided bounds for the tails of the compound negative binomial distribution, which also generalize and improve a result of Willmot & Lin (1997). For the heavy-tailed case, we use the method developed by Cai & Garrido (1999b). In addition, we give two-sided bounds for stop-loss premiums of compound negative binomial distributions. Furthermore, we derive bounds for the stop-loss premiums of general compound distributions among the classes of HNBUE and HNWUE. Journal: Scandinavian Actuarial Journal Pages: 102-120 Issue: 2 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066818 File-URL: http://hdl.handle.net/10.1080/034612300750066818 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:2:p:102-120 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151015_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: S. David Promislow Author-X-Name-First: S. David Author-X-Name-Last: Promislow Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Title: Equity and Credibility Abstract: We build on previous work concerned with measuring equity and consider the problem of using observed claim data or other information to calculate premiums which maximize equity. When these optimal premiums are used, we show that gathering more information or refining the risk classification always increases equity. We study the case for which the premium is constrained to be an affine function of the claim data and obtain results analogous to classical credibility theory, including the inhomogeneous and homogeneous cases of the Bu¨hlmann-Straub model. We derive formulas for the credibility weights in certain cases. Journal: Scandinavian Actuarial Journal Pages: 121-146 Issue: 2 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066827 File-URL: http://hdl.handle.net/10.1080/034612300750066827 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:2:p:121-146 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151016_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Author-Name: Christian Hipp Author-X-Name-First: Christian Author-X-Name-Last: Hipp Title: Ruin Problems for Phase-Type(2) Risk Processes Abstract: In this paper we consider a risk process in which claim inter-arrival times have a phase-type(2) distribution, a distribution with a density satisfying a second order linear differential equation. We consider some ruin related problems. In particular, we consider the compound geometric representation of the infinite time survival probability, as well as the (defective) distributions of the surplus immediately prior to ruin and of the deficit at ruin. We also consider explicit solutions for the infinite time ruin probability in the case where the individual claim amount distribution is phase-type. Journal: Scandinavian Actuarial Journal Pages: 147-167 Issue: 2 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066836 File-URL: http://hdl.handle.net/10.1080/034612300750066836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:2:p:147-167 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151017_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: W. J. Willemse Author-X-Name-First: W. J. Author-X-Name-Last: Willemse Author-Name: H. Koppelaar Author-X-Name-First: H. Author-X-Name-Last: Koppelaar Title: Knowledge Elicitation of Gompertz' Law of Mortality Abstract: A new formulation of Gompertz' law of mortality is proposed. Explicit formulas for moment generating function and moments of this formulation are derived. The new formulation is applied to the theory of heterogeneous populations and formulas for stop-loss transformations are derived. Journal: Scandinavian Actuarial Journal Pages: 168-179 Issue: 2 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066845 File-URL: http://hdl.handle.net/10.1080/034612300750066845 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:2:p:168-179 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151018_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Erratum Journal: Pages: 180-180 Issue: 2 Volume: 2000 Year: 2000 X-DOI: 10.1080/034612300750066854 File-URL: http://hdl.handle.net/10.1080/034612300750066854 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2000:y:2000:i:2:p:180-180 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151019_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Diane Bédard Author-X-Name-First: Diane Author-X-Name-Last: Bédard Author-Name: Daniel Dufresne Author-X-Name-First: Daniel Author-X-Name-Last: Dufresne Title: Pension Funding with Moving Average Rates of Return Abstract: In the context of the model of pension funding introduced by Dufresne in 1986, explicit expressions are found for the first two moments of fund level and total contributions, when (1) actuarial gains and losses are amortized over N years, and (2) arithmetic rates of return on assets form a moving average process. The results are obtained via a Markovian representation for the bilinear process obtained for the actuarial losses. One conclusion is that the dependence between successive rates of return may have very significant effects on the financial results obtained. Journal: Scandinavian Actuarial Journal Pages: 1-17 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077275 File-URL: http://hdl.handle.net/10.1080/034612301750077275 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:1-17 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151020_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Farida Enikeeva Author-X-Name-First: Farida Author-X-Name-Last: Enikeeva Author-Name: Vladimir Kalashnikov Author-X-Name-First: Vladimir Author-X-Name-Last: Kalashnikov Author-Name: Deimante Rusaityte Author-X-Name-First: Deimante Author-X-Name-Last: Rusaityte Title: Continuity Estimates for Ruin Probabilities Abstract: A method of continuity analysis of ruin probabilities with respect to variation of parameters governing risk processes is proposed. It is based on the representation of the ruin probability as the stationary probability of a reversed process. We apply Kartashov's technique designed for continuity analysis of stationary distributions of general Markov chains in order to obtain desired continuity estimates. The method is illustrated by the Sparre Andersen and Markov modulated risk models. Journal: Scandinavian Actuarial Journal Pages: 18-39 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077293 File-URL: http://hdl.handle.net/10.1080/034612301750077293 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:18-39 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151021_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: Comparison of Methods for Evaluation of the Convolution of Two Compound R 1 Distributions Abstract: In the present paper we compare four methods for evaluating the convolution of two compound R 1 distributions by counting the numbers of elementary algebraic operations required. Two of the methods are applicable in general, whereas the remaining two are restricted to the case when the two compound distributions have the same severity distribution. This case is discussed separately. We consider in particular the special case when this common severity distribution is concentrated in one, that is, evaluation of the convolution of two R 1 distributions. Journal: Scandinavian Actuarial Journal Pages: 40-54 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077310 File-URL: http://hdl.handle.net/10.1080/034612301750077310 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:40-54 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151022_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: Optimal Proportional Reinsurance Policies in a Dynamic Setting Abstract: We consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model. Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed. Journal: Scandinavian Actuarial Journal Pages: 55-68 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077338 File-URL: http://hdl.handle.net/10.1080/034612301750077338 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:55-68 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151023_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Knut Aase Author-X-Name-First: Knut Author-X-Name-Last: Aase Title: On the St. Petersburg Paradox Abstract: The classical St. Petersburg Paradox is discussed in terms of doubling strategies. It is claimed that what was originally thought of as a ''paradox'' can hardly be considered as very surprising today, but viewed in terms of doubling strategies, we get some results that look paradoxical, at least to the practically oriented investor. Journal: Scandinavian Actuarial Journal Pages: 69-78 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077356 File-URL: http://hdl.handle.net/10.1080/034612301750077356 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:69-78 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151024_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Maria Lindbergson Author-X-Name-First: Maria Author-X-Name-Last: Lindbergson Title: Mortality Among the Elderly in Sweden 1988–1997 Abstract: By replacing the exponential growth in a Makeham function with a straight line at very high ages, graduated mortality rates gives an acceptable adherence to observed data. Journal: Scandinavian Actuarial Journal Pages: 79-94 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077374 File-URL: http://hdl.handle.net/10.1080/034612301750077374 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:79-94 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151025_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Malcolm Campbell Author-X-Name-First: Malcolm Author-X-Name-Last: Campbell Title: Book Review Journal: Pages: 95-96 Issue: 1 Volume: 2001 Year: 2001 X-DOI: 10.1080/034612301750077392 File-URL: http://hdl.handle.net/10.1080/034612301750077392 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:1:p:95-96 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151026_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Arne Sandström Author-X-Name-First: Arne Author-X-Name-Last: Sandström Title: SAJ to Become a Quarterly Journal Journal: Pages: 97-97 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592746 File-URL: http://hdl.handle.net/10.1080/03461230152592746 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:97-97 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151027_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghislain Léveillé Author-X-Name-First: Ghislain Author-X-Name-Last: Léveillé Author-Name: José Garrido Author-X-Name-First: José Author-X-Name-Last: Garrido Title: Recursive Moments of Compound Renewal Sums with Discounted Claims Abstract: Under regularity conditions, Le´veille´& Garrido [6] gives a derivation of the first two moments (resp. asymptotic) of a Compound Renewal Present Value Risk (CRPVR) process using renewal theory arguments. In this paper, with the same procedure and assuming that all the moments of the claim severity and the claims number process exist, we get recursive formulas for all the moments (resp. asymptotic) of the CRPVR process. Journal: Scandinavian Actuarial Journal Pages: 98-110 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592755 File-URL: http://hdl.handle.net/10.1080/03461230152592755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:98-110 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151028_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jan Beirlant Author-X-Name-First: Jan Author-X-Name-Last: Beirlant Author-Name: Armelle Guillou Author-X-Name-First: Armelle Author-X-Name-Last: Guillou Title: Pareto Index Estimation Under Moderate Right Censoring Abstract: Real claim data sometimes are censored from above at a high value induced by the sum insured. In this note we examine the behaviour of extreme-value methods in such settings and propose an adaptation of the popular Hill (1975) estimator. It is argued that the censoring typically cannot exceed 5% for an effective use of the methods suggested. Journal: Scandinavian Actuarial Journal Pages: 111-125 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592764 File-URL: http://hdl.handle.net/10.1080/03461230152592764 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:111-125 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151029_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Title: On Bonus and Bonus Prognoses in Life Insurance Abstract: The surplus on a life insurance policy is defined, at any time during the term of the contract, as the difference between the second order retrospective reserve and the first order prospective reserve. General principles for redistribution of the systematic part of the surplus as bonus are formulated, and various special bonus schemes are discussed. Techniques for forecasting future bonuses are worked out in an extended model with stochastic experience basis. Numerical illustrations are provided. Journal: Scandinavian Actuarial Journal Pages: 126-147 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592773 File-URL: http://hdl.handle.net/10.1080/03461230152592773 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:126-147 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151030_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Philippe Picard Author-X-Name-First: Philippe Author-X-Name-Last: Picard Author-Name: Claude Lefèvre Author-X-Name-First: Claude Author-X-Name-Last: Lefèvre Title: On the Probability of (Non-) Ruin in Infinite Time Abstract: In the context of the classical Poisson ruin model Gerber (1988a,b) and Shiu (1987, 1989) have obtained two formulae for the ruin and non ruin probabilities in infinite time. Here these two formulae are generalized to the case of an arbitrary premium process when all claims are integer-valued, as in Picard & Lefèvre (1997). Moreover, this generalization throws a new light on the two known formulae and it then leads very simply to a third new formula. Journal: Scandinavian Actuarial Journal Pages: 148-161 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592782 File-URL: http://hdl.handle.net/10.1080/03461230152592782 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:148-161 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151031_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Holger Rootzén Author-X-Name-First: Holger Author-X-Name-Last: Rootzén Author-Name: Nader Tajvidi Author-X-Name-First: Nader Author-X-Name-Last: Tajvidi Title: Can Losses Caused by Wind Storms be Predicted from Meteorological Observations? Abstract: This paper contains a study of the extent to which aggregate losses due to severe wind storms can be explained by wind measurements. The analysis is based on 12 years of data for a region, Ska § ne, in southern Sweden. A previous investigation indicated that wind measurements from six recording stations in Ska § ne was insufficient to obtain accurate prediction. The present study instead uses geostrophic winds calculated from pressure readings, at a regular grid of size 50 kilometres over Ska § ne. However, also this meteorological data set is seen to be insufficient for accurate prediction of insurance risk. The results indicate that currently popular methods of evaluating wind storm risks from meteorological data should not be used uncritically by insurers or reinsurers. Nevertheless, wind data does contain some information on insurance. risks. There is a need for further research on how to use this information to improve risk assessment. Journal: Scandinavian Actuarial Journal Pages: 162-175 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592791 File-URL: http://hdl.handle.net/10.1080/03461230152592791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:162-175 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151032_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Harald Hannerz Author-X-Name-First: Harald Author-X-Name-Last: Hannerz Title: Presentation and Derivation of a Five-Parameter Survival Function Intended to Model Mortality in Modern Female Populations Abstract: A single analytical expression for the probability of survival from birth to age x that would hold good for all ages in the entire human life span has been sought for centuries. With an eight-parameter function, Heligman and Pollard achieved this goal, for integer values of x , in 1980. The present paper introduces a five-parameter survival function intended to model human mortality in modern female populations. The introduced function is not only defined for integers. It is defined for all ages. Journal: Scandinavian Actuarial Journal Pages: 176-187 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592809 File-URL: http://hdl.handle.net/10.1080/03461230152592809 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:176-187 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151033_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Title: Book Review Journal: Pages: 188-189 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592818 File-URL: http://hdl.handle.net/10.1080/03461230152592818 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:188-189 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151034_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Acknowledgements to our Referees Journal: Pages: 190-190 Issue: 2 Volume: 2001 Year: 2001 X-DOI: 10.1080/03461230152592827 File-URL: http://hdl.handle.net/10.1080/03461230152592827 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2001:y:2001:i:2:p:190-190 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151035_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Useful Information from the Publisher Journal: Pages: 1-2 Issue: 1 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612301753432349 File-URL: http://hdl.handle.net/10.1080/034612301753432349 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:1-2 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151036_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Christian Genest Author-X-Name-First: Christian Author-X-Name-Last: Genest Author-Name: Étienne Marceau Author-X-Name-First: Étienne Author-X-Name-Last: Marceau Title: Criteria for the Stochastic Ordering of Random Sums, with Actuarial Applications Abstract: It is shown that vectors ( S M 1 , … , S Mn ) and ( S' M'1 , …, S' M'n ) of random sums of positive random variables are stochastically ordered by upper orthant dependence, lower orthant dependence, concordance or by the supermodular ordering whenever their corresponding random numbers of terms ( M 1 , … , M n ) and ( M' 1 , … , M' n ) are themselves ordered in this fashion. Actuarial applications of these results are given to different dependence structures for the collective risk model with several classes of business. Journal: Scandinavian Actuarial Journal Pages: 3-16 Issue: 1 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106192 File-URL: http://hdl.handle.net/10.1080/03461230110106192 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:3-16 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151037_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alessandro Juri Author-X-Name-First: Alessandro Author-X-Name-Last: Juri Title: Supermodular Order and Lundberg Exponents Abstract: A risk process where the claims are sums of dependent random variables is considered. Using the supermodular order the influence, the dependence has on the infinite- and finite-time Lundberg exponent is investigated and monotonicity results are obtained. Journal: Scandinavian Actuarial Journal Pages: 17-36 Issue: 1 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106200 File-URL: http://hdl.handle.net/10.1080/03461230110106200 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:17-36 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151038_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: E. Gómez-Déniz Author-X-Name-First: E. Author-X-Name-Last: Gómez-Déniz Author-Name: A. Hernández-Bastida Author-X-Name-First: A. Author-X-Name-Last: Hernández-Bastida Author-Name: F.J. Vázquez-Polo Author-X-Name-First: F.J. Author-X-Name-Last: Vázquez-Polo Title: Bounds for Ratios of Posterior Expectations: Applications in the Collective Risk Model Abstract: This paper considers the collective risk model for the insurance claims process. We will adopt a Bayesian point of view, where uncertainty concerning the specification of the prior distribution is a common question. The robust Bayesian approach uses a class of prior distributions which model uncertainty about the prior, instead of a single distribution. Relatively little research has dealt with robustness with respect to ratios of posterior expectations as occurs with the Esscher and Variance premium principles. Appropriate techniques are developed in this paper to solve this problem using the k -contamination class in the collective risk model. Journal: Scandinavian Actuarial Journal Pages: 37-44 Issue: 1 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106246 File-URL: http://hdl.handle.net/10.1080/03461230110106246 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:37-44 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151039_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: S -Convex Extrema, Taylor-Type Expansions and Stochastic Approximations Abstract: The present work studies s -convex orders using a remarkable probabilistic generalization of Taylor's theorem obtained by Massey & Whitt (1993) and further discussed by Lin (1994). We propose two methods for approximating a given risk with known first moments by means of s -convex extremal distributions. The goodness of those approximations is explored using stop-loss distances. Several applications show the interest of this approach in actuarial sciences. Journal: Scandinavian Actuarial Journal Pages: 45-67 Issue: 1 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106228 File-URL: http://hdl.handle.net/10.1080/03461230110106228 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:45-67 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151040_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book Reviews Journal: Pages: 68-71 Issue: 1 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612301753432394 File-URL: http://hdl.handle.net/10.1080/034612301753432394 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:68-71 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151041_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Knut Aase Author-X-Name-First: Knut Author-X-Name-Last: Aase Title: Perspectives of Risk Sharing Abstract: In this paper we present an overview of the standard risk sharing model of insurance. We discuss and characterize a competitive equilibrium, Pareto optimality, and representative agent pricing, including its implications for insurance premiums. We only touch upon the existence problem of a competitive equilibrium, primarily by presenting several examples. Risk tolerance and aggregation is the subject of one section. Risk adjustment of the probability measure is one topic, as well as the insurance version of the capital asset pricing model. The competitive paradigm may be a little demanding in practice, so we alternatively present a game theoretic view of risk sharing, where solutions end up in the core. Properly interpreted, this may give rise to a range of prices of each risk, often visualized in practice by an ask price and a bid price. The nice aspect of this is that these price ranges can be explained by "first principles", not relying on transaction costs or other frictions. We also include a short discussion of moral hazard in risk sharing between an insurer and a prospective insurance buyer. We end the paper by indicating the implications of our results for a pure stock market. In particular we find it advantageous to discuss the concepts of incomplete markets in this general setting, where it is possible to use results for closed, convex subspaces of an L 2 -space to discuss optimal risk allocation problems in incomplete financial markets. Journal: Scandinavian Actuarial Journal Pages: 73-128 Issue: 2 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106237 File-URL: http://hdl.handle.net/10.1080/03461230110106237 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:2:p:73-128 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151042_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Maria de Lourdes Centeno Author-X-Name-First: Maria Author-X-Name-Last: de Lourdes Centeno Author-Name: João Manuel Andrade Silva Author-X-Name-First: João Manuel Andrade Author-X-Name-Last: Silva Title: Optimal Bonus Scales Under Path-Dependent Bonus Rules Abstract: Bonus malus systems have been studied by several authors under the framework of Markov chains. Optimal scales have been deduced by Norberg (1976), Borgan, Hoem & Norberg (1981) and Gilde & Sundt (1989). In these articles the authors assumed that the bonus system forms a first order Markov chain. In the present paper we deduce the optimal scales, using the same criteria as in the cited papers, for bonus systems that are not first order Markovian processes, but that can be regarded as Markovian by increasing the number of states of the system. Journal: Scandinavian Actuarial Journal Pages: 129-136 Issue: 2 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106264 File-URL: http://hdl.handle.net/10.1080/03461230110106264 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:2:p:129-136 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151043_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Arne Sandström Author-X-Name-First: Arne Author-X-Name-Last: Sandström Title: Information from the Editor Journal: Pages: 137-137 Issue: 3 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612302320179836 File-URL: http://hdl.handle.net/10.1080/034612302320179836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:3:p:137-137 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151044_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stathis Chadjiconstantinidis Author-X-Name-First: Stathis Author-X-Name-Last: Chadjiconstantinidis Author-Name: Demetrios Antzoulakos Author-X-Name-First: Demetrios Author-X-Name-Last: Antzoulakos Title: Moments of Compound Mixed Poisson Distributions Abstract: Recursive formulae are derived for the evaluation of the moments and the descending factorial moments about a point n of mixed Poisson and compound mixed Poisson distributions, in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. As byproduct, we also obtain recursive formulae for the evaluation of the moments about the origin, central moments, descending and ascending factorial moments of these distributions. Examples are also presented for a number of mixing densities. Journal: Scandinavian Actuarial Journal Pages: 138-161 Issue: 3 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612302320179845 File-URL: http://hdl.handle.net/10.1080/034612302320179845 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:3:p:138-161 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151045_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xeni Dimakos Author-X-Name-First: Xeni Author-X-Name-Last: Dimakos Author-Name: Arnoldo Di Rattalma Author-X-Name-First: Arnoldo Author-X-Name-Last: Di Rattalma Title: Bayesian Premium Rating with Latent Structure Abstract: We propose a fully Bayesian approach to non-life risk premium rating, based on hierarchical models with latent variables for both claim frequency and claim size. Inference is based on the joint posterior distribution and is performed by Markov Chain Monte Carlo. Rather than plug-in point estimates of all unknown parameters, we take into account all sources of uncertainty simultaneously when the model is used to predict claims and estimate risk premiums. Several models are fitted to both a simulated dataset and a small portfolio regarding theft from cars. We show that interaction among latent variables can improve predictions significantly. We also investigate when interaction is not necessary. We compare our results with those obtained under a standard generalized linear model and show through numerical simulation that geographically located and spatially interacting latent variables can successfully compensate for missing covariates. However, when applied to the real portfolio data, the proposed models are not better than standard models due to the lack of spatial structure in the data. Journal: Scandinavian Actuarial Journal Pages: 162-184 Issue: 3 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612302320179854 File-URL: http://hdl.handle.net/10.1080/034612302320179854 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:3:p:162-184 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151046_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mary Hardy Author-X-Name-First: Mary Author-X-Name-Last: Hardy Title: Bayesian Risk Management for Equity-Linked Insurance Abstract: This paper describes how to apply Markov Chain Monte Carlo (MCMC) techniques to a regime switching model of the stock price process to generate a sample from the joint posterior distribution of the parameters of the model. The MCMC output can be used to generate a sample from the predictive distribution of losses from equity linked contracts, assuming first an actuarial approach to risk management and secondly a financial economics approach. The predictive distribution is used to show the effect of parameter uncertainty on risk management calculations. We also explore model uncertainty by assuming a GARCH model in place of the regime switching model. The results indicate that the financial economics approach to risk management is substantially more robust to parameter uncertainty and model uncertainty than the actuarial approach. Journal: Scandinavian Actuarial Journal Pages: 185-211 Issue: 3 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612302320179863 File-URL: http://hdl.handle.net/10.1080/034612302320179863 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:3:p:185-211 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151047_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Dahan Author-X-Name-First: M. Author-X-Name-Last: Dahan Author-Name: E. Frostig Author-X-Name-First: E. Author-X-Name-Last: Frostig Author-Name: N. A. Langberg Author-X-Name-First: N. A. Author-X-Name-Last: Langberg Title: Life Insurance Policies with Statistical Heterogeneous Population Abstract: In the paper we consider an endowment insurance contract with a twelve months maturation time. Using the majorization order and Schur-convex functions we derive upper and lower bounds of the premium, the death and survival benefits for a hetrogeneous population of insureds. The bounds are obtained for the exponential, Balducci, and linear approximations. Journal: Scandinavian Actuarial Journal Pages: 212-222 Issue: 3 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612302320179872 File-URL: http://hdl.handle.net/10.1080/034612302320179872 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:3:p:212-222 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151048_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book Review Journal: Pages: 223-224 Issue: 3 Volume: 2002 Year: 2002 X-DOI: 10.1080/034612302320179881 File-URL: http://hdl.handle.net/10.1080/034612302320179881 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:3:p:223-224 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151049_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bjarne Højgaard Author-X-Name-First: Bjarne Author-X-Name-Last: Højgaard Title: Optimal Dynamic Premium Control in Non-life Insurance. Maximizing Dividend Pay-outs Abstract: In this paper we consider the problem of finding optimal dynamic premium policies in non-life insurance. The reserve of a company is modeled using the classical Cramér-Lundberg model with premium rates calculated via the expected value principle. The company controls dynamically the relative safety loading with the possibility of gaining or loosing customers. It distributes dividends according to a 'barrier strategy' and the objective of the company is to find an optimal premium policy and dividend barrier maximizing the expected total, discounted pay-out of dividends. In the case of exponential claim size distributions optimal controls are found on closed form, while for general claim size distributions a numerical scheme for approximations of the optimal control is derived. Based on the idea of De Vylder going back to the 1970s, the paper also investigates the possibilities of approximating the optimal control in the general case by using the closed form solution of an approximating problem with exponential claim size distributions. Journal: Scandinavian Actuarial Journal Pages: 225-245 Issue: 4 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106291 File-URL: http://hdl.handle.net/10.1080/03461230110106291 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:4:p:225-245 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151050_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Virginia Young Author-X-Name-First: Virginia Author-X-Name-Last: Young Author-Name: Thaleia Zariphopoulou Author-X-Name-First: Thaleia Author-X-Name-Last: Zariphopoulou Title: Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility Abstract: We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze. Journal: Scandinavian Actuarial Journal Pages: 246-279 Issue: 4 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106327 File-URL: http://hdl.handle.net/10.1080/03461230110106327 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:4:p:246-279 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151051_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mette Hansen Author-X-Name-First: Mette Author-X-Name-Last: Hansen Author-Name: Kristian Miltersen Author-X-Name-First: Kristian Author-X-Name-Last: Miltersen Title: Minimum Rate of Return Guarantees: The Danish Case Abstract: We analyze minimum rate of return guarantees for life-insurance (investment) contracts and pension plans with a smooth surplus distribution mechanism. We specifically model the smoothing mechanism used by most Danish life-insurance companies and pension funds. The annual distribution of bonus will be based on this smoothing mechanism after taking the minimum rate of return guarantee into account. In addition, based on the contribution method the customer will receive a final (non-negative) undistributed surplus when the contract matures. We consider two different methods that the company can use to collect payment for issuing these minimum rate of return guarantee contracts: the direct method where the company gets a fixed (percentage) fee of the customer's savings each year, e.g. 0.5% in Denmark, and the indirect method where the company gets a share of the distributed surplus. In both cases we analyze how to set the terms of the contract in order to have a fair contract between an individual customer and the company. Having analyzed the one-customer case, we turn to analyzing the case with two customers. We consider the consequences of pooling the undistributed surplus over two inhomogeneous customers. This implies setting up different mechanisms for distributing final bonus (undistributed surplus) between the customers. Journal: Scandinavian Actuarial Journal Pages: 280-318 Issue: 4 Volume: 2002 Year: 2002 X-DOI: 10.1080/03461230110106282 File-URL: http://hdl.handle.net/10.1080/03461230110106282 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2002:y:2002:i:4:p:280-318 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151052_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Konstadinos Politis Author-X-Name-First: Konstadinos Author-X-Name-Last: Politis Title: Semiparametric Estimation for Non-Ruin Probabilities Abstract: We consider the classical risk model with unknown claim size distribution F and unknown Poisson arrival rate u . Given a sample of claims from F and a sample of interarrival times for these claims, we construct an estimator for the function Z ( u ), which gives the probability of non-ruin in that model for initial surplus u . We obtain strong consistency and asymptotic normality for that estimator for a large class of claim distributions F . Confidence bounds for Z ( u ) based on the bootstrap are also given and illustrated by some numerical examples. Journal: Scandinavian Actuarial Journal Pages: 75-96 Issue: 1 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230308487 File-URL: http://hdl.handle.net/10.1080/03461230308487 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:1:p:75-96 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151053_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Johan Irbäck Author-X-Name-First: Johan Author-X-Name-Last: Irbäck Title: Asymptotic Theory for a Risk Process with a High Dividend Barrier Abstract: The only way to avoid ruin in the classical model of the collective risk theory is that the surplus increases to infinity. We consider a modified model with a dividend barrier that prevents this behavior. It is shown that there is a simple approximation formula for the time of ruin when the level of the dividend barrier is high and the Cramér-Lundberg condition is satisfied. A numerical example is presented in the case when the claims are exponentially distributed. The relation to queuing theory is used to derive the proportion of time the surplus is below some given level. Journal: Scandinavian Actuarial Journal Pages: 97-118 Issue: 2 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106345 File-URL: http://hdl.handle.net/10.1080/03461230110106345 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:2:p:97-118 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151054_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Sequential Quasi-Credibility for Scale Dispersion Models Abstract: The sequential approach to credibility, developed by Landsman and Makov [(1999a) On stochastic approximation and credibility. Scand. Actuarial J.1, 15-31; (1999b) Sequential credibility evaluation for symmetric location claim distributions. Insurance: Math. Econ.24, 291-300] is extended to the scale dispersion family, which contains distributions often used in actuarial science: log-normal, Weibull, Half normal, Stable, Pareto, to mention only a few. For members of this family a sequential quasi-credibility formula is devised, which can also be used for heavy tailed claims. The results are illustrated by a study of log-normal claims. Journal: Scandinavian Actuarial Journal Pages: 119-135 Issue: 2 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106363 File-URL: http://hdl.handle.net/10.1080/03461230110106363 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:2:p:119-135 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151055_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: E. Frostig Author-X-Name-First: E. Author-X-Name-Last: Frostig Author-Name: S. Haberman Author-X-Name-First: S. Author-X-Name-Last: Haberman Author-Name: B. Levikson Author-X-Name-First: B. Author-X-Name-Last: Levikson Title: Generalized Life Insurance: Ruin Probabilities Abstract: We study ruin probabilities for generalized life insurance programs. These programs include among others whole life and long term care contracts. Clearly, in such programs the claims in successive years are dependent, hence the structure of our problem is different from that of ruin probabilities in general insurance where claims over time are independent. First, we develop algorithms calculating the ruin probabilities for life and LTC insurance programs. Further, upper and lower bounds for these probabilities are derived. These new bounds take into account the joint distribution of claims over time. Journal: Scandinavian Actuarial Journal Pages: 136-152 Issue: 2 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106390 File-URL: http://hdl.handle.net/10.1080/03461230110106390 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:2:p:136-152 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10151056_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: P. Linnemann Author-X-Name-First: P. Author-X-Name-Last: Linnemann Title: An Actuarial Analysis of Participating Life Insurance Abstract: An actuarial model is developed to reveal the intrinsic nature of participating life insurance. The basic safe-side criterion is examined. It is established how the first-order prospective net premium reserve includes safety margins or bonus loadings, and it is demonstrated how the bonus loadings are currently released. It is demonstrated how surplus may be distributed and accumulated as a terminal bonus in an equitable way. The level premium is divided into a variable recurrent single premium and a variable natural premium, and an alternative to the prospective net premium reserve is examined. A capitalization of future safety margins or bonus loadings, which are related to past premiums and the paid-up benefit, may allow the insurance company a considerable increase in investment freedom. The theory is illustrated by numerical results. Journal: Scandinavian Actuarial Journal Pages: 153-176 Issue: 2 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106336 File-URL: http://hdl.handle.net/10.1080/03461230110106336 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:2:p:153-176 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614023_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jostein Paulsen Author-X-Name-First: Jostein Author-X-Name-Last: Paulsen Author-Name: Bo Normann Rasmussen Author-X-Name-First: Bo Normann Author-X-Name-Last: Rasmussen Title: Simulating Ruin Probabilities for a Class of Semimartingales by Importance Sampling Methods Abstract: We consider the problem of finding the probability of ruin when the risk process is assumed to be a special semimartingale with absolutely continuous characteristics. We show how the generalized Girsanov theorem can be used in connection with Monte Carlo simulation to obtain estimates of the ruin probabilities. It is shown by both analytical and numerical examples that these methods can be significantly better than ordinary simulations provided the new measure is chosen with some care. Journal: Scand Actuarial Journal Pages: 178-216 Issue: 3 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106354 File-URL: http://hdl.handle.net/10.1080/03461230110106354 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:3:p:178-216 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614024_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jin Ma Author-X-Name-First: Jin Author-X-Name-Last: Ma Author-Name: Xiaodong Sun Author-X-Name-First: Xiaodong Author-X-Name-Last: Sun Title: Ruin Probabilities for Insurance Models Involving Investments Abstract: In this paper we study the ruin problem for insurance models that involve investments. Our risk reserve process is an extension of the classical Cramér-Lundberg model, which will contain stochastic interest rates, reserve-dependent expense loading, diffusion perturbed models, and many others as special cases. By introducing a new type of exponential martingale parametrized by a general rate function, we put various Cramér-Lundberg type estimations into a unified framework. We show by examples that many existing Lundberg-type bounds for ruin probabilities can be recovered by appropriately choosing the rate functions. Journal: Scand Actuarial Journal Pages: 217-237 Issue: 3 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106381 File-URL: http://hdl.handle.net/10.1080/03461230110106381 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:3:p:217-237 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614025_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vladimir Kalashnikov Author-X-Name-First: Vladimir Author-X-Name-Last: Kalashnikov Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Title: On the Sensitivity of Premiums and Reserves to Changes in Valuation Elements Abstract: Upon differentiating the Thiele differential equations and the equivalence condition with respect to some parameter appearing in the equations, one obtains differential equations for the derivatives of the state-wise reserves and the premium level with respect to the parameter. The solution to these equations measures the impact on premiums and reserves of a change in the parameter. Typically only numerical results can be obtained, but the method applies quite generally to multi-state policies and to virtually any parameter, and so represents a panacea in (the vast majority of) situations where analytical results are out of reach. Extensions to higher order derivatives and higher order conditional moments are straightforward. A difference method for computation is devised, and numerical results are reported for some practical cases. Journal: Scand Actuarial Journal Pages: 238-256 Issue: 3 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106408 File-URL: http://hdl.handle.net/10.1080/03461230110106408 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:3:p:238-256 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614075_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Héléne Cossette Author-X-Name-First: Héléne Author-X-Name-Last: Cossette Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Étienne Marceau Author-X-Name-First: Étienne Author-X-Name-Last: Marceau Title: Ruin Probabilities in the Compound Markov Binomial Model Abstract: In this paper, we present a compound Markov binomial model which is an extension of the compound binomial model proposed by Gerber (1988a, b) and further examined by Shiu (1989) and Willmot (1993). The compound Markov binomial model is based on the Markov Bernoulli process which introduces dependency between claim occurrences. Recursive formulas are provided for the computation of the ruin probabilities over finite- and infinite-time horizons. A Lundberg exponential bound is derived for the ruin probability and numerical examples are also provided. Journal: Scand Actuarial Journal Pages: 301-323 Issue: 4 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106462 File-URL: http://hdl.handle.net/10.1080/03461230110106462 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:4:p:301-323 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614076_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: Genetics and Insurance: What have we Learned So Far? Abstract: Genetics and insurance is an area unusually exposed to rapid scientific advance, close public and political scrutiny, and popular myth. It may be leading the way towards evidence-based underwriting. This survey paper describes some of the experience gained since actuarial involvement began in the mid-1990s, particularly the vital link with genetic epidemiology. We survey the relevant aims and outputs of genetic epidemiology, mainly relating to single-gene disorders, and the use of genetic epidemiology in actuarial models. The part that actuarial models might play in evidence-based approaches to underwriting and policy-making is discussed. Journal: Scand Actuarial Journal Pages: 324-348 Issue: 4 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106426 File-URL: http://hdl.handle.net/10.1080/03461230110106426 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:4:p:324-348 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614077_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book Review Journal: Scand Actuarial Journal Pages: 349-349 Issue: 4 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230310017207 File-URL: http://hdl.handle.net/10.1080/03461230310017207 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:4:p:349-349 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614074_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mogens Bladt Author-X-Name-First: Mogens Author-X-Name-Last: Bladt Author-Name: Antonio Gonzalez Author-X-Name-First: Antonio Author-X-Name-Last: Gonzalez Author-Name: Steffen L. Lauritzen Author-X-Name-First: Steffen L. Author-X-Name-Last: Lauritzen Title: The estimation of phase-type related functionals using Markov chain Monte Carlo methods Abstract: In this paper we present a method for estimation of functionals depending on one or several phase-type distributions. This could for example be the ruin probability in a risk reserve process where claims are assumed to be of phase-type. The proposed method uses a Markov chain Monte Carlo simulation to reconstruct the Markov jump processes underlying the phase-type variables in combination with Gibbs sampling to obtain a stationary sequence of phase-type probability measures from the posterior distribution of these given the observations. This enables us to find quantiles of posterior distributions of functionals of interest, thereby representing estimation uncertainty in a flexible way. We compare our estimates to those obtained by the method of maximum likelihood and find a good agreement. We illustrate the statistical potential of the method by estimating ruin probabilities in simulated examples. Journal: Scand Actuarial Journal Pages: 280-300 Issue: 4 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106435 File-URL: http://hdl.handle.net/10.1080/03461230110106435 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:4:p:280-300 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_9614073_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kristian R. Miltersen Author-X-Name-First: Kristian R. Author-X-Name-Last: Miltersen Author-Name: Svein-arne Persson Author-X-Name-First: Svein-arne Author-X-Name-Last: Persson Title: Guaranteed Investment Contracts: Distributed and Undistributed Excess Return Abstract: Annual minimum rate of return guarantees are analyzed together with rules for distribution of positive excess return, i.e. investment returns in excess of the guaranteed minimum return. Together with the level of the annual minimum rate of return guarantee both the customer's and the insurer's fractions of the positive excess return are determined so that the market value of the insurer's capital inflow (determined by the fraction of the positive excess return) equals the market value of the insurer's capital outflow (determined by the minimum rate of return guarantee) at the inception of the contract. The analysis is undertaken both with and without a surplus distribution mechanism. The surplus distribution mechanism works through a bonus account that serves as a buffer in the following sense: in (‘bad’) years when the investment returns are lower than the minimum rate of return guarantee, funds are transferred from the bonus account to the customer's account. In (‘good’) years when the investment returns are above the minimum rate of return guarantee, a part of the positive excess return is credited to the bonus account. In addition to characterizations of fair combinations of the level of the annual minimum rate of return guarantee and the sharing rules of the positive excess return, our analysis indicates that the presence of a surplus distribution mechanism allows the insurer to offer a much wider menu of contracts to the customer than without a surplus distribution mechanism. Journal: Scand Actuarial Journal Pages: 257-279 Issue: 4 Volume: 2003 Year: 2003 X-DOI: 10.1080/03461230110106417 File-URL: http://hdl.handle.net/10.1080/03461230110106417 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2003:y:2003:i:4:p:257-279 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064582_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Rosa E. Lillo Author-X-Name-First: Rosa E. Author-X-Name-Last: Lillo Author-Name: Patrizia Semeraro Author-X-Name-First: Patrizia Author-X-Name-Last: Semeraro Title: Stochastic Bounds for Discrete-time Claim Processes with Correlated Risks Abstract: The purpose of this paper is to derive bounds on the marginal distributions of a discrete-time claim process S with correlated claims. These bounds are based on stochastic comparison in convex order and in Laplace transform order of the process S with two corresponding processes and having, respectively, uncorrelated and weakly correlated claims. The relevance of these comparisons is due to the simple structure of the processes and , which are nothing else than a random walk and a mixed random walk. The paper also contains the proof of the closure under mixture property of some dependence orders, like supermodular and PQD, and some applications of the main results. Journal: Scandinavian Actuarial Journal Pages: 1-13 Issue: 1 Volume: 2004 Year: 2004 X-DOI: 10.1080/034612301106453 File-URL: http://hdl.handle.net/10.1080/034612301106453 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:1:p:1-13 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064583_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: S. Zacks Author-X-Name-First: S. Author-X-Name-Last: Zacks Author-Name: B. Levikson Author-X-Name-First: B. Author-X-Name-Last: Levikson Title: Claiming Strategies and Premium Levels for Bonus Malus Systems Abstract: In this paper we study a bonus malus system (bms) with deductibles. A bms is characterized by its premium levels and the transition rules among them. An insured is being moved among premium levels according to his/her claim record. Thus, an insured has to find an optimal strategy of submitting claims. Here optimal is in the sense of minimizing the total expected present value (epv) costs. Such strategies are found both for finite and infinite horizons. Furthermore, premium levels balancing the cost to the insured and the payoff of the insurer are given. The methods used to analyze the problem are from dynamic programming and Markov chains. Journal: Scandinavian Actuarial Journal Pages: 14-27 Issue: 1 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230110106444 File-URL: http://hdl.handle.net/10.1080/03461230110106444 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:1:p:14-27 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064584_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marek Kaluszka Author-X-Name-First: Marek Author-X-Name-Last: Kaluszka Title: Mean-Variance Optimal Reinsurance Arrangements Abstract: Reinsurance reduces the risk but it also reduces the potential profit. The aim of the paper is to derive optimal, from the cedent's point of view, reinsurance arrangements balancing the risk measured by variance and expected profits under various mean-variance premium principles of the reinsurer. We find that quota share, excess of loss or combinations of excess of loss with quota share are the optimal rules according to a fixed expected gain of the cedent Journal: Scandinavian Actuarial Journal Pages: 28-41 Issue: 1 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410019222 File-URL: http://hdl.handle.net/10.1080/03461230410019222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:1:p:28-41 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064585_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Cecilia Mancini Author-X-Name-First: Cecilia Author-X-Name-Last: Mancini Title: Estimation of the Characteristics of the Jumps of a General Poisson-Diffusion Model Abstract: We consider a filtered probability space with a standard Brownian motion W, a simple Poisson process N with constant intensity λ>0, and we consider the process Y such that Y0∈ℝ and where a, σ are predictable bounded stochastic processes, and γ is a predictable process which is bounded away from zero. A discrete record of n+1 observations {Y0, Yt1, …, Ytn−1, Ytn} is available, with ti=ih. Using such observations, we construct estimators of Nti, i=1, …, n, λ and γτj, where τj are the instants of jump within [0, nh]. They are consistent and asymptotically controlled when the number of observations increases and the step h tends to zero. Journal: Scandinavian Actuarial Journal Pages: 42-52 Issue: 1 Volume: 2004 Year: 2004 X-DOI: 10.1080/034612303100170091 File-URL: http://hdl.handle.net/10.1080/034612303100170091 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:1:p:42-52 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064586_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Grzegorz A. Rempala Author-X-Name-First: Grzegorz A. Author-X-Name-Last: Rempala Author-Name: Konrad Szatzschneider Author-X-Name-First: Konrad Author-X-Name-Last: Szatzschneider Title: Bootstrapping Parametric Models of Mortality Abstract: We consider a general problem of modeling a mortality law of a population of failing units with some parametric function. In this setting we define a mortality table of crude rates as a statistical estimator with multinomial distribution and show its consistency as well as asymptotic normality. We further derive the statistical properties of parameter estimators in a parametric mortality model based on a weighted square loss function. We use the obtained results to study consistency and appropriateness of the parametric bootstrap method in our setting. We derive the conditions on the assumed parametric mortality law and the loss function, under which the bootstrap is consistent for estimating the model parameters, their standard errors and corresponding confidence intervals. We apply our results to a model of Aggregate US Mortality Table based on a so called mixture of extreme value distributions suggested by Carriere (1992). Journal: Scandinavian Actuarial Journal Pages: 53-78 Issue: 1 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230110106499 File-URL: http://hdl.handle.net/10.1080/03461230110106499 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:1:p:53-78 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063241_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Demetrios L. Antzoulakos Author-X-Name-First: Demetrios L. Author-X-Name-Last: Antzoulakos Author-Name: Stathis Chadjiconstantinidis Author-X-Name-First: Stathis Author-X-Name-Last: Chadjiconstantinidis Title: On Mixed and Compound Mixed Poisson Distributions Abstract: Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented. Journal: Scandinavian Actuarial Journal Pages: 161-188 Issue: 3 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230110106525 File-URL: http://hdl.handle.net/10.1080/03461230110106525 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:3:p:161-188 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063242_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Manfred Schäl Author-X-Name-First: Manfred Author-X-Name-Last: Schäl Title: On Discrete-Time Dynamic Programming in Insurance: Exponential Utility and Minimizing the Ruin Probability Abstract: This paper studies an insurance model where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is either the expected exponential utility of the terminal surplus or the ruin probability. It is shown that the problems can be imbedded in the framework of discrete-time stochastic dynamic programming but with some special features. A short introduction to control theory with infinite state space is provided which avoids the measure-theoretic apparatus by use of the so-called structure assumption. Moreover, in order to treat models without discount factor, a weak contraction property is derived. Explicit conditions are obtained for the optimality of employing no reinsurance. Journal: Scandinavian Actuarial Journal Pages: 189-210 Issue: 3 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230110106507 File-URL: http://hdl.handle.net/10.1080/03461230110106507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:3:p:189-210 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063243_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Extreme Value Theory and Archimedean Copulas Abstract: Using the language of copulas, we generalize the famous Fisher-Tippett Theorem of extreme value theory to the case with sequences of dependent random variables. The dependence structure is modelled using archimedean copulas. This generalization enables to study the behaviour of the maxima of dependent random sequences. Journal: Scandinavian Actuarial Journal Pages: 211-228 Issue: 3 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230110106539 File-URL: http://hdl.handle.net/10.1080/03461230110106539 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:3:p:211-228 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063244_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Title: The Ruin Probability of a Discrete Time Risk Model under Constant Interest Rate with Heavy Tails Abstract: This paper investigates the ultimate ruin probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the ruin probability is derived and compared to existing results. Journal: Scandinavian Actuarial Journal Pages: 229-240 Issue: 3 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230310017531 File-URL: http://hdl.handle.net/10.1080/03461230310017531 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:3:p:229-240 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064234_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: The deficit at ruin in the stationary renewal risk model Abstract: Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given that ruin occurs) is derived, as well as a stochastic decomposition involving the residual lifetime associated with the maximal aggregate loss. When the individual claims have a phase-type distribution, the deficit at ruin is also of phase-type. Journal: Scandinavian Actuarial Journal Pages: 241-255 Issue: 4 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230310016974 File-URL: http://hdl.handle.net/10.1080/03461230310016974 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:4:p:241-255 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064235_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: J. Gaier Author-X-Name-First: J. Author-X-Name-Last: Gaier Author-Name: P. Grandits Author-X-Name-First: P. Author-X-Name-Last: Grandits Title: Ruin probabilities and investment under interest force in the presence of regularly varying tails Abstract: This paper consists of three parts. In the first part we derive the asymptotic behavior of the optimal ruin probability of an insurer who invests optimally in a stock in the presence of positive interest force and claims with tails of regular variation. Our results extend previously obtained results by Gaier & Grandits (2002) with zero interest, and by Klüppelberg & Stadtmüller (1998) without investment possibility. In the second part we prove an existence theorem for the integro-differential equation for the survival probability of an insurer, who invests a constant fraction of his wealth in a risky stock, and his remaining wealth in a bond with nonnegative interest. Our result extends a previously known result by Wang & Wu (2001). Finally, in the third part we derive the asymptotic behavior of the ruin probability of the insurer, introduced in the second part, in the presence of claims with tails of regular variation. Journal: Scandinavian Actuarial Journal Pages: 256-278 Issue: 4 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410020310 File-URL: http://hdl.handle.net/10.1080/03461230410020310 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:4:p:256-278 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064236_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: Huntington's disease, critical illness insurance and life insurance Abstract: We describe briefly a model of Huntington's disease (HD), a highly penetrant, dominantly inherited, fatal neurological disorder. Although it is a single-gene disorder, mutations are variable in their effects, depending on the number of times that the CAG trinucleotide is repeated in a certain region of the HD gene. The model covers: (a) rates of onset, depending on CAG repeat length as well as age; (b) post-onset rates of mortality; and (c) the distribution of CAG repeat lengths in the population. Using these, we study the critical illness and life insurance markets. We calculate premiums based on genetic test results that disclose the CAG repeat length, or more simply on a family history of HD. These vary widely with age and policy term; some are exceptionally high, but in a large number of cases cover could be offered within normal underwriting limits. We then consider the possible costs of adverse selection, in terms of increased premiums, under various possible moratoria on the use of genetic information, including family history. These are uniformly very small, because of the rarity of HD, but do show that the costs would be much larger in relative terms if family history could not be used in underwriting. We point out some difficulties involved in applying a moratorium that recognises simply a dichotomy between ‘carriers’ and ‘non-carriers’ of any mutation in a gene when these mutations are, in fact, very variable in their effects. These complexities suggest that restrictions on the disclosure, rather than on the use, of genetic information, if it became established as a principle, could deprive insurers of information needed for risk management even if not used in underwriting. Journal: Scandinavian Actuarial Journal Pages: 279-313 Issue: 4 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230310016992 File-URL: http://hdl.handle.net/10.1080/03461230310016992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:4:p:279-313 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10064237_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book review Journal: Scandinavian Actuarial Journal Pages: 314-315 Issue: 4 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410020329 File-URL: http://hdl.handle.net/10.1080/03461230410020329 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:4:p:314-315 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063973_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Christian Hipp Author-X-Name-First: Christian Author-X-Name-Last: Hipp Title: Asymptotics of ruin probabilities for controlled risk processes in the small claims case Abstract: We consider a risk process with the possibility of investment into a risky asset. The aim of the paper is to obtain the asymptotic behaviour of the ruin probability under the optimal investment strategy in the small claims case. In addition we prove convergence of the optimal investment level as the initial capital tends to infinity. Journal: Scandinavian Actuarial Journal Pages: 321-335 Issue: 5 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410000538 File-URL: http://hdl.handle.net/10.1080/03461230410000538 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:5:p:321-335 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063974_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: J. M. Reinhard Author-X-Name-First: J. M. Author-X-Name-Last: Reinhard Author-Name: M. Snoussi Author-X-Name-First: M. Author-X-Name-Last: Snoussi Title: A monotonically converging algorithm for the severity of ruin in a discrete semi-markov risk model Abstract: This paper deals with the severity of ruin in a discrete semi-Markov risk model. It is shown that the work of Reinhard and Snoussi (Stochastic Models, 18) can be extended to cover the case where the premium is an integer value and no restriction on the annual result is imposed. In particular, it is shown that the severity of ruin without initial surplus is solution of a system of equations. It can be obtained by a monotonically converging algorithm when the claims are bounded. Journal: Scandinavian Actuarial Journal Pages: 336-354 Issue: 5 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410019024 File-URL: http://hdl.handle.net/10.1080/03461230410019024 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:5:p:336-354 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063975_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nicole Bäuerle Author-X-Name-First: Nicole Author-X-Name-Last: Bäuerle Title: Traditional versus non-traditional reinsurance in a dynamic setting Abstract: We consider a stochastic risk reserve process whose risk exposure can be controlled dynamically by applying proportional reinsurance and by issuing CAT Bonds. The CAT Bond payments are only partly correlated with the insurers losses. The aim is to minimize the probability of ruin. Using a two-dimensional diffusion approximation we obtain a controlled diffusion problem which can be solved explicitly with the help of the HJB equation. We present some numerical results and discuss to which extend the proportional reinsurance can be replaced by issuing CAT Bonds. Journal: Scandinavian Actuarial Journal Pages: 355-371 Issue: 5 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230310016983 File-URL: http://hdl.handle.net/10.1080/03461230310016983 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:5:p:355-371 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063976_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Løchte Jørgensen Author-X-Name-First: Peter Løchte Author-X-Name-Last: Jørgensen Title: On accounting standards and fair valuation of life insurance and pension liabilities Abstract: The actuarial profession is increasingly teaming up with financial economists for a fruitful cooperation on the proper valuation of life insurance and pension (L&P) liabilities. This has been a natural consequence of a recent sharply increased focus on market values in financial reports of L&P companies from regulators, standard setters, the financial press, stakeholders, and others with an interest in the L&P business. This article provides a financial economist's point of view on recent developments in relation to the fair valuation of L&P liabilities. The role of accounting standards and the background for the international harmonization in this field are first discussed. We then review and explain the concept of fair value and provide a general view on appropriate techniques for estimating fair values of L&P liabilities in accordance with the definition of the concept. The paper also contains a section which briefly reviews recent and quite innovative regulatory initiatives in relation to market value reporting in the Danish market for life and pension insurance. Journal: Scandinavian Actuarial Journal Pages: 372-394 Issue: 5 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410000556 File-URL: http://hdl.handle.net/10.1080/03461230410000556 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:5:p:372-394 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10063977_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book review Journal: Scandinavian Actuarial Journal Pages: 395-395 Issue: 5 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410000547 File-URL: http://hdl.handle.net/10.1080/03461230410000547 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:5:p:395-395 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10060410_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: V. K. Kaishev Author-X-Name-First: V. K. Author-X-Name-Last: Kaishev Title: Optimal retention levels, given the joint survival of cedent and reinsurer Abstract: A certain volume of risks is insured and there is a reinsurance contract, according to which claims and total premium income are shared between a direct insurer and a reinsurer in such a way, that the finite horizon probability of their joint survival is maximized. An explicit expression for the latter probability, under an excess of loss (XL) treaty is derived, using the improved version of the Ignatov and Kaishev's ruin probability formula (see Ignatov, Kaishev & Krachunov. 2001a) and assuming, Poisson claim arrivals, any discrete joint distribution of the claims, and any increasing real premium income function. An explicit expression for the probability of survival of the cedent only, under an XL contract is also derived and used to determine the probability of survival of the reinsurer, given survival of the cedent. The absolute value of the difference between the probability of survival of the cedent and the probability of survival of the reinsurer, given survival of the cedent is used for the choice of optimal retention level. We derive formulae for the expected profit of the cedent and of the reinsurer, given their joint survival up to the finite time horizon. We illustrate how optimal retention levels can be set, using an optimality criterion based on the expected profit formulae. The quota share contract is also considered under the same model. It is shown that the probability of joint survival of the cedent and the reinsurer coincides with the probability of survival of solely the insurer. Extensive, numerical comparisons, illustrating the performance of the proposed reinsurance optimality criteria are presented. Journal: Scandinavian Actuarial Journal Pages: 401-430 Issue: 6 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410020437 File-URL: http://hdl.handle.net/10.1080/03461230410020437 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:6:p:401-430 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10060411_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Dahan Author-X-Name-First: M. Author-X-Name-Last: Dahan Author-Name: E. Frostig Author-X-Name-First: E. Author-X-Name-Last: Frostig Author-Name: N. A. Langberg Author-X-Name-First: N. A. Author-X-Name-Last: Langberg Title: Insurance contracts portfolios with heterogenous parametric life distributions Abstract: In this paper we consider two portfolios: one of m endowment insurance contracts and one of m whole life insurance contracts. We introduce the majorization order, Schur functions, and parametric families of distribution functions. We assume that the owners of the portfolios are exposed to different members of a known parametric family of distributions and study the effect of this stochastic heterogeneity on the premiums and death benefits of the insurance contracts. We show that the premiums paid in both contracts are Schur concave and that the death benefit awarded in the whole life contract is Schur convex. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for four parametric families of distribution functions used frequently in the Actuarial Sciences. Journal: Scandinavian Actuarial Journal Pages: 431-447 Issue: 6 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410020383 File-URL: http://hdl.handle.net/10.1080/03461230410020383 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:6:p:431-447 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10060412_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yu Luo Author-X-Name-First: Yu Author-X-Name-Last: Luo Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Author-Name: Edward W. Frees Author-X-Name-First: Edward W. Author-X-Name-Last: Frees Title: Credibility ratemaking using collateral information Abstract: Credibility ratemaking is a technique used in pricing health care, property and casualty, workers’ compensation, and group life coverages. It has been a part of actuarial practice since the time of Mowbray's (1914) contribution. In earlier work, we showed how many types of credibility models could be expressed as special cases of mixed linear models. This article extends this approach to credibility by formally introducing collateral information through the use of Bayesian methods. Specifically, we derive credibility estimators and mean square errors for normal hierarchical linear models. We provide intuition for the credibility estimators by establishing the link between these estimators and homogeneous and inhomogeneous estimators that appear in non-Bayesian credibility theory. Journal: Scandinavian Actuarial Journal Pages: 448-461 Issue: 6 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230310017513 File-URL: http://hdl.handle.net/10.1080/03461230310017513 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:6:p:448-461 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10060413_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ulf Linder Author-X-Name-First: Ulf Author-X-Name-Last: Linder Author-Name: Vesa Ronkainen Author-X-Name-First: Vesa Author-X-Name-Last: Ronkainen Title: Solvency II – towards a new insurance supervisory system in the EU Abstract: This article describes the current state of affairs in the EU Solvency II project. The background and international context of the project is discussed, as well as the general outline of a future EU solvency system. In particular, several areas where further technical work is needed are outlined. These topics could provide interesting objects of study for professionals of actuarial sciences as well as to those of other related sciences. Journal: Scandinavian Actuarial Journal Pages: 462-474 Issue: 6 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410000574 File-URL: http://hdl.handle.net/10.1080/03461230410000574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:6:p:462-474 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10060414_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Book review Journal: Scandinavian Actuarial Journal Pages: 475-475 Issue: 6 Volume: 2004 Year: 2004 X-DOI: 10.1080/03461230410000600 File-URL: http://hdl.handle.net/10.1080/03461230410000600 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2004:y:2004:i:6:p:475-475 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_10338241_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Author-Name: Lothar Breuer Author-X-Name-First: Lothar Author-X-Name-Last: Breuer Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Author-Name: Guy Latouche Author-X-Name-First: Guy Author-X-Name-Last: Latouche Author-Name: David Stanford Author-X-Name-First: David Author-X-Name-Last: Stanford Title: The surplus prior to ruin and the deficit at ruin for a correlated risk process Abstract: This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inter-claim times. The marginal density function of the surplus immediately prior to ruin is specifically considered. Several numerical examples are presented to illustrate the application of this result. Journal: Scandinavian Actuarial Journal Pages: 433-445 Issue: 6 Volume: 2005 Year: 2005 X-DOI: 10.1080/03461230510009835 File-URL: http://hdl.handle.net/10.1080/03461230510009835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2005:y:2005:i:6:p:433-445 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_121530_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Grandits Author-X-Name-First: Peter Author-X-Name-Last: Grandits Title: Minimal ruin probabilities and investment under interest force for a class of subexponential distributions Abstract: We consider the infinite-time ruin probability of an insurance company investing in the stock market. This is done under the following assumptions: For the claim surplus process we use the classical Cramér-Lundberg model, where the claims have a distribution function, belonging to certain subclasses of the class of subexponential distributions. The stock price movement is modeled by geometric Brownian motion, and we allow positive interest rates for the riskless bond. In this setting we analyze the Hamilton-Jacobi-Bellman equation for the minimal ruin probability. We give asymptotic expressions for the minimal ruin probability, as well as for the optimal investment strategy. It turns out that the asymptotic order of the minimal ruin probability is different from the previous considered case of zero interest on the bond. Journal: Scandinavian Actuarial Journal Pages: 401-416 Issue: 6 Volume: 2005 Year: 2005 X-DOI: 10.1080/03461230500215479 File-URL: http://hdl.handle.net/10.1080/03461230500215479 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2005:y:2005:i:6:p:401-416 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_136177_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: Roger Laeven Author-X-Name-First: Roger Author-X-Name-Last: Laeven Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Author-Name: Raluca Vernic Author-X-Name-First: Raluca Author-X-Name-Last: Vernic Title: The Tail Probability of Discounted Sums of Pareto-like Losses in Insurance Abstract: In an insurance context, the discounted sum of losses within a finite or infinite time period can be described as a randomly weighted sum of a sequence of independent random variables. These independent random variables represent the amounts of losses in successive development years, while the weights represent the stochastic discount factors. In this paper, we investigate the problem of approximating the tail probability of this weighted sum in the case when the losses have Pareto-like distributions and the discount factors are mutually dependent. We also give some simulation results. Journal: Scandinavian Actuarial Journal Pages: 446-461 Issue: 6 Volume: 2005 Year: 2005 X-DOI: 10.1080/03461230500361943 File-URL: http://hdl.handle.net/10.1080/03461230500361943 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2005:y:2005:i:6:p:446-461 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_136189_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yuliya Bregman Author-X-Name-First: Yuliya Author-X-Name-Last: Bregman Author-Name: Claudia Klüppelberg Author-X-Name-First: Claudia Author-X-Name-Last: Klüppelberg Title: Ruin estimation in multivariate models with Clayton dependence structure Abstract: We consider the estimation of the ruin probability in a linear portfolio of insurance risk processes. We model the total claim amount of different business activities by compound Poisson processes. We allow for dependence of the components, which we model by a Lévy copula. We study in detail a Clayton-Pareto model as representative for a large claims model and a Clayton-exponential model as a small claims model. We compare the ruin probability in the Clayton dependence model with the corresponding independent and completely dependent models. Journal: Scandinavian Actuarial Journal Pages: 462-480 Issue: 6 Volume: 2005 Year: 2005 X-DOI: 10.1080/03461230500362065 File-URL: http://hdl.handle.net/10.1080/03461230500362065 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2005:y:2005:i:6:p:462-480 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_136287_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claudio Macci Author-X-Name-First: Claudio Author-X-Name-Last: Macci Author-Name: Gabriele Stabile Author-X-Name-First: Gabriele Author-X-Name-Last: Stabile Author-Name: Giovanni Luca Torrisi Author-X-Name-First: Giovanni Author-X-Name-Last: Luca Torrisi Title: Lundberg parameters for non standard risk processes Abstract: We consider risk processes with delayed claims in a Markovian environment, and we study the asymptotic behaviour of finite and infinite horizon ruin probabilities under the small claim assumption. We also consider multivariate risk processes of the same kind, and we give upper and lower bounds for the Lundberg parameters of the corresponding total reserve. Our results have strong analogies with those one in the paper by Juri (Super modular order and Lundberg exponents, 2002). Journal: Scandinavian Actuarial Journal Pages: 417-432 Issue: 6 Volume: 2005 Year: 2005 X-DOI: 10.1080/03461230500363048 File-URL: http://hdl.handle.net/10.1080/03461230500363048 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2005:y:2005:i:6:p:417-432 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_158906_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion Abstract: We consider a diffusion perturbed classical compound Poisson risk model in the presence of a constant dividend barrier. An integro-differential equation with certain boundary conditions for the n-th moment of the discounted dividend payments prior to ruin is derived and solved. Its solution can be expressed in terms of the expected discounted penalty (Gerber-Shiu) functions due to oscillation in the corresponding perturbed risk model without a barrier. When the discount factor δ is zero, we show that all the results can be expressed in terms of the non-ruin probability in the perturbed risk model without a barrier. Journal: Scandinavian Actuarial Journal Pages: 73-85 Issue: 2 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600589237 File-URL: http://hdl.handle.net/10.1080/03461230600589237 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:2:p:73-85 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_163019_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Søren Asmussen c Author-X-Name-First: Søren Author-X-Name-Last: Asmussen c Title: Ruin probabilities and aggregrate claims distributions for shot noise Cox processes Abstract: We consider a risk process R t where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim size distributions, asymptotic estimates for infinite-time and finite-time ruin probabilities are derived. Moreover, we discuss an extension of the model to an adaptive premium rule that is dynamically adjusted according to past claims experience. Journal: Scandinavian Actuarial Journal Pages: 86-110 Issue: 2 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600630395 File-URL: http://hdl.handle.net/10.1080/03461230600630395 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:2:p:86-110 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_176837_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: G. Yin Author-X-Name-First: G. Author-X-Name-Last: Yin Author-Name: Y. J. Liu Author-X-Name-First: Y. J. Author-X-Name-Last: Liu Author-Name: H. Yang Author-X-Name-First: H. Author-X-Name-Last: Yang Title: Bounds of ruin probability for regime-switching models using time scale separation Abstract: This paper is concerned with regime-switching insurance risk models. The regime-switching is modeled by a continuous-time Markov chain. Owing to various modeling considerations, the state space is likely to be very large. A two-time-scale formulation is used to reduce the complexity. Under simple conditions, limits of ultimate survival probabilities and ultimate ruin probabilities are obtained. These results reveal that, for example, as a decision maker, one may ignore the detailed variations, and use the limit ultimate ruin probabilities to approximate that of the actual ones. Moreover, the differences of the original and limit ruin probabilities are examined. Error bounds are developed. Journal: Scandinavian Actuarial Journal Pages: 111-127 Issue: 2 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600768807 File-URL: http://hdl.handle.net/10.1080/03461230600768807 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:2:p:111-127 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_171493_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Saralees Nadarajah Author-X-Name-First: Saralees Author-X-Name-Last: Nadarajah Author-Name: Samuel Kotz Author-X-Name-First: Samuel Author-X-Name-Last: Kotz Title: Compound Mixed Poisson Distributions II Abstract: The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. This paper provides the second part of the list of approximate forms for the compound mixed Poisson distribution (following up from Nadarajah and Kotz (2006)). The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science. Journal: Scandinavian Actuarial Journal Pages: 163-181 Issue: 3 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600715253 File-URL: http://hdl.handle.net/10.1080/03461230600715253 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:3:p:163-181 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_178288_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Saralees Nadarajah Author-X-Name-First: Saralees Author-X-Name-Last: Nadarajah Author-Name: Samuel Kotz Author-X-Name-First: Samuel Author-X-Name-Last: Kotz Title: Compound mixed Poisson distributions I Abstract: The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. In this paper, comprehensive collections of approximate forms are derived for the compound mixed Poisson distribution. The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science. Journal: Scandinavian Actuarial Journal Pages: 141-162 Issue: 3 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600783384 File-URL: http://hdl.handle.net/10.1080/03461230600783384 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:3:p:141-162 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_182473_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kam-Chuen Yuen Author-X-Name-First: Kam-Chuen Author-X-Name-Last: Yuen Author-Name: Junyi Guo Author-X-Name-First: Junyi Author-X-Name-Last: Guo Title: Some results on the compound Markov binomial model Abstract: This paper considers the compound Markov binomial risk model proposed by Cossette et al. (2003 2004). Two discrete-time renewal (ordinary renewal and delayed renewal) risk processes associated with the compound Markov binomial risk model are analyzed. Based on the associated ordinary renewal process, a defective renewal equation for the conditional Gerber–Shiu expected discounted penalty function is obtained. The relationship between the conditional expected discounted penalty function in the ordinary renewal case and that in the delayed renewal case is then established. From these results, the conditional ultimate probability of ruin as well as the conditional joint distribution of the surplus just prior to ruin and the deficit at ruin are studied. Finally, it is shown that a modified version of the compound Markov binomial risk model is a special case of the discrete-time semi-Markov risk model introduced by Reinhard and Snoussi (2001 2002). Journal: Scandinavian Actuarial Journal Pages: 129-140 Issue: 3 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600825359 File-URL: http://hdl.handle.net/10.1080/03461230600825359 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:3:p:129-140 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_188889_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Esbjörn Ohlsson Author-X-Name-First: Esbjörn Author-X-Name-Last: Ohlsson Title: A Course in Credibility Theory and its Applications, by H. Bühlmann and A. Gisler. Published by Springer 2005 Journal: Pages: 182-182 Issue: 3 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600889660 File-URL: http://hdl.handle.net/10.1080/03461230600889660 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:3:p:182-182 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_180337_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marie-Claire Koissi Author-X-Name-First: Marie-Claire Author-X-Name-Last: Koissi Title: Longevity and adjustment in pension annuities, with application to Finland Abstract: The aim of this paper is twofold. First, the improvement in adult mortality in Finland is studied. Lee-Carter (LC) Poisson log-bilinear model is used for mortality forecasting. Secondly, the paper studies how the pension annuities are adjusted to unexpected mortality pattern. A formula for funded plan is proposed. Application is made with Finnish mortality rates predicted using the LC model. Journal: Scandinavian Actuarial Journal Pages: 226-242 Issue: 4 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600803935 File-URL: http://hdl.handle.net/10.1080/03461230600803935 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:4:p:226-242 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_188887_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Laurence Lescourret Author-X-Name-First: Laurence Author-X-Name-Last: Lescourret Author-Name: Christian Robert Author-X-Name-First: Christian Author-X-Name-Last: Robert Title: Extreme dependence of multivariate catastrophic losses Abstract: Natural catastrophes cause insurance losses in several different lines of business. An approach to modelling the dependence in loss severities is to assume that they are related to the intensity of the natural disaster. In this paper we introduce a factor model and investigate the extreme dependence. We derive a specific extreme dependence structure when considering an heavy-tailed intensity. Estimation procedures are presented and their moderate sample properties are compared in a simulation study. We also motivate our approach by an illustrative example from storm insurance. Journal: Scandinavian Actuarial Journal Pages: 203-225 Issue: 4 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600889645 File-URL: http://hdl.handle.net/10.1080/03461230600889645 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:4:p:203-225 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_188888_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Title: On the severity of ruin in a Markov-modulated risk model Abstract: We consider a Markov-modulated risk model in which the claim inter-arrivals, amounts and premiums are influenced by an external Markovian environment process. A system of Laplace transforms of the probabilities of the severity of ruin, given the initial environment state, is established from a system of integro-differential equations derived by Snoussi [The severity of ruin in Markov-modulated risk models Schweiz Aktuarver. Mitt., 2002, 1, 31–43]. In the two-state model, explicit formulas for probabilities of the severity of ruin are derived, when the initial reserve is zero or when both claim amount distributions are from the rational family. Numerical illustrations are also given. Journal: Scandinavian Actuarial Journal Pages: 183-202 Issue: 4 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600889652 File-URL: http://hdl.handle.net/10.1080/03461230600889652 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:4:p:183-202 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_195199_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jaap Spreeuw Author-X-Name-First: Jaap Author-X-Name-Last: Spreeuw Title: Types of dependence and time-dependent association between two lifetimes in single parameter copula models Abstract: Spreeuw, J. Types of dependence and time-dependent association between two lifetimes in single parameter copula models. Scandinavian Actuarial Journal. Most publications on modeling insurance contracts on two lives, assuming dependence of the two lifetimes involved, focus on the time of inception of the contract. The dependence between the lifetimes is usually modeled through a copula and the effect of this dependence on the pricing of a joint life policy is measured. This paper investigates the effect of association at the outset on the mortality in the future. The conditional law of mortality of an individual, given his survival and given the life status of the partner is derived. The conditional joint survival distribution of a couple at any duration, given that the two lives are then alive, is also derived. We analyze how the degree of dependence between the two members of a couple varies throughout the duration of a contract. We have done that for (mainly Archimedean) copula models, with one parameter for the degree of dependence. The conditional distributions hence derived provide the basis for the calculation of prospective provisions. Journal: Scandinavian Actuarial Journal Pages: 286-309 Issue: 5 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600952880 File-URL: http://hdl.handle.net/10.1080/03461230600952880 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:5:p:286-309 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_198514_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sandra Pitrebois Author-X-Name-First: Sandra Author-X-Name-Last: Pitrebois Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Jean-François Walhin Author-X-Name-First: Jean-François Author-X-Name-Last: Walhin Title: An actuarial analysis of the French bonus-malus system Abstract: The bonus-malus system in force in France differs from most of those used in industrialized countries around the world. Policyholders do not move inside a scale but their premium is obtained with the help of multiplicative CRM coefficients (CRM stands for the acronym of the French coefficient de réduction-majoration). The French bonus-malus system has been the topic of very few scientific investigations in the actuarial literature. This paper purposes to analyze this bonus-malus system in details. Despite its apparent simplicity, it will be seen that it leads to nontrivial mathematical problems. The financial equilibrium of the bonus-malus system is also investigated thanks to the multivariate De Pril's algorithm for the convolution of independent and identically distributed random vectors. Journal: Scandinavian Actuarial Journal Pages: 247-264 Issue: 5 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600986136 File-URL: http://hdl.handle.net/10.1080/03461230600986136 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:5:p:247-264 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_199127_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mathieu Boudreault Author-X-Name-First: Mathieu Author-X-Name-Last: Boudreault Author-Name: Hélène Cossette Author-X-Name-First: Hélène Author-X-Name-Last: Cossette Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Etienne Marceau Author-X-Name-First: Etienne Author-X-Name-Last: Marceau Title: On a risk model with dependence between interclaim arrivals and claim sizes Abstract: We consider an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent. In Albrecher and Teugels (2006), an arbitrary dependence structure among the interclaim time and the subsequent claim size expressed through a copula is considered and they derived asymptotic results for both the finite and infinite-time ruin probabilities. In this paper, we consider a particular dependence structure among the interclaim time and the subsequent claim size and we derive the defective renewal equation satisfied by the expected discounted penalty function. Based on the compound geometric tail representation of the Laplace transform of the time to ruin, we also obtain an explicit expression for this Laplace transform for a large class of claim size distributions. The ruin probability being a special case of the Laplace transform of the time to ruin, explicit expressions are therefore obtained for this particular ruin related quantity. Finally, we measure the impact of the various dependence structures in the risk model on the ruin probability via the comparison of their Lundberg coefficients. Journal: Scandinavian Actuarial Journal Pages: 265-285 Issue: 5 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600992266 File-URL: http://hdl.handle.net/10.1080/03461230600992266 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:5:p:265-285 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_198513_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jin Ma Author-X-Name-First: Jin Author-X-Name-Last: Ma Author-Name: Yuhua Yu Author-X-Name-First: Yuhua Author-X-Name-Last: Yu Title: Principle of equivalent utility and universal variable life insurance pricing Abstract: In this paper we study the pricing problem for a class of universal variable life (UVL) insurance products, using the idea of principle of equivalent utility. As the main features of UVL products we allow the (death) benefit to depend on certain indices or assets that are not necessarily tradable (e.g., pension plans), and we also consider the “multiple decrement” cases in which various status of the insured are allowed and the benefit varies in accordance with the status. Following the general theory of indifference pricing, we formulate the pricing problem as stochastic control problems, and derive the corresponding HJB equations for the value functions. In the case of exponential utilities, we show that the prices can be expressed explicitly in terms of the global, bounded solutions of a class of semilinear parabolic PDEs with exponential growth. In the case of general insurance models where multiple decrements and random time benefit payments are all allowed, we show that the price should be determined by the solutions to a system of HJB equations, each component corresponds to the value function of an optimization problem with the particular status of the insurer. Journal: Scandinavian Actuarial Journal Pages: 311-337 Issue: 6 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230600986128 File-URL: http://hdl.handle.net/10.1080/03461230600986128 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:6:p:311-337 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_202558_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eng Hock Gui Author-X-Name-First: Eng Author-X-Name-Last: Hock Gui Author-Name: Baopeng Lu Author-X-Name-First: Baopeng Author-X-Name-Last: Lu 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: The Genetics of Breast and Ovarian Cancer III: A new model of family history with insurance applications Abstract: Insurers’ access to genetic test results is often restricted and the only genetic information that might be collected during underwriting in some countries is family history. Previous studies have included family history in a simple way but only for diseases which have no cause other than gene mutations, because then the event ‘affected parent’ contributes all possible information short of a genetic test result. We construct a model of breast cancer (BC) and ovarian cancer (OC) — common diseases with rare genetic variants — in which the development of a family history is represented explicitly as a transition between states, hence as part of the applicant's own life history. This allows the impact of a moratorium to be modelled. We then apply this family history model to life insurance in a semi-Markov framework and to critical illness (CI) insurance in a Markov framework to: (a) estimate premium ratings depending on genotype or family history; and (b) model the potential cost of adverse selection. Journal: Scandinavian Actuarial Journal Pages: 338-367 Issue: 6 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230601026635 File-URL: http://hdl.handle.net/10.1080/03461230601026635 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:6:p:338-367 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_205514_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: T.K.J. Herbert Author-X-Name-First: T.K.J. Author-X-Name-Last: Herbert Author-Name: W.F. Scott Author-X-Name-First: W.F. Author-X-Name-Last: Scott Title: On de-seasonalising adjusted-average formulae Abstract: The techniques of Borgan (1979) are extended to cover data with seasonal variations. Examples are given, and it is suggested that the formulae presented here give smoother results than those traditionally employed to deal with economic time series subject to seasonal variations. Journal: Scandinavian Actuarial Journal Pages: 368-377 Issue: 6 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230601056103 File-URL: http://hdl.handle.net/10.1080/03461230601056103 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:6:p:368-377 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_207510_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Arne Sandström. Solvency, Models, Assessment and Regulation. Chapman & Hall/CRC, 2005) Journal: Pages: 378-379 Issue: 6 Volume: 2006 Year: 2006 X-DOI: 10.1080/03461230601075749 File-URL: http://hdl.handle.net/10.1080/03461230601075749 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2006:y:2006:i:6:p:378-379 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_206886_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nicole Bäuerle Author-X-Name-First: Nicole Author-X-Name-Last: Bäuerle Author-Name: Mirko Kötter Author-X-Name-First: Mirko Author-X-Name-Last: Kötter Title: Markov-modulated diffusion risk models Abstract: In this paper we consider Markov-modulated diffusion risk reserve processes. Using diffusion approximation we show the relation to classical Markov-modulated risk reserve processes. In particular we derive a representation for the adjustment coefficient and prove some comparison results. Among others we show that increasing the volatility of the diffusion increases the probability of ruin. Journal: Scandinavian Actuarial Journal Pages: 34-52 Issue: 1 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230601069528 File-URL: http://hdl.handle.net/10.1080/03461230601069528 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:1:p:34-52 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_208765_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jon Holtan Author-X-Name-First: Jon Author-X-Name-Last: Holtan Title: Pragmatic insurance option pricing Abstract: This paper deals with theoretical and practical pricing of non-life insurance contracts within a financial option pricing context. The market-based assumption approach of the option context fits well into the practical nature of non-life insurance pricing and valuation. The fundamental characteristics of most insurance markets, such as the apparent variation in insurer price offers for the same risk in the same market, support the need for a market based approach. The paper outlines insurance and option pricing in a parallel setup. First it takes a complete market approach, focusing on dynamic hedging, no-arbitrage and risk-neutral martingale valuation principles within insurance and options. Secondly it takes an incomplete market view by introducing supply and demand effects via purchasing preferences in the market. Finally the paper discusses market-based insurance price models, parameter estimation techniques and international best practice of insurance pricing. The general purpose of the paper is to describe and unite the headlines of the more or less common insurance and option pricing theory, and hence increase the pragmatic understanding of this theory from a business point of view. Journal: Scandinavian Actuarial Journal Pages: 53-70 Issue: 1 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230601088213 File-URL: http://hdl.handle.net/10.1080/03461230601088213 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:1:p:53-70 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_210981_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: On composite lognormal-Pareto models Abstract: Recently, Cooray & Ananda (2005) proposed a composite lognormal-Pareto model for use with loss payments data of the sort arising in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density thereafter. Here we identify and discuss limitations of this composite lognormal-Pareto model which are likely to severely curtail its potential for practical application to real world data sets. In addition, we present two different composite models based on lognormal and Pareto models in order to address these concerns. The performance of all three composite models is discussed and compared in the context of an example based upon a well-known fire insurance data set. Journal: Scandinavian Actuarial Journal Pages: 20-33 Issue: 1 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230601110447 File-URL: http://hdl.handle.net/10.1080/03461230601110447 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:1:p:20-33 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_216430_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Association and heterogeneity of insured lifetimes in the Lee–Carter framework Abstract: This paper is devoted to the study of some unexpected consequences of the Lee–Carter model for mortality projection. The fact that survival probabilities are governed by a stochastic process induces some positive dependence between insured lifetimes (namely, association). This, in turn, has an impact on solvency capital (as measured by distortion risk measures, for instance). Failing to take this dependence into account, by assuming falsely that the lifetimes are independent, leads to systematic underestimations of the risk capital. The heterogeneity between the policy benefits and the insured lifetimes is also studied (with the help of majorisation, Schur-increasingness and a frailty model). Journal: Scandinavian Actuarial Journal Pages: 1-19 Issue: 1 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230601165029 File-URL: http://hdl.handle.net/10.1080/03461230601165029 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:1:p:1-19 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_216448_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Grandits Author-X-Name-First: Peter Author-X-Name-Last: Grandits Author-Name: Friedrich Hubalek Author-X-Name-First: Friedrich Author-X-Name-Last: Hubalek Author-Name: Walter Schachermayer Author-X-Name-First: Walter Author-X-Name-Last: Schachermayer Author-Name: Mislav Žigo Author-X-Name-First: Mislav Author-X-Name-Last: Žigo Title: Optimal expected exponential utility of dividend payments in a Brownian risk model Abstract: We consider the following optimisation problem for an insurance company Here U(x) = (1−exp(−γx))/γ denotes an exponential utility function with risk aversion parameter γ, C denotes the accumulated dividend process, and β a discount factor. We show that – assuming that a certain integral equation has a solution – the optimal strategy is a barrier strategy. The barrier function is a solution of the integral equation and turns out to be time-dependent. In addition, we study the problem from a different point of view, namely by using a certain ansatz for the value function and the barrier. Journal: Scandinavian Actuarial Journal Pages: 73-107 Issue: 2 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230601165201 File-URL: http://hdl.handle.net/10.1080/03461230601165201 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:2:p:73-107 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_224961_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Arne Sandström Author-X-Name-First: Arne Author-X-Name-Last: Sandström Title: Solvency II: Calibration for skewness Abstract: The standard formula for the calculation of the capital requirement within the EU's Solvency II project will be modular based. Each capital charge from the modules will be calculated consistent with the overall capital charge, i.e. with the same risk measure, the same confidence level and time horizon. If any of the underlying probability distributions are skewed, then the model must be calibrated for that to retain the consistency. This paper proposes and discusses one way of calibrating for skewness. The main objective of the paper is to show, by two simple examples, the effect of not calibrating for skewness if some of the underlying distributions are skew. Journal: Scandinavian Actuarial Journal Pages: 126-134 Issue: 2 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701250481 File-URL: http://hdl.handle.net/10.1080/03461230701250481 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:2:p:126-134 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_225058_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Markus Buchwalder Author-X-Name-First: Markus Author-X-Name-Last: Buchwalder Author-Name: Hans Bühlmann Author-X-Name-First: Hans Author-X-Name-Last: Bühlmann 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: Valuation portfolio in non-life insurance Abstract: The purpose of this paper is the construction of the Valuation Portfolio (VaPo) for a non-life insurance company. The VaPo represents the obligations of the insurer for the whole period of his insurance contracts. These obligations are not simply measured by a one-dimensional figure (as standard for reserves in practice), but are expressed as a portfolio of financial instruments. Hence, the actuarial reserves become multidimensional. The financial instruments in the VaPo are a properly chosen basis to represent the future cashflows resulting from the insurance contracts. In this setup, financial and technical risks are clearly separated. The financial fluctuations derive from the basis elements, the technical fluctuations are covered by an increased number of basis elements (VaPo protected against technical risks). We show how this protection can be calculated in the case of a non-life insurance company. Journal: Scandinavian Actuarial Journal Pages: 108-125 Issue: 2 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701251455 File-URL: http://hdl.handle.net/10.1080/03461230701251455 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:2:p:108-125 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_225621_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ronkainen Vesa Author-X-Name-First: Ronkainen Author-X-Name-Last: Vesa Author-Name: Koskinen Lasse Author-X-Name-First: Koskinen Author-X-Name-Last: Lasse Author-Name: Berglund Raoul Author-X-Name-First: Berglund Author-X-Name-Last: Raoul Title: Topical modelling issues in Solvency II Abstract: The main reasons for giving European insurance companies the option to apply internal models for calculating the main solvency requirement within the Solvency II framework is to enhance better risk management in the firms, and to provide the opportunity to derive a more accurate risk-oriented capital requirement than the standard Solvency Capital Requirement (SCR) could provide. The possibility to use internal models within pillar 1 basically means freedom to calculate the solvency requirement using some other formula and even principles than those given by the standard formula. This freedom is more limited with partial models. This paper gives a brief introduction and update to the Solvency II project, reviews and discusses some topical aspects of internal models from the supervisory point of view, and points out some relating results of the Quantitative Impact Studies carried out, thus far, in the EU by CEIOPS. Journal: Scandinavian Actuarial Journal Pages: 135-146 Issue: 2 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701257098 File-URL: http://hdl.handle.net/10.1080/03461230701257098 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:2:p:135-146 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_216161_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Abdelhakim Necir Author-X-Name-First: Abdelhakim Author-X-Name-Last: Necir Author-Name: Djamel Meraghni Author-X-Name-First: Djamel Author-X-Name-Last: Meraghni Author-Name: Fatima Meddi Author-X-Name-First: Fatima Author-X-Name-Last: Meddi Title: Statistical estimate of the proportional hazard premium of loss Abstract: The well known Proportional Hazard Premium Principle, introduced by Wang (1996), depends upon the survival function of the insured risk and a risk aversion index. Using this premium principle, we propose an asymptotically normal semi-parametric estimator for the net-premium of a high-excess loss layer of heavy-tailed claim amounts. An algorithm to compute confidence bounds is given. Moreover, a comparison between this estimator and the non-parametric estimator, proposed by Necir & Boukhetala (2004), is carried out. Journal: Scandinavian Actuarial Journal Pages: 147-161 Issue: 3 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230601162323 File-URL: http://hdl.handle.net/10.1080/03461230601162323 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:3:p:147-161 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_238916_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vytaras Brazauskas Author-X-Name-First: Vytaras Author-X-Name-Last: Brazauskas Author-Name: Bruce Jones Author-X-Name-First: Bruce Author-X-Name-Last: Jones Author-Name: Madan Puri Author-X-Name-First: Madan Author-X-Name-Last: Puri Author-Name: Ričardas Zitikis Author-X-Name-First: Ričardas Author-X-Name-Last: Zitikis Title: Nested -statistics and their use in comparing the riskiness of portfolios Abstract: Inspired by the problem of testing hypotheses about the equality of several risk measure values, we find that the ‘nested L-statistic’—a notion introduced herein—is natural and particularly convenient. Indeed, the test statistic that we explore in this paper is a nested L-statistic. We discuss large-sample properties of the statistic, investigate its performance using a simulation study, and consider an example involving the comparison of risk measure values where the risks of interest are those associated with tornado damage in different time periods and different regions. Journal: Scandinavian Actuarial Journal Pages: 162-179 Issue: 3 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701390287 File-URL: http://hdl.handle.net/10.1080/03461230701390287 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:3:p:162-179 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_241361_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Susanne Gschlößl Author-X-Name-First: Susanne Author-X-Name-Last: Gschlößl Author-Name: Claudia Czado Author-X-Name-First: Claudia Author-X-Name-Last: Czado Title: Spatial modelling of claim frequency and claim size in non-life insurance Abstract: In this paper, models for claim frequency and average claim size in non-life insurance are considered. Both covariates and spatial random effects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model, we allow for dependencies between claim size and claim frequency. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion and the predictive model choice criterion, we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial effects significantly improves the models for both claim frequency and claim size, and also leads to more accurate predictions of the total claim sizes. Further, we detect significant dependencies between the number of claims and claim size. Both spatial and number of claims effects are interpreted and quantified from an actuarial point of view. Journal: Scandinavian Actuarial Journal Pages: 202-225 Issue: 3 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701414764 File-URL: http://hdl.handle.net/10.1080/03461230701414764 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:3:p:202-225 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_248445_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ugur Tuncay Alparslan Author-X-Name-First: Ugur Tuncay Author-X-Name-Last: Alparslan Author-Name: Gennady Samorodnitsky Author-X-Name-First: Gennady Author-X-Name-Last: Samorodnitsky Title: Asymptotic analysis of the ruin with stationary stable steps generated by dissipative flows Abstract: We study the exceedance probability of a high threshold (ruin probability) for a random walk with a negative linear drift, where the steps of the walk (claim sizes) constitute a stationary ergodic symmetric α-stable process. We casually use the language of insurance, although this is a popular problem in many other fields of applied probability as well. We refer to ergodic theory to split the step process into two independent processes. We focus on the processes generated by dissipative flows, which are known to have a mixed moving average representation, and we restrict our attention to regular moving averages with non-negative kernels. We give results for the order of magnitude of the exceedance probability as the threshold goes to infinity in the cases of discrete-time and continuous-time claim processes. Journal: Scandinavian Actuarial Journal Pages: 180-201 Issue: 3 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701485681 File-URL: http://hdl.handle.net/10.1080/03461230701485681 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:3:p:180-201 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_254990_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: Corrigendum Journal: Scandinavian Actuarial Journal Pages: 226-226 Issue: 3 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701551318 File-URL: http://hdl.handle.net/10.1080/03461230701551318 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:3:p:226-226 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_239533_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Title: Analysis of a threshold dividend strategy for a MAP risk model Abstract: We consider a class of Markovian risk models in which the insurer collects premiums at rate c1(c2) whenever the surplus level is below (above) a constant threshold level b. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the LST (with respect to time) of the joint distribution of the time to ruin, the surplus prior to ruin, and the deficit at ruin. By interpreting that the insurer pays dividends continuously at rate c1−c2 whenever the surplus level is above b, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained by making use of an existing connection which links an insurer's surplus process to an embedded fluid flow process. Journal: Scandinavian Actuarial Journal Pages: 227-247 Issue: 4 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701396474 File-URL: http://hdl.handle.net/10.1080/03461230701396474 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:4:p:227-247 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_255257_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gillian Heller Author-X-Name-First: Gillian Author-X-Name-Last: Heller Author-Name: D. Mikis Stasinopoulos Author-X-Name-First: D. Author-X-Name-Last: Mikis Stasinopoulos Author-Name: Robert Rigby Author-X-Name-First: Robert Author-X-Name-Last: Rigby Author-Name: Piet De Jong Author-X-Name-First: Piet Author-X-Name-Last: De Jong Title: Mean and dispersion modelling for policy claims costs Abstract: A model for the statistical analysis of the total amount of insurance paid out on a policy is developed and applied. The model simultaneously deals with the number of claims (zero or more) and the amount of each claim. The number of claims is from a Poisson-based discrete distribution. Individual claim sizes are from a continuous right skewed distribution. The resulting distribution of total claim size is a mixed discrete-continuous model, with positive probability of a zero claim. The means and dispersions of the claim frequency and claim size distribution are modeled in terms of risk factors. The model is applied to a car insurance data set. Journal: Scandinavian Actuarial Journal Pages: 281-292 Issue: 4 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701553983 File-URL: http://hdl.handle.net/10.1080/03461230701553983 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:4:p:281-292 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_255259_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Arthur Chiragiev Author-X-Name-First: Arthur Author-X-Name-Last: Chiragiev Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Title: Multivariate Pareto portfolios: TCE-based capital allocation and divided differences Abstract: Determination of risk capital is a subject of active interest to researchers, regulators of financial institutions, and commercial vendors of financial products and services. Recently, there has been growing concentration among the insurance companies and regulators on the use of tail conditional expectation (TCE) as measure of risk. The present study examines the TCE-based portfolio allocation for multivariate dependent Pareto risks. This family is broadly popular in actuarial sciences, mostly because of modeling heavy-tailed dependent losses. We show that the tool of divided differences, actually important in numerical analysis and polynomial's approximations, is quite convenient in the problem of capital asset allocation. Journal: Scandinavian Actuarial Journal Pages: 261-280 Issue: 4 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701554007 File-URL: http://hdl.handle.net/10.1080/03461230701554007 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:4:p:261-280 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_255267_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Author-Name: Steve Drekic Author-X-Name-First: Steve Author-X-Name-Last: Drekic Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Title: On the analysis of a multi-threshold Markovian risk model Abstract: We consider a class of Markovian risk models perturbed by a multiple threshold dividend strategy in which the insurer collects premiums at rate ci whenever the surplus level resides in the i-th surplus layer, i=1, 2, …,n+1 where n<∞. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the discounted joint density of the surplus prior to ruin and the deficit at ruin. By interpreting that the insurer, whose gross premium rate is c, pays dividends continuously at rate di=c−ci whenever the surplus level resides in the i-th surplus layer, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained via a recursive approach which makes use of an existing connection, linking an insurer's surplus process to an embedded fluid flow process. Journal: Scandinavian Actuarial Journal Pages: 248-260 Issue: 4 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701554080 File-URL: http://hdl.handle.net/10.1080/03461230701554080 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:4:p:248-260 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_264092_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tine Buch-Kromann Author-X-Name-First: Tine Author-X-Name-Last: Buch-Kromann Author-Name: Martin Englund Author-X-Name-First: Martin Author-X-Name-Last: Englund Author-Name: Jim Gustafsson Author-X-Name-First: Jim Author-X-Name-Last: Gustafsson Author-Name: Jens Perch Nielsen Author-X-Name-First: Jens Author-X-Name-Last: Perch Nielsen Author-Name: Fredrik Thuring Author-X-Name-First: Fredrik Author-X-Name-Last: Thuring Title: Non-parametric estimation of operational risk losses adjusted for under-reporting Abstract: Not all claims are reported when a database for financial operational risk is created. The probability of reporting increases with the size of the operational risk loss, and converges towards one for big losses. Losses in operational risk have different causes, and usually follow a wide variety of distributional shapes. Therefore, a method for modelling operational risk based on one or two parametric models is deemed to fail. In this paper, we introduce a semi-parametric method for modelling operational risk that is capable of taking under-reporting into account and being guided by prior knowledge of the distributional shape. Journal: Scandinavian Actuarial Journal Pages: 293-304 Issue: 4 Volume: 2007 Year: 2007 X-DOI: 10.1080/03461230701642471 File-URL: http://hdl.handle.net/10.1080/03461230701642471 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2007:y:2007:i:4:p:293-304 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_264093_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Title: Randomized dividends in the compound binomial model with a general premium rate Abstract: In this paper, we consider the compound binomial model with a multi-threshold dividend structure and randomized dividend payments. Using the roots of a generalization of Lundberg's fundamental equation and the general theory on difference equations, we derive an explicit expression for the Gerber-Shiu discounted penalty function with any initial surplus u (u∈ℕ). This result generalizes the main result of Tan & Yang (2006) regarding the recursive calculation of some Gerber-Shiu functions in a special class of risk models, namely the compound binomial model with a unit premium and a single threshold dividend structure. Finally, an explicit expression is also derived for the expected discounted dividend payments before ruin. Journal: Scandinavian Actuarial Journal Pages: 1-15 Issue: 1 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701642489 File-URL: http://hdl.handle.net/10.1080/03461230701642489 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:1:p:1-15 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_272193_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alexandros Zimbidis Author-X-Name-First: Alexandros Author-X-Name-Last: Zimbidis Title: Premium and reinsurance control of an ordinary insurance system with liabilities driven by a fractional Brownian motion Abstract: This paper investigates the problem of premium and reinsurance control of an ordinary insurance system when liabilities are driven by a fractional Brownian motion. The reserve equation is considered using two alternative routes: the first with no reinsurance option, and the second with some controllable proportional reinsurance coverage. Recent results from the theory of fractional linear-quadratic control (fractional calculus) are discussed, partially extended and utilized to derive compact analytical formulae for the optimal functionals of the safety loading (consequently for the respective premium rate), and the volume of the retained risk (or equivalently, for the proportion of the reinsurance coverage). Journal: Scandinavian Actuarial Journal Pages: 16-33 Issue: 1 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701722810 File-URL: http://hdl.handle.net/10.1080/03461230701722810 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:1:p:16-33 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_272198_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yaniv Zaks Author-X-Name-First: Yaniv Author-X-Name-Last: Zaks Title: The optimal claiming strategies in a Bonus-Malus System and the monotony property Abstract: In the classical Bonus-Malus System (BMS) there are several premium levels, e.g., M. A premium level i consists of a premium (πi) and a deductible (di). In this paper, we consider the expected cost for a horizon of n periods of a policyholder in level i. This expectation is denoted by En(i). When damage of size x occurs, the policyholder should decide whether or not to claim. The minimum damage for which the policyholder will claim should be the solution of . We will show that En−1(i−1) − En−1(i+1), hence x=di+En−1(i+1) ≤ En−1(i−1), is a valid solution. Journal: Scandinavian Actuarial Journal Pages: 34-40 Issue: 1 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701722869 File-URL: http://hdl.handle.net/10.1080/03461230701722869 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:1:p:34-40 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_276673_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Dietmar Pfeifer Author-X-Name-First: Dietmar Author-X-Name-Last: Pfeifer Author-Name: Doreen Strassburger Author-X-Name-First: Doreen Author-X-Name-Last: Strassburger Title: Solvency II: stability problems with the SCR aggregation formula Abstract: One of the central issues in the Solvency II process will be an appropriate calculation of the Solvency Capital Requirement (SCR). This is the economic capital that an insurance company must hold in order to guarantee a one-year ruin probability of at most 0.5%. In the so-called standard formula, the overall SCR is calculated from individual SCRs in a particular way that imitates the calculation of the standard deviation for a sum of normally distributed risks (SCR aggregation formula). However, in order to cope with skewness in the individual risk distributions, this formula must be calibrated accordingly in order to maintain the prescribed level of confidence. In this paper, we want to show that the methods proposed and discussed thus far still show stability problems within the general setup. Journal: Scandinavian Actuarial Journal Pages: 61-77 Issue: 1 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701766825 File-URL: http://hdl.handle.net/10.1080/03461230701766825 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:1:p:61-77 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_276679_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claude Lefèvre Author-X-Name-First: Claude Author-X-Name-Last: Lefèvre Author-Name: Stéphane Loisel Author-X-Name-First: Stéphane Author-X-Name-Last: Loisel Title: On finite-time ruin probabilities for classical risk models Abstract: This paper examines the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard & Lefèvre (1997) for the probability of (non-)ruin within finite time. First, a standard method based on the ballot theorem and an argument of Seal-type provides an initial (known) formula for that probability. Then, a concept of pseudo-distributions for the cumulated claim amounts, combined with some simple implications of the ballot theorem, leads to the desired formula. Two expressions for the (non-)ruin probability over an infinite horizon are also deduced as corollaries. Finally, an illustration within the framework of Solvency II is briefly presented. Journal: Scandinavian Actuarial Journal Pages: 41-60 Issue: 1 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701766882 File-URL: http://hdl.handle.net/10.1080/03461230701766882 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:1:p:41-60 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_279629_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mikkel Dahl Author-X-Name-First: Mikkel Author-X-Name-Last: Dahl Author-Name: Martin Melchior Author-X-Name-First: Martin Author-X-Name-Last: Melchior Author-Name: Thomas Møller Author-X-Name-First: Thomas Author-X-Name-Last: Møller Title: On systematic mortality risk and risk-minimization with survivor swaps Abstract: A new market for so-called mortality derivatives is now appearing with survivor swaps (also called mortality swaps), longevity bonds and other specialized solutions. The development of these new financial instruments is triggered by the increased focus on the systematic mortality risk inherent in life insurance contracts, and their main focus is thus to allow the life insurance companies to hedge their systematic mortality risk. At the same time, this new class of financial contract is interesting from an investor's point of view, since it increases the possibility for an investor to diversify the investment portfolio. The systematic mortality risk stems from the uncertainty related to the future development of the mortality intensities. Mathematically, this uncertainty is described by modeling the underlying mortality intensities via stochastic processes. We consider two different portfolios of insured lives, where the underlying mortality intensities are correlated, and study the combined financial and mortality risk inherent in a portfolio of general life insurance contracts. In order to hedge this risk, we allow for investments in survivor swaps and derive risk-minimizing strategies in markets where such contracts are available. The strategies are evaluated numerically. Journal: Scandinavian Actuarial Journal Pages: 114-146 Issue: 2-3 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701795873 File-URL: http://hdl.handle.net/10.1080/03461230701795873 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:2-3:p:114-146 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_298142_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mika Mäkinen Author-X-Name-First: Mika Author-X-Name-Last: Mäkinen Title: Reference mortality K2004 of personal life insurance policies in Finland Abstract: This article presents the reference mortality model K2004 approved by the Actuarial Society of Finland and the technique that was implemented in developing it. Initially, I will present the historical development of individual mortality rates in Finland. Then, the requirements posed for a modern mortality modelling will be presented. Reference mortality model K2004 is based on total population mortality rates, which were adjusted to correspond with that portion of the population that has a life insurance policy. First, the model presents a margin of the observed life insurance mortality rate in the total population with a Lee-Carter method together with a forecast, where the downward trend in mortality rates is expected to continue at the rate illustrated since the 1960s. Then, the mortality rate has been adjusted into life insurance mortality per age so that it corresponds to the differences observed between total population and the portion of population that has a life insurance during 1991–2001. Finally, a cohort and gender-specific functional margin will be presented to obtained data. Journal: Scandinavian Actuarial Journal Pages: 174-183 Issue: 2-3 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230801979765 File-URL: http://hdl.handle.net/10.1080/03461230801979765 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:2-3:p:174-183 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_308085_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren Jarner Author-X-Name-First: Søren Author-X-Name-Last: Jarner Author-Name: Esben Kryger Author-X-Name-First: Esben Author-X-Name-Last: Kryger Author-Name: Chresten Dengsøe Author-X-Name-First: Chresten Author-X-Name-Last: Dengsøe Title: The evolution of death rates and life expectancy in Denmark Abstract: From 1835 to date Denmark has experienced an increase in life expectancy at birth of about 40 years for both sexes. Over the course of the last 170 years, life expectancy at birth has increased from 40 to 80 years for women and from 36 to 76 years for men, and it continues to rise. Using a new methodology, we show that about half of the total historic increase can be attributed to the sharp decline in infant and young age death rates up to 1950. However, life expectancy gains from 1950 to date can be primarily attributed to improvements in the age-specific death rates for the age group from 50 to 80, although there is also a noticeable contribution from the further decline in infant mortality over this period. With age-specific death rates up to age 60 now at a very low absolute level, substantial future life expectancy improvements must necessarily arise from improvements in age-specific death rates for ages 60 and above. Using the developed methodology, we quantify the impact of further reductions in age-specific mortality. Despite being one of countries with the highest life expectancy at the beginning of the 20th century, and despite the spectacular historic increase in life expectancy since then, Denmark is, in fact, lagging behind compared to many other countries, notably the other Nordic countries. The main reason is an alarming excess mortality for cause-specific death rates related to ischaemic heart diseases and, in particular, a number of cancer diseases. Age-specific death rates continue to improve in most countries, and a likely scenario is that in the future Denmark will experience improvement rates at the international level or perhaps even higher as a result of a catch-up effect. Journal: Scandinavian Actuarial Journal Pages: 147-173 Issue: 2-3 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230802079193 File-URL: http://hdl.handle.net/10.1080/03461230802079193 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:2-3:p:147-173 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_308088_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ellinor Samuelsson Author-X-Name-First: Ellinor Author-X-Name-Last: Samuelsson Title: Mortality among Swedish insured Abstract: In this paper, the mortality among the Swedish voluntarily insured is described. It is based on calculations of the mortality among the Swedish insured from 2001 to 2005, and in the total Swedish population. The total population data has been used to compute the mortality trend with the Lee–Carter model. Journal: Scandinavian Actuarial Journal Pages: 184-199 Issue: 2-3 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230802079227 File-URL: http://hdl.handle.net/10.1080/03461230802079227 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:2-3:p:184-199 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_317526_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Modelling and management of mortality risk: a review Abstract: In the first part of the paper, we consider the wide range of extrapolative stochastic mortality models that have been proposed over the last 15–20 years. A number of models that we consider are framed in discrete time and place emphasis on the statistical aspects of modelling and forecasting. We discuss how these models can be evaluated, compared and contrasted. We also discuss a discrete-time market model that facilitates valuation of mortality-linked contracts with embedded options. We then review several approaches to modelling mortality in continuous time. These models tend to be simpler in nature, but make it possible to examine the potential for dynamic hedging of mortality risk. Finally, we review a range of financial instruments (traded and over-the-counter) that could be used to hedge mortality risk. Some of these, such as mortality swaps, already exist, while others anticipate future developments in the market. Journal: Scandinavian Actuarial Journal Pages: 79-113 Issue: 2-3 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230802173608 File-URL: http://hdl.handle.net/10.1080/03461230802173608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:2-3:p:79-113 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_228655_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Greg Taylor Author-X-Name-First: Greg Author-X-Name-Last: Taylor Title: Second-order Bayesian revision of a generalised linear model Abstract: It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e., multivariate EDF subject to a link function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second-order Bayes estimators of parameters of the posterior. The family of second-order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with the acquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case. A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section 5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readily derived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this is obtained (Section 6.3). Section 1.2 provides an indication of how the theory developed here might be applied to loss reserving. A sequel paper, providing numerical illustrations of this, is planned. Journal: Scandinavian Actuarial Journal Pages: 202-242 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701287517 File-URL: http://hdl.handle.net/10.1080/03461230701287517 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:202-242 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_272215_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario Wüthrich Author-X-Name-First: Mario Author-X-Name-Last: Wüthrich Author-Name: Michael Merz Author-X-Name-First: Michael Author-X-Name-Last: Merz Author-Name: Hans Bühlmann Author-X-Name-First: Hans Author-X-Name-Last: Bühlmann Title: Bounds on the estimation error in the chain ladder method Abstract: Buchwalder et al. (2006) have illustrated that there are different approaches for the derivation of an estimate for the parameter estimation error in the distribution-free chain ladder reserving method. In this paper, we demonstrate that these approaches provide estimates that are close to each other for typical parameters. This is carried out by proving upper and lower bounds. Journal: Scandinavian Actuarial Journal Pages: 283-300 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701723032 File-URL: http://hdl.handle.net/10.1080/03461230701723032 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:283-300 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_286456_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: John Lau Author-X-Name-First: John Author-X-Name-Last: Lau Author-Name: Tak Siu Author-X-Name-First: Tak Author-X-Name-Last: Siu Title: Modelling long-term investment returns via Bayesian infinite mixture time series models Abstract: This paper introduces the class of Bayesian infinite mixture time series models first proposed in Lau & So (2004) for modelling long-term investment returns. It is a flexible class of time series models and provides a flexible way to incorporate full information contained in all autoregressive components with various orders by utilizing the idea of Bayesian averaging or mixing. We adopt a Bayesian sampling scheme based on a weighted Chinese restaurant process for generating partitions of investment returns to estimate the Bayesian infinite mixture time series models. Instead of using the point estimates, as in the classical or non-Bayesian approach, the estimation in this paper is performed by the full Bayesian approach, utilizing the idea of Bayesian averaging to incorporate all information contained in the posterior distributions of the random parameters. This provides a natural way to incorporate model risk or uncertainty. The proposed models can also be used to perform clustering of investment returns and detect outliers of returns. We employ the monthly data from the Toronto Stock Exchange 300 (TSE 300) indices to illustrate the implementation of our models and compare the simulated results from the estimated models with the empirical characteristics of the TSE 300 data. We apply the Bayesian predictive distribution of the logarithmic returns obtained by the Bayesian averaging or mixing to evaluate the quantile-based and conditional tail expectation risk measures for segregated fund contracts via stochastic simulation. We compare the risk measures evaluated from our models with those from some well-known and important models in the literature, and highlight some features that can be obtained from our models. Journal: Scandinavian Actuarial Journal Pages: 243-282 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701862889 File-URL: http://hdl.handle.net/10.1080/03461230701862889 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:243-282 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_288030_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Esbjörn Ohlsson Author-X-Name-First: Esbjörn Author-X-Name-Last: Ohlsson Title: Combining generalized linear models and credibility models in practice Abstract: Rating of non-life insurance contracts commonly employs multiplicative models, which are estimated by generalized linear models (GLMs); another useful tool for rate making are credibility models. The object of this paper is to demonstrate how these can be combined in practice, to solve the problem with multi-level factors – rating factors with too many levels for GLM estimation. In particular, we consider car model classification in motor insurance, using data from a Swedish insurance company. Journal: Scandinavian Actuarial Journal Pages: 301-314 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230701878612 File-URL: http://hdl.handle.net/10.1080/03461230701878612 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:301-314 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_344904_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Dietmar Pfeifer Author-X-Name-First: Dietmar Author-X-Name-Last: Pfeifer Author-Name: Doreen Strassburger Author-X-Name-First: Doreen Author-X-Name-Last: Strassburger Title: Solvency II: stability problems with the SCR aggregation formula Journal: Scandinavian Actuarial Journal Pages: 315-315 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230802447366 File-URL: http://hdl.handle.net/10.1080/03461230802447366 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:315-315 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_348880_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Title: Book Review Journal: Pages: 316-316 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230802487123 File-URL: http://hdl.handle.net/10.1080/03461230802487123 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:316-316 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_360607_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: 39 INTERNATIONAL ASTIN COLLOQUIUM Journal: Scandinavian Actuarial Journal Pages: 317-317 Issue: 4 Volume: 2008 Year: 2008 X-DOI: 10.1080/03461230802604396 File-URL: http://hdl.handle.net/10.1080/03461230802604396 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2008:y:2008:i:4:p:317-317 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_279632_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Łukasz Delong Author-X-Name-First: Łukasz Author-X-Name-Last: Delong Title: Indifference pricing of a life insurance portfolio with systematic mortality risk in a market with an asset driven by a Lévy process Abstract: In this paper, we investigate the problem of pricing and hedging of life insurance liabilities. We consider a financial market consisting of a risk-free asset with a constant rate of return, and a risky asset whose price is driven by a Lévy process. We take into account a systematic mortality risk and model mortality intensity as a diffusion process. The principle of equivalent utility is chosen as the valuation rule. In order to solve our optimization problems, we apply techniques from the stochastic control theory. An exponential utility is considered in detail. We arrive at three pricing equations and investigate some properties of the premiums. An estimate of the finite-time ruin probability is derived. Indifference pricing with respect to a quadratic loss function is also briefly discussed. Journal: Scandinavian Actuarial Journal Pages: 1-26 Issue: 1 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230701795907 File-URL: http://hdl.handle.net/10.1080/03461230701795907 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:1:p:1-26 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_286452_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claudia Flores Author-X-Name-First: Claudia Author-X-Name-Last: Flores Title: Management of catastrophic risks considering the existence of early warning systems Abstract: It is crucially important to incorporate the notion of early warning systems in insurance mathematics. We develop the theory of an arrival process taking into account an early warning system, and we use it to create appropriate actuarial models. Then, we formulate a stochastic optimization problem to find an investment strategy for the management of a fund from the perspective of a risk-averse government. The solution is given using the Föllmer-Schweizer strategy. Journal: Scandinavian Actuarial Journal Pages: 38-62 Issue: 1 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230701862848 File-URL: http://hdl.handle.net/10.1080/03461230701862848 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:1:p:38-62 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_298139_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario Wüthrich Author-X-Name-First: Mario Author-X-Name-Last: Wüthrich Author-Name: Michael Merz Author-X-Name-First: Michael Author-X-Name-Last: Merz Author-Name: Natalia Lysenko Author-X-Name-First: Natalia Author-X-Name-Last: Lysenko Title: Uncertainty of the claims development result in the chain ladder method Abstract: Using the distribution-free chain ladder method, we estimate the total ultimate claim amounts at time I, and after updating the information, at time I+1. The observable claims development result at time I+1 for accounting year (I, I+1] is then defined to be the difference between these two successive best estimate predictions for the ultimate claim. We analyze the uncertainty of this observable claims development result. Journal: Scandinavian Actuarial Journal Pages: 63-84 Issue: 1 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230801979732 File-URL: http://hdl.handle.net/10.1080/03461230801979732 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:1:p:63-84 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_362951_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Colin Ramsay Author-X-Name-First: Colin Author-X-Name-Last: Ramsay Title: The distribution of compound sums of Pareto distributed losses Abstract: An expression is derived for the cumulative distribution function of , the aggregate losses in a period, where N is the random number of losses and the Xk's are independent and identically distributed. Pareto random variables. Specific expressions are derived for the two most commonly used compound models in actuarial risk theory: the compound Poisson and the compound negative binomial. Journal: Scandinavian Actuarial Journal Pages: 27-37 Issue: 1 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802627835 File-URL: http://hdl.handle.net/10.1080/03461230802627835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:1:p:27-37 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_286450_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Willem Albers Author-X-Name-First: Willem Author-X-Name-Last: Albers Author-Name: Wilbert Kallenberg Author-X-Name-First: Wilbert Author-X-Name-Last: Kallenberg Author-Name: Viktor Lukocius Author-X-Name-First: Viktor Author-X-Name-Last: Lukocius Title: A flexible model for actuarial risks under dependence Abstract: Methods for computing risk measures, such as stop-loss premiums, tacitly assume independence of the underlying individual risks. This can lead to huge errors even when only small dependencies occur. In the present paper, a general model is developed which covers what happens in practice in a realistic way. Moreover, it is also flexible, in the sense that it allows application in practice. Accurate and transparent approximations are presented, and the results obtained are illustrated through explicit examples. Journal: Scandinavian Actuarial Journal Pages: 152-167 Issue: 2 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230701862822 File-URL: http://hdl.handle.net/10.1080/03461230701862822 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:2:p:152-167 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_294120_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Title: Elliptical families and copulas: tilting and premium; capital allocation Abstract: Elliptical copula measures with symmetrical marginals are proposed as a natural generalization of the elliptical family, which preserves the symmetrical character of marginals, but is more flexible in the choice of their shape parameters. The properties of these copulas are investigated and the elliptical copula tilting and corresponding premium are proposed as a natural tool for portfolio capital allocation. For the case of the multivariate normal family, such a tilting and premium coincide with the Esscher transform and premium. Journal: Scandinavian Actuarial Journal Pages: 85-103 Issue: 2 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230801939546 File-URL: http://hdl.handle.net/10.1080/03461230801939546 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:2:p:85-103 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_302384_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Georgios Psarrakos Author-X-Name-First: Georgios Author-X-Name-Last: Psarrakos Author-Name: Konstadinos Politis Author-X-Name-First: Konstadinos Author-X-Name-Last: Politis Title: Monotonicity properties and the deficit at ruin in the Sparre Andersen model Abstract: Let Hu(y) be the (proper) distribution function of the deficit at ruin, given that ruin occurs with initial surplus u, in the Sparre Andersen model of risk theory. Dickson & dos Reis (1996) discussed the monotonicity of Hu(y) as a function of u. In this paper, we obtain various monotonicity results for Hu(y) and other related quantities for the decreasing/increasing failure rate (DFR/IFR) and the increasing/decreasing mean residual lifetime (IMRL/DMRL) classes of distributions. These results in particular extend and make more concrete the results of Dickson & dos Reis (1996) and Willmot & Lin (1998). A new class of distributions (increasing convolution ratio; ICR) is introduced. This class extends the well-known class of distributions with IFR. Specifically, we show that if the ladder height distribution F in the model is ICR, the ratio is a non-decreasing function of u, where ψ(u) denotes the ruin probability and . Further, we obtain generalizations (expressed in terms of the distribution of the deficit) of the well-known new worse than used (NWU) property of the probability of non-ruin. Journal: Scandinavian Actuarial Journal Pages: 104-118 Issue: 2 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802022169 File-URL: http://hdl.handle.net/10.1080/03461230802022169 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:2:p:104-118 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_328271_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jérôme Barbarin Author-X-Name-First: Jérôme Author-X-Name-Last: Barbarin Author-Name: Tanguy De Launois Author-X-Name-First: Tanguy Author-X-Name-Last: De Launois Author-Name: Pierre Devolder Author-X-Name-First: Pierre Author-X-Name-Last: Devolder Title: Risk minimization with inflation and interest rate risk: applications to non-life insurance Abstract: This paper aims at studying the asset allocation problem of a non-life insurance company when inflation risk and interest rate risk are taken into account. To this purpose, we apply the risk-minimization theory developed by Föllmer & Sondermann (1986) and extended by Møller (2001). We derive the general form of the risk-minimizing strategies when the cumulative payments of the insurer are described, as suggested by Arjas (1989), by a process adapted to the natural filtration of a marked point process and when the inflation and the term structure of interest rates are simultaneously described by the HJM model of Jarrow & Yildirim (2003). We then apply our general results in two collective models and two individual models of non-life insurance payments. Journal: Scandinavian Actuarial Journal Pages: 119-151 Issue: 2 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802281047 File-URL: http://hdl.handle.net/10.1080/03461230802281047 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:2:p:119-151 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_348882_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Title: Book Review Journal: Pages: 168-168 Issue: 2 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802487149 File-URL: http://hdl.handle.net/10.1080/03461230802487149 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:2:p:168-168 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_298207_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Author-X-Name-Last: Chi-Liang Tsai Title: On the ordering of ruin probabilities for the surplus process perturbed by diffusion Abstract: In this paper, we study orders of pairs of ruin probabilities resulting from two individual claim size random variables for corresponding continuous time surplus processes perturbed by diffusion with different premium rates, relative security loadings, and variance parameters of the diffusion processes. We show that high frequency and low severity risks yield smaller ruin probabilities than low frequency and high severity risks. These ordering relationships can also be used to obtain upper and/or lower bounds on ruin probabilities. Finally, some examples are given to illustrate the results of the theorems. Journal: Scandinavian Actuarial Journal Pages: 187-204 Issue: 3 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230801980417 File-URL: http://hdl.handle.net/10.1080/03461230801980417 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:3:p:187-204 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_309206_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mogens Steffensen Author-X-Name-First: Mogens Author-X-Name-Last: Steffensen Author-Name: Stephan Waldstrøm Author-X-Name-First: Stephan Author-X-Name-Last: Waldstrøm Title: A two-account model of pension saving contracts Abstract: Saving contracts studied in the literature and available on the pension market share certain characteristics. An overview implies a unified formalization that exposes, at the same time, the common characteristics and the important differences. This article presents such a formalization in terms of two interacting accounts and specifies a series of examples from the literature and the market. We solve the valuation problem by derivation of a partial difference-differential equation and implementation of a numerical finite difference procedure. Illustrations are included. Journal: Scandinavian Actuarial Journal Pages: 169-186 Issue: 3 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802090406 File-URL: http://hdl.handle.net/10.1080/03461230802090406 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:3:p:169-186 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_328267_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andriy Andreev Author-X-Name-First: Andriy Author-X-Name-Last: Andreev Author-Name: Hans-Kristian Sjöholm Author-X-Name-First: Hans-Kristian Author-X-Name-Last: Sjöholm Title: Projections of pension fund solvency under alternative valuation regimes Abstract: This paper examines the impact of three alternative valuation regimes on perceived pension fund solvency. Deterministic valuation assumes smoothed valuation of assets and liabilities. National valuation is based on market valuation of assets and on smoothed valuation of liabilities. International valuation marks assets and liabilities to market values. Using closed-form methods based on the funding ratio return, we exemplify the dramatic effect that the choice of valuation approach has on long-horizon solvency projections. Journal: Scandinavian Actuarial Journal Pages: 239-251 Issue: 3 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802281005 File-URL: http://hdl.handle.net/10.1080/03461230802281005 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:3:p:239-251 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_331415_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: Ken Tan Author-X-Name-First: Ken Author-X-Name-Last: Tan Title: Ruin probabilities in a discrete time risk model with dependent risks of heavy tail Abstract: This paper establishes some asymptotic results for both finite and ultimate ruin probabilities in a discrete time risk model with constant interest rates, and individual net losses in , the class of regular variation with index α>0. The individual net losses are allowed to be generally dependent while they have zero index of upper tail dependence, so that our results partially generalize the counterparts in Tang (2004). The procedure of deriving our results also demonstrates a new approach of achieving asymptotic formulation for ruin probabilities when the individual risks are dependent. Journal: Scandinavian Actuarial Journal Pages: 205-218 Issue: 3 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802312487 File-URL: http://hdl.handle.net/10.1080/03461230802312487 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:3:p:205-218 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_342751_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Knut Aase Author-X-Name-First: Knut Author-X-Name-Last: Aase Title: The Nash bargaining solution vs. equilibrium in a reinsurance syndicate Abstract: We compare the Nash bargaining solution in a reinsurance syndicate to the competitive equilibrium allocation, focusing on uncertainty and risk aversion. Restricting attention to proportional reinsurance treaties, we find that, although these solution concepts are very different, one may just appear as a first order Taylor series approximation of the other, in certain cases. This may be good news for the Nash solution, or for the equilibrium allocation, all depending upon one's point of view. Our model also allows us to readily identify some properties of the equilibrium allocation not be shared by the bargaining solution, and vice versa, related to both risk aversions and correlations. Journal: Scandinavian Actuarial Journal Pages: 219-238 Issue: 3 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802425834 File-URL: http://hdl.handle.net/10.1080/03461230802425834 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:3:p:219-238 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_328274_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Weidong Tian Author-X-Name-First: Weidong Author-X-Name-Last: Tian Title: Optimal design of equity-linked products with a probabilistic constraint Abstract: There is a rich variety of tailored investment products available to the retail investor. These products combine upside participation in bull markets with downside protection in bear markets. Examples include the equity-linked products sold by insurance companies and the structured products marketed by banks. This paper examines a particular contract design for products of this nature. The paper finds the optimal design from the investor's viewpoint. It is assumed that the investor wishes to maximize expected utility of the terminal wealth subject to certain constraints. These constraints include a guaranteed rate of return as well as the opportunity to outperform a benchmark portfolio with a given probability. We derive the explicit form of the optimal design assuming both constraints apply and we illustrate the nature of the solution using some specific examples. Journal: Scandinavian Actuarial Journal Pages: 253-280 Issue: 4 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802281070 File-URL: http://hdl.handle.net/10.1080/03461230802281070 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:4:p:253-280 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_342227_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xueyuan Wu Author-X-Name-First: Xueyuan Author-X-Name-Last: Wu Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: On the discounted penalty function in a discrete time renewal risk model with general interclaim times Abstract: In this paper a discrete time renewal risk model with arbitrary interclaim times is discussed. We show that the expected discounted penalty function satisfies a recursive formula. In particular, the probability generating function of the time of ruin, as a function of the initial surplus, has a compound geometric tail. When the claim amounts follow a geometric distribution, explicit expression for the Gerber-Shiu function can be obtained for the specially chosen penalty function. The constant claim amounts and mixed geometric claim amounts are also examined. Journal: Scandinavian Actuarial Journal Pages: 281-294 Issue: 4 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230802420595 File-URL: http://hdl.handle.net/10.1080/03461230802420595 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:4:p:281-294 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_375520_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Esther Frostig Author-X-Name-First: Esther Author-X-Name-Last: Frostig Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Ruin probabilities and optimal capital allocation for heterogeneous life annuity portfolios Abstract: A large part of the actuarial literature is devoted to the derivation of ruin probabilities in various non-life insurance risk models. On the contrary, very few papers deal with ruin probabilities for life insurance portfolios. The difficulties arise from the dependence and non-stationarity of the annual payments made by the insurance company. This paper shows that the ruin probability in case of life annuity portfolios can be computed from algorithms derived by De Pril (1989) and Dhaene & Vandebroek (1995). Approximations for ruin probabilities are discussed. The present article complements the works of Frostig et al. (2003) who considered whole life, endowment, and temporary assurances, and of Denuit & Frostig (2008) who considered homogeneous life annuities portfolios. Here, heterogeneous portfolios (with respect to age and/or face amounts) are studied. Particular attention is paid to the capital allocation problem. The total amount of reserve is shared among the risk classes in order to minimize the ruin probability. It is then fair to charge a higher margin to the risk classes requiring more capital. Journal: Scandinavian Actuarial Journal Pages: 295-305 Issue: 4 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230902753507 File-URL: http://hdl.handle.net/10.1080/03461230902753507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:4:p:295-305 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_424147_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Susanna Björkwall Author-X-Name-First: Susanna Author-X-Name-Last: Björkwall Author-Name: Ola Hössjer Author-X-Name-First: Ola Author-X-Name-Last: Hössjer Author-Name: Esbjörn Ohlsson Author-X-Name-First: Esbjörn Author-X-Name-Last: Ohlsson Title: Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving Abstract: In the literature, one of the main objects of stochastic claims reserving is to find models underlying the chain-ladder method in order to analyze the variability of the outstanding claims, either analytically or by bootstrapping. In bootstrapping these models are used to find a full predictive distribution of the claims reserve, even though there is a long tradition of actuaries calculating the reserve estimate according to more complex algorithms than the chain-ladder, without explicit reference to an underlying model. In this paper we investigate existing bootstrap techniques and suggest two alternative bootstrap procedures, one non-parametric and one parametric, by which the predictive distribution of the claims reserve can be found for other age-to-age development factor methods than the chain-ladder, using some rather mild model assumptions. For illustration, the procedures are applied to three different development triangles. Journal: Scandinavian Actuarial Journal Pages: 306-331 Issue: 4 Volume: 2009 Year: 2009 X-DOI: 10.1080/03461230903239738 File-URL: http://hdl.handle.net/10.1080/03461230903239738 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2009:y:2009:i:4:p:306-331 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_342228_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Adamic Author-X-Name-First: Peter Author-X-Name-Last: Adamic Title: Modeling multiple risks in the presence of double censoring Abstract: Self-consistent (SC) iterative algorithms will be proposed to non-parametrically estimate the cause-specific cumulative incidence functions in a multiple decrement, doubly censored context. Double censoring is defined to include both left and right censored observations, in addition to exact observations. The algorithms are a generalization of the classical univariate algorithms of Efron and Turnbull. Unlike any previous competing risk models proposed in the literature to date, the proposed algorithms will be fully non-parametric while also explicitly allowing for the possibility of masked modes of failure, whereby failure is known only to occur due to a subset from the set of all possible causes. In short, the method is useful in any actuarial application that encounters censored and/or masked risks. The paper concludes by showing how the method can be applied to employee benefits modeling. Journal: Scandinavian Actuarial Journal Pages: 68-81 Issue: 1 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802420603 File-URL: http://hdl.handle.net/10.1080/03461230802420603 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:1:p:68-81 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_354112_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michael Preisel Author-X-Name-First: Michael Author-X-Name-Last: Preisel Author-Name: Søren Jarner Author-X-Name-First: Søren Author-X-Name-Last: Jarner Author-Name: Rune Eliasen Author-X-Name-First: Rune Author-X-Name-Last: Eliasen Title: Investing for retirement through a with-profits pension scheme: a client's perspective Abstract: Saving for retirement by with-profits pension contracts is markedly different from traditional savings vehicles in at least two aspects: premia committed to the company are managed according to the preferences of the company – which may not coincide with the long-term interests of the client – and the return on investments is not directly transferred to client's savings but awaits a decision by the company to spend it as bonus. We show that a management's general aversion to (short term) insolvency risk results in investment strategies dynamically scaling investment risk up and down with the current funding status of the company. The resultant dynamics hugely impacts the long-term funding status of the pension company and thereby the investment outcome of with-profits contracts. We show that for a one-period optimizing company there exists a stationary regime only for moderately aggressive investment strategies, and we derive an analytical approximation to the stationary funding ratio distribution when it exists. In contrast to the one-period case, we show that the highest expected bonus level in stationarity is not achieved for the most aggressive investment strategy available. The reason being that if investments become too aggressive the company will spend a lot of time at low funding ratios where bonus cannot be attributed impairing the average bonus. Journal: Scandinavian Actuarial Journal Pages: 15-35 Issue: 1 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802539444 File-URL: http://hdl.handle.net/10.1080/03461230802539444 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:1:p:15-35 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_355232_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Domenico De Giovanni Author-X-Name-First: Domenico Author-X-Name-Last: De Giovanni Title: Lapse rate modeling: a rational expectation approach Abstract: The surrender option embedded in many life insurance products is a clause that allows policyholders to terminate the contract early. Pricing techniques based on the American Contingent Claim (ACC) theory are often used, though the actual policyholders' behavior is far from optimal. Inspired by many prepayment models for mortgage backed securities, this paper builds a Rational Expectation (RE) model describing the policyholders' behavior in lapsing the contract. A market model with stochastic interest rates is considered, and the pricing is carried out through numerical approximation of the corresponding two-space-dimensional parabolic partial differential equation. Extensive numerical experiments show the differences in terms of pricing and interest rate elasticity between the ACC and RE approaches as well as the sensitivity of the contract price with respect to changes in the policyholders' behavior. Journal: Scandinavian Actuarial Journal Pages: 56-67 Issue: 1 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802550649 File-URL: http://hdl.handle.net/10.1080/03461230802550649 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:1:p:56-67 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_359277_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lihua Bai Author-X-Name-First: Lihua Author-X-Name-Last: Bai Author-Name: Junyi Guo Author-X-Name-First: Junyi Author-X-Name-Last: Guo Title: Optimal dividend payments in the classical risk model when payments are subject to both transaction costs and taxes Abstract: In this paper, we study optimal dividend problem in the classical risk model. Transaction costs and taxes are required when dividends occur. The problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality, we obtain the analytical solutions of the optimal return function and the optimal dividend strategy when claims are exponentially distributed. We also find a formula for the expected time between dividends. The results show that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments. Journal: Scandinavian Actuarial Journal Pages: 36-55 Issue: 1 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802591098 File-URL: http://hdl.handle.net/10.1080/03461230802591098 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:1:p:36-55 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_369483_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Author-Name: Kenneth McIvor Author-X-Name-First: Kenneth Author-X-Name-Last: McIvor Title: Pensions and genetics: can longevity genes be reliable risk factors for annuity pricing? Abstract: We consider a number of gene variants that have been found to affect longevity. Their effects have been modelled using Cox or logistic regressions, whose fitted parameters have simple asymptotic sampling distributions. The expected present value of a life annuity allowing for these genetic risk estimates inherits a sampling distribution, which can be found by simulation. We find that possibly significant uncertainty about annuity premiums may be overlooked if the standard errors of parameters estimated in medical studies are ignored by medical underwriters. Such considerations may play an important part when the acceptability of using a risk factor in underwriting is conditional on proof of its relevance and reliability. This is the current position in respect of genetic information in many countries, most prominently in the UK. Journal: Scandinavian Actuarial Journal Pages: 1-14 Issue: 1 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802693134 File-URL: http://hdl.handle.net/10.1080/03461230802693134 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:1:p:1-14 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_367550_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zina Benouaret Author-X-Name-First: Zina Author-X-Name-Last: Benouaret Author-Name: Djamil Aïssani Author-X-Name-First: Djamil Author-X-Name-Last: Aïssani Title: Strong stability in a two-dimensional classical risk model with independent claims Abstract: In this paper, we study the strong stability of ruin probabilities in risk models. The question of stability naturally arises in risk theory since the governing parameters in these models can only be estimated with uncertainty. Moreover, in most cases there are not explicit expressions known for the ruin probabilities. Our objective is to present the applicability of the strong stability method to the bivariate classical risk model with independent claims. After clarifying the conditions to approximate the two-dimensional risk model with disturbance parameters by the two-dimensional classical risk model, we obtain the stability inequalities with an exact computation of the constants. Journal: Scandinavian Actuarial Journal Pages: 83-92 Issue: 2 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802673805 File-URL: http://hdl.handle.net/10.1080/03461230802673805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:83-92 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_370259_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alexandru Asimit Author-X-Name-First: Alexandru Author-X-Name-Last: Asimit Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Title: Extremes on the discounted aggregate claims in a time dependent risk model Abstract: This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model. Journal: Scandinavian Actuarial Journal Pages: 93-104 Issue: 2 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230802700897 File-URL: http://hdl.handle.net/10.1080/03461230802700897 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:93-104 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_372442_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Christian Hipp Author-X-Name-First: Christian Author-X-Name-Last: Hipp Author-Name: Dominik Kortschak Author-X-Name-First: Dominik Author-X-Name-Last: Kortschak Title: Higher-order expansions for compound distributions and ruin probabilities with subexponential claims Abstract: Let X i (i=1,2, …) be a sequence of subexponential positive independent and identically distributed random variables. In this paper, we offer two alternative approaches to obtain higher-order expansions of the tail of and subsequently for ruin probabilities in renewal risk models with claim sizes X i . In particular, these emphasize the importance of the term for the accuracy of the resulting asymptotic expansion of . Furthermore, we present a more rigorous approach to the often suggested technique of using approximations with shifted arguments. The cases of a Pareto type, Weibull and Lognormal distribution for X i are discussed in more detail and numerical investigations of the increase in accuracy by including higher-order terms in the approximation of ruin probabilities for finite realistic ranges of s are given. Journal: Scandinavian Actuarial Journal Pages: 105-135 Issue: 2 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230902722726 File-URL: http://hdl.handle.net/10.1080/03461230902722726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:105-135 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_381743_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Author-Name: Jonas Rinné Author-X-Name-First: Jonas Author-X-Name-Last: Rinné Title: Can stocks help mend the asset and liability mismatch? Abstract: Stocks are generally used to provide higher returns in the long run. But the dramatic fall in equity prices at the beginning of this century, triggering large underfundings in pension plans, raised the question as to whether stocks can really help mend the asset and liability mismatch. To understand some aspects of this topical issue, we examine whether existing major equity indexes can close this gap, given the liability profile of a typical pension fund. We also compare the non-market capitalization weighted equity indexes recently introduced as Research Affiliates Fundamental Indexes® (RAFI®) with traditional market capitalization weighted equity indexes from an asset and liability management perspective. The analysis of the behavior of the solvency ratio clearly indicates that interest rate sensitive stocks have a large potential to improve the link between assets and liabilities. Compared with market capitalization weighted equity indexes, RAFI® shows a substantially better potential to mend the asset and liability mismatch, while also improving returns. Journal: Scandinavian Actuarial Journal Pages: 148-160 Issue: 2 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230902815736 File-URL: http://hdl.handle.net/10.1080/03461230902815736 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:148-160 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_385188_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: On the maximum severity of ruin in the compound Poisson model with a threshold dividend strategy Abstract: We study the distribution and moments of the maximum severity of ruin in the compound Poisson risk process with a threshold dividend strategy. The distribution can be analyzed through the probability that the surplus process attains a given level from the initial surplus without first falling below zero. This note extends the results in Picard (1994) and shows that the distribution of the maximum severity of ruin can be expressed explicitly in terms of the ruin probabilities of two classical risk models with different premium rates. The moments of the maximum severity of ruin can be obtained through its distribution function. Journal: Scandinavian Actuarial Journal Pages: 136-147 Issue: 2 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230902850162 File-URL: http://hdl.handle.net/10.1080/03461230902850162 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:136-147 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_434596_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andreas Lagerås Author-X-Name-First: Andreas Author-X-Name-Last: Lagerås Title: Commutation functions under Gompertz–Makeham mortality Abstract: It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz–Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life insurances can be expressed with an incomplete gamma function with a negative shape parameter. This is not of much use if ones software cannot calculate these values. The aim of this note is to show that one can express the commutation functions using only the exponential function, the (ordinary) gamma function and the gamma distribution function, which are all implemented in common statistical and spreadsheet software. This eliminates the need to evaluate the commutation functions and expected remaining life-length with numerical integration. Journal: Scandinavian Actuarial Journal Pages: 161-164 Issue: 2 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903344181 File-URL: http://hdl.handle.net/10.1080/03461230903344181 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:161-164 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_374754_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghislain Léveillé Author-X-Name-First: Ghislain Author-X-Name-Last: Léveillé Author-Name: José Garrido Author-X-Name-First: José Author-X-Name-Last: Garrido Author-Name: Ya Fang Wang Author-X-Name-First: Ya Author-X-Name-Last: Fang Wang Title: Moment generating functions of compound renewal sums with discounted claims Abstract: Léveillé & Garrido (2001a, 2001b) have obtained recursive formulas for the moments of compound renewal sums with discounted claims, which incorporate both, Andersen's (1957) generalization of the classical risk model, where the claim number process is an ordinary renewal process, and Taylor's (1979), where the joint effect of the claims cost inflation and investment income on a compound Poisson risk process is considered. In this paper, assuming certain regularity conditions, we improve the preceding results by examining more deeply the asymptotic and finite time moment generating functions of the discounted aggregate claims process. Examples are given for claim inter-arrival times and claim severity following phase-type distributions, such as the Erlang case. Journal: Scandinavian Actuarial Journal Pages: 165-184 Issue: 3 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230902745842 File-URL: http://hdl.handle.net/10.1080/03461230902745842 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:165-184 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_388573_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 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: Gerber–Shiu analysis with a generalized penalty function Abstract: A generalization of the usual penalty function is proposed, and a defective renewal equation is derived for the Gerber–Shiu discounted penalty function in the classical risk model. This is used to derive the trivariate distribution of the deficit at ruin, the surplus prior to ruin, and the surplus immediately following the second last claim before ruin. The marginal distribution of the last interclaim time before ruin is derived and studied, and its joint distribution with the claim causing ruin is derived. Journal: Scandinavian Actuarial Journal Pages: 185-199 Issue: 3 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230902884013 File-URL: http://hdl.handle.net/10.1080/03461230902884013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:185-199 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_411392_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Cary Tsai Author-X-Name-First: Cary Author-X-Name-Last: Tsai Author-Name: Yi Lu Author-X-Name-First: Yi Author-X-Name-Last: Lu Title: An effective method for constructing bounds for ruin probabilities for the surplus process perturbed by diffusion Abstract: In this paper, we first study orders, valid up to a certain positive initial surplus, between a pair of ruin probabilities resulting from two individual claim size random variables for corresponding continuous time surplus processes perturbed by diffusion. The results are then applied to obtain a smooth upper (lower) bound for the underlying ruin probability; the upper (lower) bound is constructed from exponentially distributed claims, provided that the mean residual lifetime function of the underlying random variable is non-decreasing (non-increasing). Finally, numerical examples are given to illustrate the constructed upper bounds for ruin probabilities with comparisons to some existing ones. Journal: Scandinavian Actuarial Journal Pages: 200-220 Issue: 3 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903112190 File-URL: http://hdl.handle.net/10.1080/03461230903112190 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:200-220 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_421373_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Héléne Cossette Author-X-Name-First: Héléne Author-X-Name-Last: Cossette Author-Name: Etienne Marceau Author-X-Name-First: Etienne Author-X-Name-Last: Marceau Author-Name: Fouad Marri Author-X-Name-First: Fouad Author-X-Name-Last: Marri Title: Analysis of ruin measures for the classical compound Poisson risk model with dependence Abstract: In this paper, we consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie–Gumbel–Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber–Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution. Journal: Scandinavian Actuarial Journal Pages: 221-245 Issue: 3 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903211992 File-URL: http://hdl.handle.net/10.1080/03461230903211992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:221-245 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_507927_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Abdelhakim Necir Author-X-Name-First: Abdelhakim Author-X-Name-Last: Necir Author-Name: Brahim Brahimi Author-X-Name-First: Brahim Author-X-Name-Last: Brahimi Author-Name: Djamel Meraghni Author-X-Name-First: Djamel Author-X-Name-Last: Meraghni Title: Erratum to: ‘Statistical estimate of the proportional hazard premium of loss’ Abstract: The asymptotic variance of the risk premium estimator, proposed by Necir et al. (2007), is revised, by using the right asymptotic approximation of the uniform empirical quantile process. Journal: Scandinavian Actuarial Journal Pages: 246-247 Issue: 3 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461238.2010.507927 File-URL: http://hdl.handle.net/10.1080/03461238.2010.507927 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:246-247 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_413651_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Adamic Author-X-Name-First: Peter Author-X-Name-Last: Adamic Author-Name: Stephanie Dixon Author-X-Name-First: Stephanie Author-X-Name-Last: Dixon Author-Name: Daniel Gillis Author-X-Name-First: Daniel Author-X-Name-Last: Gillis Title: Multiple decrement modeling in the presence of interval censoring and masking Abstract: A self-consistent algorithm will be proposed to non-parametrically estimate the cause-specific cumulative incidence functions (CIFs) in an interval censored, multiple decrement context. More specifically, the censoring mechanism will be assumed to be a mixture of case 2 interval-censored data with the additional possibility of exact observations. The proposed algorithm is a generalization of the classical univariate algorithms of Efron and Turnbull. However, unlike any previous non-parametric models proposed in the literature to date, the algorithm will explicitly allow for the possibility of any combination of masked modes of failure, where failure is known only to occur due to a subset from the set of all possible causes. A simulation study is also conducted to demonstrate the consistency of the estimators of the CIFs produced by the proposed algorithm, as well as to explore the effect of masking. The paper concludes by applying the method to masked mortality data obtained for Pueblo County, CO, for three risks: death by cancer; cardiovascular failure; or other. Journal: Scandinavian Actuarial Journal Pages: 312-327 Issue: 4 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903134780 File-URL: http://hdl.handle.net/10.1080/03461230903134780 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:4:p:312-327 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_416220_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Raluca Vernic Author-X-Name-First: Raluca Author-X-Name-Last: Vernic Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Bjørn Sundt Author-X-Name-First: Bjørn Author-X-Name-Last: Sundt Title: Inequalities for the De Pril approximation to the distribution of the number of policies with claims Abstract: In the present paper, we give sufficient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given. Journal: Scandinavian Actuarial Journal Pages: 249-267 Issue: 4 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903160470 File-URL: http://hdl.handle.net/10.1080/03461230903160470 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:4:p:249-267 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_418623_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Georgios Psarrakos Author-X-Name-First: Georgios Author-X-Name-Last: Psarrakos Title: Some results on the joint distribution prior to and at the time of ruin in the classical model Abstract: For the classical risk model (i.e. with Poisson arrivals), we study the tail of the joint distribution of the surplus prior to and at ruin. In particular, we obtain some inequalities and monotonicity results for it. Let S be the random variable with distribution function the probability of non-ruin, 1−ψ(u), and the probability the surplus just before ruin exceeds x, given that ruin occurs. We estimate the distance between the residual lifetime of S, Pr(S>u+y∣S>u) and the product , where the tail convolution includes again the random variable S. Finally, based on this distance, we derive a lower bound for the probability of ruin, and we compare this against a bound available in the literature. Journal: Scandinavian Actuarial Journal Pages: 268-283 Issue: 4 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903184504 File-URL: http://hdl.handle.net/10.1080/03461230903184504 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:4:p:268-283 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_433341_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Enrico Biffis Author-X-Name-First: Enrico Author-X-Name-Last: Biffis Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Pierre Devolder Author-X-Name-First: Pierre Author-X-Name-Last: Devolder Title: Stochastic mortality under measure changes Abstract: We provide a self-contained analysis of a class of continuous-time stochastic mortality models that have gained popularity in the last few years. We describe some of their advantages and limitations, examining whether their features survive equivalent changes of measures. This is important when using the same model for both market-consistent valuation and risk management of life insurance liabilities. We provide a numerical example based on the calibration to the French annuity market of a risk-neutral version of the model proposed by Lee & Carter (1992). Journal: Scandinavian Actuarial Journal Pages: 284-311 Issue: 4 Volume: 2010 Year: 2010 X-DOI: 10.1080/03461230903331634 File-URL: http://hdl.handle.net/10.1080/03461230903331634 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2010:y:2010:i:4:p:284-311 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_426827_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ola Haug Author-X-Name-First: Ola Author-X-Name-Last: Haug Author-Name: Xeni Dimakos Author-X-Name-First: Xeni Author-X-Name-Last: Dimakos Author-Name: Jofrid Vårdal Author-X-Name-First: Jofrid Author-X-Name-Last: Vårdal Author-Name: Magne Aldrin Author-X-Name-First: Magne Author-X-Name-Last: Aldrin Author-Name: Elisabeth Meze-Hausken Author-X-Name-First: Elisabeth Author-X-Name-Last: Meze-Hausken Title: Future building water loss projections posed by climate change Abstract: The insurance industry, like other parts of the financial sector, is vulnerable to climate change. Life as well as non-life products are affected and knowledge of future loss levels is valuable. Risk and premium calculations may be updated accordingly, and dedicated loss-preventive measures can be communicated to customers and regulators. We have established statistical claims models for the coherence between externally inflicted water damage to private buildings in Norway and selected meteorological variables. Based on these models and downscaled climate predictions from the Hadley centre HadAM3H climate model, the estimated loss level of a future scenario period (2071–2100) is compared to that of a control period (1961–1990). In spite of substantial estimation uncertainty, our analyses identify an incontestable increase in the claims level along with some regional variability. Of the uncertainties inherently involved in such predictions, only the error due to model fit is quantifiable. Journal: Scandinavian Actuarial Journal Pages: 1-20 Issue: 1 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461230903266533 File-URL: http://hdl.handle.net/10.1080/03461230903266533 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_430361_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anders Jessen Author-X-Name-First: Anders Author-X-Name-Last: Jessen Author-Name: Niels Rietdorf Author-X-Name-First: Niels Author-X-Name-Last: Rietdorf Title: Diagonal effects in claims reserving Abstract: In this paper we present two different approaches to how one can include diagonal effects in non-life claims reserving based on run-off triangles. Empirical analyses suggest that the approaches in Zehnwirth (2003) and Kuang et al. (2008a, 2008b) do not work well with low-dimensional run-off triangles because estimation uncertainty is too large. To overcome this problem we consider similar models with a smaller number of parameters. These are closely related to the framework considered in Verbeek (1972) and Taylor (1977, 2000); the separation method. We explain that these models can be interpreted as extensions of the multiplicative Poisson models introduced by Hachemeister & Stanard (1975) and Mack (1991). Journal: Scandinavian Actuarial Journal Pages: 21-37 Issue: 1 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461230903301876 File-URL: http://hdl.handle.net/10.1080/03461230903301876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:1:p:21-37 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_442327_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Stanford Author-X-Name-First: David Author-X-Name-Last: Stanford 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 Title: Erlangian approximation to finite time ruin probabilities in perturbed risk models Abstract: In this paper, we consider a class of perturbed risk processes that have an underlying Markov structure, including Markov-modulated risk processes, and Sparre–Andersen risk processes when both inter-claim times and claim sizes are phase-type. We apply the Erlangization method to the risk process in the class in order to obtain an accurate approximation of the finite time ruin probability. In addition, we develop an efficient recursive procedure by recognizing a repeating structure in the probability matrices we work with. We believe the present work is among the first to either compute or approximate finite time ruin probabilities in the perturbed risk model. Journal: Scandinavian Actuarial Journal Pages: 38-58 Issue: 1 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461230903421492 File-URL: http://hdl.handle.net/10.1080/03461230903421492 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:1:p:38-58 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_442601_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Folded and log-folded- distributions as models for insurance loss data Abstract: A rich variety of probability distributions has been proposed in the actuarial literature for fitting of insurance loss data. Examples include: lognormal, log-t, various versions of Pareto, loglogistic, Weibull, gamma and its variants, and generalized beta of the second kind distributions, among others. In this paper, we supplement the literature by adding the log-folded-normal and log-folded-t families. Shapes of the density function and key distributional properties of the ‘folded’ distributions are presented along with three methods for the estimation of parameters: method of maximum likelihood; method of moments; and method of trimmed moments. Further, large and small-sample properties of these estimators are studied in detail. Finally, we fit the newly proposed distributions to data which represent the total damage done by 827 fires in Norway for the year 1988. The fitted models are then employed in a few quantitative risk management examples, where point and interval estimates for several value-at-risk measures are calculated. Journal: Scandinavian Actuarial Journal Pages: 59-74 Issue: 1 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461230903424199 File-URL: http://hdl.handle.net/10.1080/03461230903424199 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:1:p:59-74 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_460814_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ilie-Radu Mitric Author-X-Name-First: Ilie-Radu Author-X-Name-Last: Mitric Author-Name: Kristina Sendova Author-X-Name-First: Kristina Author-X-Name-Last: Sendova Title: On a multi-threshold compound Poisson surplus process with interest Abstract: We consider a multi-threshold compound Poisson surplus process. When the initial surplus is between any two consecutive thresholds, the insurer has the option to choose the respective premium rate and interest rate. Also, the model allows for borrowing the current amount of deficit whenever the surplus falls below zero. Starting from the integro-differential equations satisfied by the Gerber–Shiu function that appear in Yang et al. (2008), we consider exponentially and phase-type(2) distributed claim sizes, in which cases we are able to transform the integro-differential equations into ordinary differential equations. As a result, we obtain explicit expressions for the Gerber–Shiu function. Journal: Scandinavian Actuarial Journal Pages: 75-95 Issue: 2 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003603054 File-URL: http://hdl.handle.net/10.1080/03461231003603054 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:2:p:75-95 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_461702_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Maria Russolillo Author-X-Name-First: Maria Author-X-Name-Last: Russolillo Author-Name: Giuseppe Giordano Author-X-Name-First: Giuseppe Author-X-Name-Last: Giordano Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: Extending the Lee–Carter model: a three-way decomposition Abstract: In this paper, we focus on a Multi-dimensional Data Analysis approach to the Lee–Carter (LC) model of mortality trends. In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker3 model. The suggested methodology allows us to obtain combined estimates for the three modes: (1) time, (2) age groups and (3) different populations. From the results obtained by the Tucker3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time-series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model's goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares 10 European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation. Journal: Scandinavian Actuarial Journal Pages: 96-117 Issue: 2 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003611933 File-URL: http://hdl.handle.net/10.1080/03461231003611933 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:2:p:96-117 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_461704_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: So-Yeun Kim Author-X-Name-First: So-Yeun Author-X-Name-Last: Kim Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: The proper distribution function of the deficit in the delayed renewal risk model Abstract: The main focus of this paper is to extend the analysis of ruin-related quantities to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and a general equation that is used as a framework is derived. The equation is obtained by conditioning on the first drop below the initial surplus level. Then, we consider the deficit at ruin among many random variables associated with ruin. The properties of the distribution function (DF) of the proper deficit are examined in particular. Journal: Scandinavian Actuarial Journal Pages: 118-137 Issue: 2 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003611958 File-URL: http://hdl.handle.net/10.1080/03461231003611958 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:2:p:118-137 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_467085_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghislain Léveillé Author-X-Name-First: Ghislain Author-X-Name-Last: Léveillé Author-Name: Franck Adékambi Author-X-Name-First: Franck Author-X-Name-Last: Adékambi Title: Covariance of discounted compound renewal sums with a stochastic interest rate Abstract: Formulas have been obtained for the moments of the discounted aggregate claims process, for a constant instantaneous interest rate, and for a claims number process that is an ordinary or a delayed renewal process. In this paper, we present explicit formulas on the first two moments and the joint moment of this risk process, for a non-trivial extension to a stochastic instantaneous interest rate. Examples are given for Erlang claims number processes, and for the Ho–Lee–Merton and the Vasicek interest rate models. Journal: Scandinavian Actuarial Journal Pages: 138-153 Issue: 2 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003665632 File-URL: http://hdl.handle.net/10.1080/03461231003665632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:2:p:138-153 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_469596_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Julia Eisenberg Author-X-Name-First: Julia Author-X-Name-Last: Eisenberg Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: Minimising expected discounted capital injections by reinsurance in a classical risk model Abstract: In this paper we consider a classical continuous time risk model, where the claims are reinsured by some reinsurance with retention level , where means ‘no reinsurance’ and b=0 means ‘full reinsurance’. The insurer can change the retention level continuously. To prevent negative surplus the insurer has to inject additional capital. The problem is to minimise the expected discounted cost over all admissible reinsurance strategies. We show that an optimal reinsurance strategy exists. For some special cases we will be able to give the optimal strategy explicitly. In other cases the method will be illustrated only numerically. Journal: Scandinavian Actuarial Journal Pages: 155-176 Issue: 3 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003690747 File-URL: http://hdl.handle.net/10.1080/03461231003690747 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:3:p:155-176 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_469597_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mathieu Pigeon Author-X-Name-First: Mathieu Author-X-Name-Last: Pigeon Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Composite Lognormal–Pareto model with random threshold Abstract: This paper further considers the composite Lognormal–Pareto model proposed by Cooray & Ananda (2005) and suitably modified by Scollnik (2007). This model is based on a Lognormal density up to an unknown threshold value and a Pareto density thereafter. Instead of using a single threshold value applying uniformly to the whole data set, the model proposed in the present paper allows for heterogeneity with respect to the threshold and let it vary among observations. Specifically, the threshold value for a particular observation is seen as the realization of a positive random variable and the mixed composite Lognormal–Pareto model is obtained by averaging over the population of interest. The performance of the composite Lognormal–Pareto model and of its mixed extension is compared using the well-known Danish fire losses data set. Journal: Scandinavian Actuarial Journal Pages: 177-192 Issue: 3 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003690754 File-URL: http://hdl.handle.net/10.1080/03461231003690754 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:3:p:177-192 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_470889_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nino Savelli Author-X-Name-First: Nino Author-X-Name-Last: Savelli Author-Name: Gian Clemente Author-X-Name-First: Gian Author-X-Name-Last: Clemente Title: Hierarchical structures in the aggregation of premium risk for insurance underwriting Abstract: In the valuation of the Solvency II capital requirement, the correct appraisal of risk dependencies acquires particular relevance. These dependencies refer to the recognition of risk diversification in the aggregation process and there are different levels of aggregation and hence different types of diversification. For instance, for a non-life company at the first level the risk components of each single line of business (e.g. premium, reserve, and CAT risks) need to be combined in the overall portfolio, the second level regards the aggregation of different kind of risks as, for example, market and underwriting risk, and finally various solo legal entities could be joined together in a group. Solvency II allows companies to capture these diversification effects in capital requirement assessment, but the identification of a proper methodology can represent a delicate issue. Indeed, while internal models by simulation approaches permit usually to obtain the portfolio multivariate distribution only in the independence case, generally the use of copula functions can consent to have the multivariate distribution under dependence assumptions too. However, the choice of the copula and the parameter estimation could be very problematic when only few data are available. So it could be useful to find a closed formula based on Internal Models independence results with the aim to obtain the capital requirement under dependence assumption. A simple technique, to measure the diversification effect in capital requirement assessment, is the formula, proposed by Solvency II quantitative impact studies, focused on the aggregation of capital charges, the latter equal to percentile minus average of total claims amount distribution of single line of business (LoB), using a linear correlation matrix. On the other hand, this formula produces the correct result only for a restricted class of distributions, while it may underestimate the diversification effect. In this paper we present an alternative method, based on the idea to adjust that formula with proper calibration factors (proposed by Sandström (2007)) and appropriately extended with the aim to consider very skewed distribution too. In the last part considering different non-life multi-line insurers, we compare the capital requirements obtained, for only premium risk, applying the aggregation formula to the results derived by elliptical copulas and hierarchical Archimedean copulas. Journal: Scandinavian Actuarial Journal Pages: 193-213 Issue: 3 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461231003703672 File-URL: http://hdl.handle.net/10.1080/03461231003703672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:3:p:193-213 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_481080_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anders Jessen Author-X-Name-First: Anders Author-X-Name-Last: Jessen Author-Name: Thomas Mikosch Author-X-Name-First: Thomas Author-X-Name-Last: Mikosch Author-Name: Gennady Samorodnitsky Author-X-Name-First: Gennady Author-X-Name-Last: Samorodnitsky Title: Prediction of outstanding payments in a Poisson cluster model Abstract: We consider a simple Poisson cluster model for the payment numbers and the corresponding total payments for insurance claims arriving in a given year. Due to the Poisson structure one can give reasonably explicit expressions for the prediction of the payment numbers and total payments in future periods given the past observations of the payment numbers. One can also derive reasonably explicit expressions for the corresponding prediction errors. In the (a, b) class of Panjer's claim size distributions, these expressions can be evaluated by simple recursive algorithms. We study the conditions under which the predictions are asymptotically linear as the number of past payments becomes large. We also demonstrate that, in other regimes, the prediction may be far from linear. For example, a staircase-like pattern may arise as well. We illustrate how the theory works on real-life data, also in comparison with the chain ladder method. Journal: Scandinavian Actuarial Journal Pages: 214-237 Issue: 3 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.481080 File-URL: http://hdl.handle.net/10.1080/03461238.2010.481080 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:3:p:214-237 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_484567_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Regression modeling with actuarial and financial applications by Edward W. Frees Journal: Scandinavian Actuarial Journal Pages: 319-319 Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.484567 File-URL: http://hdl.handle.net/10.1080/03461238.2010.484567 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:319-319 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_618605_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Editorial Board Journal: Scandinavian Actuarial Journal Pages: ebi-ebi Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2011.618605 File-URL: http://hdl.handle.net/10.1080/03461238.2011.618605 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 # input file: SACT_A_484569_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Title: Nonlife actuarial models, theory, methods and evaluation by Yiu-Kuen Tse Journal: Scandinavian Actuarial Journal Pages: 319-320 Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.484569 File-URL: http://hdl.handle.net/10.1080/03461238.2010.484569 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:319-320 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_490021_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Emiliano Valdez Author-X-Name-First: Emiliano Author-X-Name-Last: Valdez Author-Name: Yugu Xiao Author-X-Name-First: Yugu Author-X-Name-Last: Xiao Title: On the distortion of a copula and its margins Abstract: This article examines the notion of distortion of copulas, a natural extension of distortion within the univariate framework. We study three approaches to this extension: (1) distortion of the margins alone while keeping the original copula structure; (2) distortion of the margins while simultaneously altering the copula structure; and (3) synchronized distortion of the copula and its margins. When applying distortion within the multivariate framework, it is important to preserve the properties of a copula function. For the first two approaches, this is a rather straightforward result; however, for the third approach, the proof has been exquisitely constructed in Morillas (2005). These three approaches unify the different types of multivariate distortion that have scarcely scattered in the literature. Our contribution in this paper is to further consider this unifying framework: we give numerous examples to illustrate and we examine their properties particularly with some aspects of ordering multivariate risks. The extension of multivariate distortion can be practically implemented in risk management where there is a need to perform aggregation and attribution of portfolios of correlated risks. Furthermore, ancillary to the results discussed in this article, we are able to generalize the formula developed by Genest & Rivest (2001) for computing the distribution of the probability integral transformation of a random vector and extend it to the case within the distortion framework. For purposes of illustration, we applied the distortion concept to value excess of loss reinsurance for an insurance policy where the loss amount could vary by type of loss. Journal: Scandinavian Actuarial Journal Pages: 292-317 Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.490021 File-URL: http://hdl.handle.net/10.1080/03461238.2010.490021 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:292-317 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_482188_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Baopeng Lu Author-X-Name-First: Baopeng Author-X-Name-Last: Lu 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 Title: The genetics of breast and ovarian cancer IV: a model of breast cancer progression Abstract: Gui et al. (2006), in Part III of a series of papers, proposed a dynamic family history model of breast cancer (BC) and ovarian cancer in which the development of a family history was represented explicitly as a transition between states, and then applied this model to life insurance and critical illness insurance. In this study, we extend the model to income protection insurance. In this paper, Part IV of the series, we construct and parameterise a semi-Markov model for the life history of a woman with BC, in which events such as diagnosis, treatment, recovery and recurrence are incorporated. In Part V, we then show: (a) estimates of premium ratings depending on genotype or family history; and (b) the impact of adverse selection under various moratoria on the use of genetic information. Journal: Scandinavian Actuarial Journal Pages: 239-266 Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.482188 File-URL: http://hdl.handle.net/10.1080/03461238.2010.482188 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:239-266 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_484566_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Actuarial mathematics for life contingent risks by David C.M. Dickson, Mary R. Hardy and Howard R. Waters Journal: Scandinavian Actuarial Journal Pages: 318-318 Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.484566 File-URL: http://hdl.handle.net/10.1080/03461238.2010.484566 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:318-318 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_482191_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Baopeng Lu Author-X-Name-First: Baopeng Author-X-Name-Last: Lu 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: Fei Yu Author-X-Name-First: Fei Author-X-Name-Last: Yu Title: The genetics of breast and ovarian cancer V: application to income protection insurance Abstract: In Part IV we presented a comprehensive model of a life history of a woman at risk of breast cancer (BC), in which relevant events such as diagnosis, treatment, recovery and recurrence were represented explicitly, and corresponding transition intensities were estimated. In this part, we study some applications to income protection insurance (IPI) business. We calculate premiums based either on genetic test results or more practically on a family history of BC. We then extend the model into an IPI market model by incorporating rates of insurance-buying behaviour, in order to estimate the possible costs of adverse selection, in terms of increased premiums, under various moratoria on the use of genetic information. Journal: Scandinavian Actuarial Journal Pages: 267-291 Issue: 4 Volume: 2011 Year: 2011 X-DOI: 10.1080/03461238.2010.482191 File-URL: http://hdl.handle.net/10.1080/03461238.2010.482191 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2011:y:2011:i:4:p:267-291 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_476492_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Damien Drieskens Author-X-Name-First: Damien Author-X-Name-Last: Drieskens Author-Name: Marc Henry Author-X-Name-First: Marc Author-X-Name-Last: Henry Author-Name: Jean-François Walhin Author-X-Name-First: Jean-François Author-X-Name-Last: Walhin Author-Name: Jürgen Wielandts Author-X-Name-First: Jürgen Author-X-Name-Last: Wielandts Title: Stochastic projection for large individual losses Abstract: In this paper we investigate how to estimate ultimate values of large losses. The method is based on the development of individual losses and therefore allows to compute the netting impact of excess of loss reinsurance. In particular the index clause is properly accounted for. A numerical example based on real-life data is provided. Journal: Scandinavian Actuarial Journal Pages: 1-39 Issue: 1 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461231003759708 File-URL: http://hdl.handle.net/10.1080/03461231003759708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:1:p:1-39 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_503426_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghislain Léveillé Author-X-Name-First: Ghislain Author-X-Name-Last: Léveillé Author-Name: Franck Adékambi Author-X-Name-First: Franck Author-X-Name-Last: Adékambi Title: Joint moments of discounted compound renewal sums Abstract: The first two moments and the covariance of the aggregate discounted claims have been found for a stochastic interest rate, from which the inflation rate has been subtracted, and for a claims number process that is an ordinary or a delayed renewal process. Hereafter we extend the preceding results by presenting recursive formulas for the joint moments of this risk process, for a constant interest rate, and non-recursive formulas for higher joint moments when the interest rate is stochastic. Examples are given for exponential claims inter-arrival times and for the Ho-Lee-Merton interest rate model. Journal: Scandinavian Actuarial Journal Pages: 40-55 Issue: 1 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.503426 File-URL: http://hdl.handle.net/10.1080/03461238.2010.503426 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:1:p:40-55 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_523515_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yasutaka Shimizu Author-X-Name-First: Yasutaka Author-X-Name-Last: Shimizu Title: Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model Abstract: A non-parametric estimator of the Gerber–Shiu function is proposed for a risk process with a compound Poisson claim process plus a diffusion perturbation; the Wiener–Poisson risk model. The estimator is based on a regularized inversion of an empirical-type estimator of the Laplace transform of the Gerber–Shiu function. We show the weak consistency of the estimator in the sense of an integrated squared error with the rate of convergence. Journal: Scandinavian Actuarial Journal Pages: 56-69 Issue: 1 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.523515 File-URL: http://hdl.handle.net/10.1080/03461238.2010.523515 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:1:p:56-69 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_534257_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alicja Nocon Author-X-Name-First: Alicja Author-X-Name-Last: Nocon Author-Name: William Scott Author-X-Name-First: William Author-X-Name-Last: Scott Title: An extension of the Whittaker–Henderson method of graduation Abstract: We present an outline and historical summary of the Whittaker–Henderson method of graduation (or data smoothing), together with an extension of the method in which the graduated values are obtained by minimising a Whittaker–Henderson criterion subject to constraints. Examples are given, using data for the global average temperature anomaly and for a set of share prices, in which the proposed method appears to give good results. Journal: Scandinavian Actuarial Journal Pages: 70-79 Issue: 1 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.534257 File-URL: http://hdl.handle.net/10.1080/03461238.2010.534257 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:1:p:70-79 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_489762_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vinzenz Erhardt Author-X-Name-First: Vinzenz Author-X-Name-Last: Erhardt Author-Name: Claudia Czado Author-X-Name-First: Claudia Author-X-Name-Last: Czado Title: Modeling dependent yearly claim totals including zero claims in private health insurance Abstract: In insurance applications yearly claim totals of different coverage fields are often dependent. In many cases there are numerous claim totals which are zero. A marginal claim distribution will have an additional point mass at zero, hence this probability function (pf) will not be continuous at zero and the cumulative distribution functions will not be uniform. Therefore using a copula approach to model dependency is not straightforward. We will illustrate how to express the joint pf by copulas with discrete and continuous margins. A pair-copula construction will be used for the fit of the continuous copula allowing to choose appropriate copulas for each pair of margins. Journal: Scandinavian Actuarial Journal Pages: 106-129 Issue: 2 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.489762 File-URL: http://hdl.handle.net/10.1080/03461238.2010.489762 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:2:p:106-129 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_485370_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Victor Korolev Author-X-Name-First: Victor Author-X-Name-Last: Korolev Author-Name: Irina Shevtsova Author-X-Name-First: Irina Author-X-Name-Last: Shevtsova Title: An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums Abstract: By a modification of the method that was applied in study of Korolev & Shevtsova (2009), here the inequalities and are proved for the uniform distance ρ(F n ,Φ) between the standard normal distribution function Φ and the distribution function F n of the normalized sum of an arbitrary number n≥1 of independent identically distributed random variables with zero mean, unit variance, and finite third absolute moment β3. The first of these two inequalities is a structural improvement of the classical Berry–Esseen inequality and as well sharpens the best known upper estimate of the absolute constant in the classical Berry–Esseen inequality since 0.33477(β3+0.429)≤0.33477(1+0.429)β3<0.4784β3 by virtue of the condition β3≥1. The latter inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry–Esseen inequality for Poisson random sums to 0.3041 which is strictly less than the least possible value 0.4097… of the absolute constant in the classical Berry–Esseen inequality. As corollaries, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined. Journal: Scandinavian Actuarial Journal Pages: 81-105 Issue: 2 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.485370 File-URL: http://hdl.handle.net/10.1080/03461238.2010.485370 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:2:p:81-105 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_490017_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jae-Kyung Woo Author-X-Name-First: Jae-Kyung Author-X-Name-Last: Woo Title: A generalized penalty function for a class of discrete renewal processes Abstract: Analysis of a generalized Gerber–Shiu function is considered in a discrete-time (ordinary) Sparre Andersen renewal risk process with time-dependent claim sizes. The results are then applied to obtain ruin-related quantities under some renewal risk processes assuming specific interclaim distributions such as a discrete K n distribution and a truncated geometric distribution (i.e. compound binomial process). Furthermore, the discrete delayed renewal risk process is considered and results related to the ordinary process are derived as well. Journal: Scandinavian Actuarial Journal Pages: 130-152 Issue: 2 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.490017 File-URL: http://hdl.handle.net/10.1080/03461238.2010.490017 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:2:p:130-152 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_490027_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Title: A unifying approach to the analysis of business with random gains Abstract: In this paper, we consider a stochastic model in which a business enterprise is subject to constant rate of expenses over time and gains which are random in both time and amount. Inspired by Albrecher & Boxma (2004), it is assumed in general that the size of a given gain has an impact on the time until the next gain. Under such a model, we are interested in various quantities related to the survival of the business after default, which include: (i) the fair price of a perpetual insurance which pays the expenses whenever the available capital reaches zero; (ii) the probability of recovery by the first gain after default if money is borrowed at the time of default; and (iii) the Laplace transforms of the time of recovery and the first duration of negative capital. To this end, a function resembling the so-called Gerber–Shiu function (Gerber & Shiu (1998)) commonly used in insurance analysis is proposed. The function's general structure is studied via the use of defective renewal equations, and its applications to the evaluation of the above-mentioned quantities are illustrated. Exact solutions are derived in the independent case by assuming that either the inter-arrival times or the gains have an arbitrary distribution. A dependent example is also considered and numerical illustrations follow. Journal: Scandinavian Actuarial Journal Pages: 153-182 Issue: 3 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.490027 File-URL: http://hdl.handle.net/10.1080/03461238.2010.490027 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:3:p:153-182 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_511034_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Pauline Barrieu Author-X-Name-First: Pauline Author-X-Name-Last: Barrieu Author-Name: Harry Bensusan Author-X-Name-First: Harry Author-X-Name-Last: Bensusan Author-Name: Nicole El Karoui Author-X-Name-First: Nicole Author-X-Name-Last: El Karoui Author-Name: Caroline Hillairet Author-X-Name-First: Caroline Author-X-Name-Last: Hillairet Author-Name: Stéphane Loisel Author-X-Name-First: Stéphane Author-X-Name-Last: Loisel Author-Name: Claudia Ravanelli Author-X-Name-First: Claudia Author-X-Name-Last: Ravanelli Author-Name: Yahia Salhi Author-X-Name-First: Yahia Author-X-Name-Last: Salhi Title: Understanding, modelling and managing longevity risk: key issues and main challenges Abstract: This article investigates the latest developments in longevity-risk modelling, and explores the key risk management challenges for both the financial and insurance industries. The article discusses key definitions that are crucial for the enhancement of the way longevity risk is understood, providing a global view of the practical issues for longevity-linked insurance and pension products that have evolved concurrently with the steady increase in life expectancy since s. In addition, the article frames the recent and forthcoming developments that are expected to action industry-wide changes as more effective regulation, designed to better assess and efficiently manage inherited risks, is adopted. Simultaneously, the evolution of longevity is intensifying the need for capital markets to be used to manage and transfer the risk through what are known as Insurance-Linked Securities (ILS). Thus, the article will examine the emerging scenarios, and will finally highlight some important potential developments for longevity-risk management from a financial perspective with reference to the most relevant modelling and pricing practices in the banking industry. Journal: Scandinavian Actuarial Journal Pages: 203-231 Issue: 3 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.511034 File-URL: http://hdl.handle.net/10.1080/03461238.2010.511034 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:3:p:203-231 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_499261_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Dickson Author-X-Name-First: David Author-X-Name-Last: Dickson Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: Erlang risk models and finite time ruin problems Abstract: We consider the joint density of the time of ruin and deficit at ruin in the Erlang(n) risk model. We give a general formula for this joint density and illustrate how the components of this formula can be found in the special case when n=2. We then show how the formula can be implemented numerically for a general value of n. We also discuss how the ideas extend to the generalised Erlang(n) risk model. Journal: Scandinavian Actuarial Journal Pages: 183-202 Issue: 3 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.499261 File-URL: http://hdl.handle.net/10.1080/03461238.2010.499261 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:3:p:183-202 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_537835_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Montserrat Guillén Author-X-Name-First: Montserrat Author-X-Name-Last: Guillén Author-Name: Jens Perch Nielsen Author-X-Name-First: Jens Author-X-Name-Last: Perch Nielsen Author-Name: Ana Pérez-Marín Author-X-Name-First: Ana Author-X-Name-Last: Pérez-Marín Author-Name: Kitt Petersen Author-X-Name-First: Kitt Author-X-Name-Last: Petersen Title: Performance measurement of pension strategies: a case study of Danish life cycle products Abstract: The Danish pension markets of life cycle products have expanded considerably since its introduction in the beginning of the millennium. The market is maturing and pensioners have the choice between a wide area of different products. It is therefore about time that financial insurance technology is developed to guide the performance measurement of available products. In this paper we develop a simple first version of such a method and we investigate life cycle products recommended on the web of the four biggest commercial Danish pension companies on one day in February 2007. All considered products are outperformed by trivial benchmark products with constant stock proportion over time. Our approach is the following: for each life cycle product we first find a trivial benchmark product with the same long-term risk and then we compare the long-term return of the two equivalent products. We primarily consider value at risk and tail value at risk as risk measures, but we also include a study where the fair value of an interest guarantee is used as risk measure. We consider both long-term mean returns and long-term median returns. We hope that our new method will be regarded as a first step towards a scientifically based ranking of the quality of pension products. Journal: Scandinavian Actuarial Journal Pages: 258-277 Issue: 4 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.537835 File-URL: http://hdl.handle.net/10.1080/03461238.2010.537835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:4:p:258-277 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_506688_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: S. J. Richards Author-X-Name-First: S. J. Author-X-Name-Last: Richards Title: A handbook of parametric survival models for actuarial use Abstract: Traditional actuarial techniques for mortality analysis are being supplanted by statistical models. Chief amongst these are survival models, which model mortality continuously at the level of the individual. An assumption of a mathematical form for the hazard function or, equivalently, the assumption of a continuous distribution for an individual's lifetime, leads automatically to smooth fitted mortality rates. This note gives an overview of the survival models commonly found in statistical packages and compares their suitability for actuarial work with the mortality ‘laws’ proposed by actuaries over the past two centuries. We find that the actuarial laws provide substantially better fits at post-retirement ages. We also give a common structure of parameterisation which gives consistent behaviour and interpretation of risk factors across all 16 survival models listed here. Finally, we consider the benefits of working directly with the log-likelihood function, including making allowance for the left truncation which is common for the data with which actuaries work. Journal: Scandinavian Actuarial Journal Pages: 233-257 Issue: 4 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.506688 File-URL: http://hdl.handle.net/10.1080/03461238.2010.506688 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:4:p:233-257 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_546147_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claudia Czado Author-X-Name-First: Claudia Author-X-Name-Last: Czado Author-Name: Rainer Kastenmeier Author-X-Name-First: Rainer Author-X-Name-Last: Kastenmeier Author-Name: Eike Brechmann Author-X-Name-First: Eike Author-X-Name-Last: Brechmann Author-Name: Aleksey Min Author-X-Name-First: Aleksey Author-X-Name-Last: Min Title: A mixed copula model for insurance claims and claim sizes Abstract: A crucial assumption of the classical compound Poisson model of Lundberg for assessing the total loss incurred in an insurance portfolio is the independence between the occurrence of a claim and its claims size. In this paper we present a mixed copula approach suggested by Song et al. to allow for dependency between the number of claims and its corresponding average claim size using a Gaussian copula. Marginally we permit for regression effects both on the number of incurred claims as well as its average claim size using generalized linear models. Parameters are estimated using adaptive versions of maximization by parts (MBP). The performance of the estimation procedure is validated in an extensive simulation study. Finally the method is applied to a portfolio of car insurance policies, indicating its superiority over the classical compound Poisson model. Journal: Scandinavian Actuarial Journal Pages: 278-305 Issue: 4 Volume: 2012 Year: 2012 X-DOI: 10.1080/03461238.2010.546147 File-URL: http://hdl.handle.net/10.1080/03461238.2010.546147 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2012:y:2012:i:4:p:278-305 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_555939_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Enkelejd Hashorva Author-X-Name-First: Enkelejd Author-X-Name-Last: Hashorva Title: On beta-product convolutions Abstract: Let R be a positive random variable independent of S which is beta distributed. In this paper we are interested on the relation between R and RS. For this model we derive first some distributional properties, and then investigate the lower tail asymptotics of RS when R is regularly varying at 0, and vice-versa. Our first application concerns the asymptotic behaviour of the componentwise sample minima related to elliptical distributions. Further, we derive the lower tail asymptotics of the aggregated risk for bivariate polar distributions. Journal: Scandinavian Actuarial Journal Pages: 69-83 Issue: 1 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.555939 File-URL: http://hdl.handle.net/10.1080/03461238.2011.555939 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:1:p:69-83 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_546138_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Montserrat Guillén Author-X-Name-First: Montserrat Author-X-Name-Last: Guillén Author-Name: Jens Nielsen Author-X-Name-First: Jens Author-X-Name-Last: Nielsen Author-Name: Ana Pérez-Marín Author-X-Name-First: Ana Author-X-Name-Last: Pérez-Marín Author-Name: Kitt Petersen Author-X-Name-First: Kitt Author-X-Name-Last: Petersen Title: Performance measurement of pension strategies: a case study of Danish life-cycle products Abstract: The Danish pension market of life-cycle products have expanded considerably since its introduction in the beginning of the millennium. The market is maturing and pensioners have the choice between a wide area of different products. It is therefore about time that financial insurance technology is developed to guide the performance measurement of available products. In this paper we develop a simple first version of such a method and we investigate life-cycle products recommended on the web of the four biggest commercial Danish pension companies on one day in February 2007. All considered products are outperformed by trivial benchmark products with constant stock proportion over time. Our approach is the following: for each life-cycle product we first find a trivial benchmark product with the same longterm risk and then we compare the long-term return of the two equivalent products. We primarily consider value at risk (VaR) and tail VaR as risk measures, but we also include a study where the fair value of an interest guarantee is used as risk measure. We consider both long-term mean returns and long-term median returns. We hope that our new method will be regarded as a first step toward a scientifically based ranking of the quality of pension products. Journal: Scandinavian Actuarial Journal Pages: 49-68 Issue: 1 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2010.546138 File-URL: http://hdl.handle.net/10.1080/03461238.2010.546138 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:1:p:49-68 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_540154_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fernando Mierzejewski Author-X-Name-First: Fernando Author-X-Name-Last: Mierzejewski Title: Raising and allocation capital principles as optimal managerial contracts Abstract: A unified framework is presented to characterise the capital structure of firms that face borrowing restrictions – which extends the classic theory of capital by incorporating elements from actuarial and agency theory. It is demonstrated that the bankruptcy and agency costs afforded by these firms can be expressed in terms of the actuarial prices of the underlying exposures. Then the optimal surplus is determined in order to maximise value – which is equivalent to minimise the cost of bankruptcy plus the opportunity cost of capital. The capital principle thus obtained explicitly depends on risk and expectations, and can be applied to allocate reserves both in financial and insurance companies. An optimal decentralised mechanism is also defined that stimulates the exchange of information inside multidivisional corporations. Journal: Scandinavian Actuarial Journal Pages: 24-48 Issue: 1 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2010.540154 File-URL: http://hdl.handle.net/10.1080/03461238.2010.540154 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:1:p:24-48 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_507582_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Rui Zhou Author-X-Name-First: Rui Author-X-Name-Last: Zhou Author-Name: Johnny Li Author-X-Name-First: Johnny Author-X-Name-Last: Li Title: A cautionary note on pricing longevity index swaps Abstract: In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. In this paper, we offer a quantitative analysis of this brand new financial innovation. First of all, we set up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices (spreads) that are fairly close to the spreads that Goldman Sachs currently offers. We then explore the uncertainty involved in this model-based pricing framework. Specifically, we study parameter risk by using Bayesian methods and model risk by examining structural changes in mortality dynamics. Our results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap. Journal: Scandinavian Actuarial Journal Pages: 1-23 Issue: 1 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2010.507582 File-URL: http://hdl.handle.net/10.1080/03461238.2010.507582 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:1:p:1-23 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_546144_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anna Castañer Author-X-Name-First: Anna Author-X-Name-Last: Castañer Author-Name: M. Claramunt Author-X-Name-First: M. Author-X-Name-Last: Claramunt Author-Name: Maude Gathy Author-X-Name-First: Maude Author-X-Name-Last: Gathy Author-Name: Claude Lefèvre Author-X-Name-First: Claude Author-X-Name-Last: Lefèvre Author-Name: Maite Mármol Author-X-Name-First: Maite Author-X-Name-Last: Mármol Title: Ruin problems for a discrete time risk model with non-homogeneous conditions Abstract: This paper is concerned with a non-homogeneous discrete time risk model where premiums are fixed but non-uniform, and claim amounts are independent but non-stationary. It allows one to account for the influence of inflation and interest and the effect of variability in the claims. Our main purpose is to develop an algorithm for calculating the finite time ruin probabilities and the associated ruin severity distributions. The ruin probabilities are shown to rely on an underlying algebraic structure of Appell type. That property makes the computational method proposed quite simple and efficient. Its application is illustrated through some numerical examples of ruin problems. The well known Lundberg bound for ultimate ruin probabilities is also reexamined within such a non-homogeneous framework. Journal: Scandinavian Actuarial Journal Pages: 83-102 Issue: 2 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2010.546144 File-URL: http://hdl.handle.net/10.1080/03461238.2010.546144 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:2:p:83-102 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_585771_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jinxia Zhu Author-X-Name-First: Jinxia Author-X-Name-Last: Zhu Title: Optimal dividend control for a generalized risk model with investment incomes and debit interest Abstract: This paper investigates dividend optimization of an insurance corporation under a more realistic model, which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive reserve and debit interest for negative reserve. Ruin occurs when the reserve drops below the critical value. The company controls the dividend pay-out dynamically with the objective to maximize the expected total discounted dividends until ruin. We show that the optimal strategy, is a band strategy and it is optimal to pay no dividends when the reserve is negative. Journal: Scandinavian Actuarial Journal Pages: 140-162 Issue: 2 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.585771 File-URL: http://hdl.handle.net/10.1080/03461238.2011.585771 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:2:p:140-162 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_574347_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hung-Hsi Huang Author-X-Name-First: Hung-Hsi Author-X-Name-Last: Huang Author-Name: Yung-Ming Shiu Author-X-Name-First: Yung-Ming Author-X-Name-Last: Shiu Author-Name: Ching-Ping Wang Author-X-Name-First: Ching-Ping Author-X-Name-Last: Wang Title: Optimal insurance contract with stochastic background wealth Abstract: This study presents an optimal insurance contract developed endogenously when insured individuals face two mutually dependent risks, background wealth and insurable loss. If background wealth is conditionally normally distributed given insurable loss, the optimal insurance contract may be proportional coinsurance above a straight deductible for a quadratic, negative exponential, or mean-variance utility function. Additionally, when the insured has a quadratic utility or mean-variance utility, the optimal retained schedule is a function of conditional expected value of background wealth given insurable loss. Moreover, the optimal insurance contracts for quadratic and negative exponential utility functions need not to be mean-variance efficient, even when the conditional normal distribution is assumed. Finally, when a portfolio problem is considered, the calculation about the optimal insurance contract remains almost unchanged. Journal: Scandinavian Actuarial Journal Pages: 119-139 Issue: 2 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.574347 File-URL: http://hdl.handle.net/10.1080/03461238.2011.574347 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:2:p:119-139 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_558186_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ka Cheung Author-X-Name-First: Ka Author-X-Name-Last: Cheung Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Title: Bounds for sums of random variables when the marginal distributions and the variance of the sum are given Abstract: In this paper, we establish several relations between convex order, variance order, and comonotonicity. In the first part, we extend Cheung (2008b) to show that when the marginal distributions are fixed, a sum with maximal variance is in fact a comonotonic sum. Thus the convex upper bound is achieved if and only if the marginal variables are comonotonic. Next, we study the situation where besides the marginal distributions; the variance of the sum is also fixed. Intuitively one expects that adding this information may lead to a bound that is sharper than the comonotonic upper bound. However, we show that such upper bound does not even exist. Nevertheless, we can still identify a special dependence structure known as upper comonotonicity, in which case the sum behaves like a convex largest sum in the upper tail. Finally, we investigate when the convex order is equivalent to the weaker variance order. Throughout this paper, interpretations and significance of the results in terms of portfolio risks will be emphasized. Journal: Scandinavian Actuarial Journal Pages: 103-118 Issue: 2 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.558186 File-URL: http://hdl.handle.net/10.1080/03461238.2011.558186 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:2:p:103-118 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_592262_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Landy Rabehasaina Author-X-Name-First: Landy Author-X-Name-Last: Rabehasaina Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Author-X-Name-Last: Chi-Liang Tsai Title: Ruin time and aggregate claim amount up to ruin time for the perturbed risk process Abstract: We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived. Journal: Scandinavian Actuarial Journal Pages: 186-212 Issue: 3 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.592262 File-URL: http://hdl.handle.net/10.1080/03461238.2011.592262 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:3:p:186-212 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_599141_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Author-Name: Hu Yang Author-X-Name-First: Hu Author-X-Name-Last: Yang Title: On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process Abstract: In this paper, we consider a Sparre Andersen risk model perturbed by a spectrally negative Lévy process (SNLP). Assuming that the interclaim times follow a Coxian distribution, we show that the Laplace transforms and defective renewal equations for the Gerber–Shiu functions can be obtained by employing the roots of a generalized Lundberg equation. When the SNLP is a combination of a Brownian motion and a compound Poisson process with exponential jumps, explicit expressions and asymptotic formulas for the Gerber–Shiu functions are obtained for exponential claim size distribution and heavy-tailed claim size distribution, respectively. Journal: Scandinavian Actuarial Journal Pages: 213-239 Issue: 3 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.599141 File-URL: http://hdl.handle.net/10.1080/03461238.2011.599141 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:3:p:213-239 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_589145_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mathieu Bargès Author-X-Name-First: Mathieu Author-X-Name-Last: Bargès Author-Name: Stéphane Loisel Author-X-Name-First: Stéphane Author-X-Name-Last: Loisel Author-Name: Xavier Venel Author-X-Name-First: Xavier Author-X-Name-Last: Venel Title: On finite-time ruin probabilities with reinsurance cycles influenced by large claims Abstract: Market cycles play a great role in reinsurance. Cycle transitions are not independent from the claim arrival process: a large claim or a high number of claims may accelerate cycle transitions. To take this into account, a semi-Markovian risk model is proposed and analyzed. A refined Erlangization method is developed to compute the finite-time ruin probability of a reinsurance company. Numerical applications and comparisons to results obtained from simulation methods are given. The impact of dependency between claim amounts and phase changes is studied. Journal: Scandinavian Actuarial Journal Pages: 163-185 Issue: 3 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.589145 File-URL: http://hdl.handle.net/10.1080/03461238.2011.589145 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:3:p:163-185 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_618545_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marcus Christiansen Author-X-Name-First: Marcus Author-X-Name-Last: Christiansen Title: Safety margins for unsystematic biometric risk in life and health insurance Abstract: In multistate life and health insurances, the pattern of states of the policyholder is random, thus exposing the insurer to an unsystematic biometric risk. For this reason safety margins are added on premiums and reserves. But in contrast to non-life insurance, traditionally the safety margins are not chosen explicitly but implicitly in form of a valuation basis of first order. If we define the implicit margins bottom-up, we are not able to control the level of safety that we finally reach for premiums and reserves. If we use a top-down approach, that means that we directly calculate explicit margins for premiums and reserves and then choose implicit safety margins that correspond to the explicit margins, we are able to control the total portfolio risk, but we have the problem that it is unclear how to allocate the total margin to partial margins for different transitions at different ages. Although the allocation of the total margin to the partial (implicit) margins is not relevant for the total portfolio risk, we have to pay attention since it can have a great effect on the calculation of surplus. In this paper we calculate asymptotic probability distributions for premiums and reserves of second order by using the functional delta method. As a result, we can not only determine the actual level of safety that is induced by given implicit safety margins, but we can also linearly decompose the total randomness of a portfolio to contributions that the different transition rates at different ages make to the total uncertainty. As a result we do not only get new insight into the sources of unsystematic biometric risk, but we also obtain a useful tool that allows to construct reasonable principles for the allocation of the total safety margin to implicit margins with respect to transitions and ages. Journal: Scandinavian Actuarial Journal Pages: 286-323 Issue: 4 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.618545 File-URL: http://hdl.handle.net/10.1080/03461238.2011.618545 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:4:p:286-323 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_602196_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Amin Zadeh Author-X-Name-First: Amin Author-X-Name-Last: Zadeh Author-Name: Martin Bilodeau Author-X-Name-First: Martin Author-X-Name-Last: Bilodeau Title: Fitting bivariate losses with phase-type distributions Abstract: Maximum likelihood estimation and (parametric bootstrap) goodness-of-fit test are considered for bivariate phase-type distributions introduced by Assaf and Colleagues. In a special case, the dependence structure of bivariate phase-type distributions is revealed. The results are used to fit a real bi-dimensional data set related to insurance losses (LOSS) and allocated loss adjustment expenses (ALAE). The fitted bivariate phase-type is used to obtain conditional quantiles and mean of ALAE for a given value of LOSS. The bivariate phase-type distribution meets all the requirements listed in the study by Klugman and Parsa. Journal: Scandinavian Actuarial Journal Pages: 241-262 Issue: 4 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.602196 File-URL: http://hdl.handle.net/10.1080/03461238.2011.602196 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:4:p:241-262 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_602477_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jingzhen Liu Author-X-Name-First: Jingzhen Author-X-Name-Last: Liu Author-Name: Ka-Fai Yiu Author-X-Name-First: Ka-Fai Author-X-Name-Last: Yiu Author-Name: Tak Siu Author-X-Name-First: Tak Author-X-Name-Last: Siu Author-Name: Wai-Ki Ching Author-X-Name-First: Wai-Ki Author-X-Name-Last: Ching Title: Optimal investment-reinsurance with dynamic risk constraint and regime switching Abstract: We study an optimal investment–reinsurance problem for an insurer who faces dynamic risk constraint in a Markovian regime-switching environment. The goal of the insurer is to maximize the expected utility of terminal wealth. Here the dynamic risk constraint is described by the maximal conditional Value at Risk over different economic states. The rationale is to provide a prudent investment–reinsurance strategy by taking into account the worst case scenario over different economic states. Using the dynamic programming approach, we obtain an analytical solution of the problem when the insurance business is modeled by either the classical Cramer–Lundberg model or its diffusion approximation. We document some important qualitative behaviors of the optimal investment–reinsurance strategies and investigate the impacts of switching regimes and risk constraint on the optimal strategies. Journal: Scandinavian Actuarial Journal Pages: 263-285 Issue: 4 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.602477 File-URL: http://hdl.handle.net/10.1080/03461238.2011.602477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:4:p:263-285 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_611893_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Jackknife empirical likelihood for parametric copulas Abstract: For fitting a parametric copula to multivariate data, a popular way is to employ the so-called pseudo maximum likelihood estimation proposed by Genest, Ghoudi, and Rivest. Although interval estimation can be obtained via estimating the asymptotic covariance of the pseudo maximum likelihood estimation, we propose a jackknife empirical likelihood method to construct confidence regions for the parameters without estimating any additional quantities such as the asymptotic covariance. A simulation study shows the advantages of the new method in case of strong dependence or having more than one parameter involved. Journal: Scandinavian Actuarial Journal Pages: 325-339 Issue: 5 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.611893 File-URL: http://hdl.handle.net/10.1080/03461238.2011.611893 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:5:p:325-339 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_618761_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lesław Gajek Author-X-Name-First: Lesław Author-X-Name-Last: Gajek Author-Name: Marcin Rudź Author-X-Name-First: Marcin Author-X-Name-Last: Rudź Title: Sharp approximations of ruin probabilities in the discrete time models Abstract: According to Solvency II directive, each insurance company could determine solvency capital requirements using its own, tailor made, internal model. This highlights the urgency of having fast numerical tools based on practically-oriented mathematical models. From the Solvency II perspective discrete time framework seems to be the most relevant one. In this paper, we propose a number of fast and accurate approximations of ruin probabilities involving some integral operator and examine them along strictly theoretical as well as numerical lines. For a few claim distributions the approximations are shown to be exact. In general, we prove that they converge with an exponential rate to the exact ruin probabilities without any restrictive assumptions on the claim distribution. A fast algorithm to approximate ruin probabilities by a numerical fixed point of the involved integral operator is given. As an application, ruin probabilities for, e.g. normally and Weibull – distributed claims are computed. Comparisons with discrete time counterparts of some continuous time approximation methods are also carried out. Numerical studies show that our approximations are precise both for small and large values of the initial surplus u. In contrast, the empirical De Vylder-type ones strongly depend on the claim distributions and are less precise for small and medium values of u. Journal: Scandinavian Actuarial Journal Pages: 352-382 Issue: 5 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.618761 File-URL: http://hdl.handle.net/10.1080/03461238.2011.618761 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:5:p:352-382 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_619271_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bojuan Zhao Author-X-Name-First: Bojuan Author-X-Name-Last: Zhao Author-Name: Xiangliang Liang Author-X-Name-First: Xiangliang Author-X-Name-Last: Liang Author-Name: Wenke Zhao Author-X-Name-First: Wenke Author-X-Name-Last: Zhao Author-Name: Delong Hou Author-X-Name-First: Delong Author-X-Name-Last: Hou Title: Modeling of group-specific mortality in China using a modified Lee–Carter model Abstract: The paper assesses sex-age-specific mortality rates of the four groups of people in China, the country, cities, towns, and counties, based on the mortality data from the China Population Statistics Yearbooks (1988–2009) using a newly proposed modified Lee–Carter model. The results show that in general, the expected age-specific mortality rates decrease over the years, and the decreasing speed increased in the past decade. During 2000–2008, the expected mortality rates decreased over the years for females of all ages and groups and males in cities, remained with no changes for males ages 13–36 in the country and towns, but increased for males ages 13–43 in counties. Predictions for 2009 are made based on the 2000–2008 data, and comparisons to the observed rates from an annual survey show that they match each other well except for males ages 13–43 in counties, whose mortality rates reached record highs around 2005, and bounced back to the level of 2000 in 2008 and was reduced a little further in 2009, benefiting from the promulgations and enforcements of some safety regulations by the government on construction and mining sites where most labors are from counties. The predicted age-specific mortality rates from the model are compared to the assumed rates in the China Life Insurance Mortality Table (2000–2003) promulgated by the China Insurance Regulatory Commission, and they show a great deal of similarity in terms of changing trends over the ages. Journal: Scandinavian Actuarial Journal Pages: 383-402 Issue: 5 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.619271 File-URL: http://hdl.handle.net/10.1080/03461238.2011.619271 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:5:p:383-402 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_618249_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Author-Name: Jyotirmoy Sarkar Author-X-Name-First: Jyotirmoy Author-X-Name-Last: Sarkar Title: Contingent means in multi-life models Abstract: Multi-life models are useful in actuarial science for studying life contingency. Contingent probabilities are well-understood by most actuaries and are discussed extensively in the existing actuarial literature. However, the mean of a life in a multi-life model involving order of deaths is often found to be rather challenging to interpret by most actuaries who do not understand measure-theoretic probability. Standard textbooks on actuarial science or statistics do not elaborate on the correct interpretation of contingent means, leaving the actuaries at risk of making a blunder. This paper presents the correct interpretation both heuristically and rigorously using a non-measure-theoretic language, so that actuaries will be aware of some common misconceptions and avoid pitfalls in their work. The primary audience of this paper is practicing actuaries, actuarial students and actuarial educators. So we have given several actuarial applications. We hope that applied statisticians also will find this paper useful. Journal: Scandinavian Actuarial Journal Pages: 340-351 Issue: 5 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.618249 File-URL: http://hdl.handle.net/10.1080/03461238.2011.618249 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:5:p:340-351 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_624194_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gordon Willmot Author-X-Name-First: Gordon Author-X-Name-Last: Willmot Title: On mixing, compounding, and tail properties of a class of claim number distributions Abstract: The mathematical structure underlying a class of discrete claim count distributions is examined in detail. In particular, the mixed Poisson nature of the class is shown to hold fairly generally. Using some ideas involving complete monotonicity, a discussion is provided on the structure of other class members which are well suited for use in aggregate claims analysis. The ideas are then extended to the analysis of the corresponding discrete tail probabilities, which arise in a variety of contexts including the analysis of the stop-loss premium. Journal: Scandinavian Actuarial Journal Pages: 403-423 Issue: 6 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.624194 File-URL: http://hdl.handle.net/10.1080/03461238.2011.624194 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:6:p:403-423 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_627745_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: C. Constantinescu Author-X-Name-First: C. Author-X-Name-Last: Constantinescu Author-Name: D. Kortschak Author-X-Name-First: D. Author-X-Name-Last: Kortschak Author-Name: V. Maume-Deschamps Author-X-Name-First: V. Author-X-Name-Last: Maume-Deschamps Title: Ruin probabilities in models with a Markov chain dependence structure Abstract: In this paper we derive explicit expressions for the probability of ruin in a renewal risk model with dependence among the increments (Zk)k>0. We study the case where the dependence structure among (Zk)k>0 is driven by a Markov chain with a transition kernel that can be described via ordinary differential equations with constant coefficients. Journal: Scandinavian Actuarial Journal Pages: 453-476 Issue: 6 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.627745 File-URL: http://hdl.handle.net/10.1080/03461238.2011.627745 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:6:p:453-476 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_624686_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Eric Cheung Author-X-Name-First: Eric Author-X-Name-Last: Cheung Author-Name: Stefan Thonhauser Author-X-Name-First: Stefan Author-X-Name-Last: Thonhauser Title: Randomized observation periods for the compound Poisson risk model: the discounted penalty function Abstract: In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities. Journal: Scandinavian Actuarial Journal Pages: 424-452 Issue: 6 Volume: 2013 Year: 2013 X-DOI: 10.1080/03461238.2011.624686 File-URL: http://hdl.handle.net/10.1080/03461238.2011.624686 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2013:y:2013:i:6:p:424-452 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_635803_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Catherine Donnelly Author-X-Name-First: Catherine Author-X-Name-Last: Donnelly Title: Quantifying mortality risk in small defined-benefit pension schemes Abstract: A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is, there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating significantly from the expected liability value, as compared to a large scheme. We quantify this risk through examining the coefficient of variation of a scheme's liability value relative to its expected value. We examine how the coefficient of variation varies with the number of members and find that, even with a few hundred members in the scheme, idiosyncratic mortality risk may still be significant. Next we quantify the amount of the mortality risk concentrated in the executive section of the scheme, where the executives receive a benefit that is higher than the non-executive benefit. We use the Euler capital allocation principle to allocate the total standard deviation of the liability value between the executive and non-executive sections. The results suggest that the mortality risk of the scheme should be monitored and managed within the sections of a scheme and not only on a scheme-wide basis. Journal: Scandinavian Actuarial Journal Pages: 41-57 Issue: 1 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.635803 File-URL: http://hdl.handle.net/10.1080/03461238.2011.635803 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:1:p:41-57 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_636502_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Clara-Cecilie Günther Author-X-Name-First: Clara-Cecilie Author-X-Name-Last: Günther Author-Name: Ingunn Tvete Author-X-Name-First: Ingunn Author-X-Name-Last: Tvete Author-Name: Kjersti Aas Author-X-Name-First: Kjersti Author-X-Name-Last: Aas Author-Name: Geir Sandnes Author-X-Name-First: Geir Author-X-Name-Last: Sandnes Author-Name: Ørnulf Borgan Author-X-Name-First: Ørnulf Author-X-Name-Last: Borgan Title: Modelling and predicting customer churn from an insurance company Abstract: Within a company's customer relationship management strategy, finding the customers most likely to leave is a central aspect. We present a dynamic modelling approach for predicting individual customers’ risk of leaving an insurance company. A logistic longitudinal regression model that incorporates time-dynamic explanatory variables and interactions is fitted to the data. As an intermediate step in the modelling procedure, we apply generalised additive models to identify non-linear relationships between the logit and the explanatory variables. Both out-of-sample and out-of-time prediction indicate that the model performs well in terms of identifying customers likely to leave the company each month. Our approach is general and may be applied to other industries as well. Journal: Scandinavian Actuarial Journal Pages: 58-71 Issue: 1 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.636502 File-URL: http://hdl.handle.net/10.1080/03461238.2011.636502 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:1:p:58-71 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_636880_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: K.C. Cheung Author-X-Name-First: K.C. Author-X-Name-Last: Cheung Author-Name: K.C.J. Sung Author-X-Name-First: K.C.J. Author-X-Name-Last: Sung Author-Name: S.C.P. Yam Author-X-Name-First: S.C.P. Author-X-Name-Last: Yam Author-Name: S.P. Yung Author-X-Name-First: S.P. Author-X-Name-Last: Yung Title: Optimal reinsurance under general law-invariant risk measures Abstract: In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided. Journal: Scandinavian Actuarial Journal Pages: 72-91 Issue: 1 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.636880 File-URL: http://hdl.handle.net/10.1080/03461238.2011.636880 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:1:p:72-91 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_628408_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fredrik Armerin Author-X-Name-First: Fredrik Author-X-Name-Last: Armerin Title: An axiomatic approach to the valuation of cash flows Abstract: We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options. Journal: Scandinavian Actuarial Journal Pages: 32-40 Issue: 1 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.628408 File-URL: http://hdl.handle.net/10.1080/03461238.2011.628408 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:1:p:32-40 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_627747_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alexey Kuznetsov Author-X-Name-First: Alexey Author-X-Name-Last: Kuznetsov Author-Name: Manuel Morales Author-X-Name-First: Manuel Author-X-Name-Last: Morales Title: Computing the finite-time expected discounted penalty function for a family of Lévy risk processes Abstract: Ever since the first introduction of the expected discounted penalty function (EDPF), it has been widely acknowledged that it contains information that is relevant from a risk management perspective. Expressions for the EDPF are now available for a wide range of models, in particular for a general class of Lévy risk processes. Yet, in order to capitalize on this potential for applications, these expressions must be computationally tractable enough as to allow for the evaluation of associated risk measures such as Value at Risk (VaR) or Conditional Value at Risk (CVaR). Most of the models studied so far offer few interesting examples for which computation of the associated EDPF can be carried out to the last instances where evaluation of risk measures is possible. Another drawback of existing examples is that the expressions are available for an infinite-time horizon EDPF only. Yet, realistic applications would require the computation of an EDPF over a finite-time horizon. In this paper we address these two issues by studying examples of risk processes for which numerical evaluation of the EDPF can be readily implemented. These examples are based on the recently introduced meromorphic processes, including the beta and theta families of Lévy processes, whose construction is tailor-made for computational ease. We provide expressions for the EDPF associated with these processes and we discuss in detail how a finite-time horizon EDPF can be computed for these families. We also provide numerical examples for different choices of parameters in order to illustrate how ruin-based risk measures can be computed for these families of Lévy risk processes. Journal: Scandinavian Actuarial Journal Pages: 1-31 Issue: 1 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.627747 File-URL: http://hdl.handle.net/10.1080/03461238.2011.627747 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:1:p:1-31 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_663730_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stathis Chadjiconstantinidis Author-X-Name-First: Stathis Author-X-Name-Last: Chadjiconstantinidis Author-Name: Spyridon Vrontos Author-X-Name-First: Spyridon Author-X-Name-Last: Vrontos Title: On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula Abstract: In this article, we consider an extension to the renewal or Sparre Andersen risk process by introducing a dependence structure between the claim sizes and the interclaim times through a Farlie–Gumbel–Morgenstern copula proposed by Cossette et al. (2010) for the classical compound Poisson risk model. We consider that the inter-arrival times follow the Erlang(n) distribution. By studying the roots of the generalised Lundberg equation, the Laplace transform (LT) of the expected discounted penalty function is derived and a detailed analysis of the Gerber–Shiu function is given when the initial surplus is zero. It is proved that this function satisfies a defective renewal equation and its solution is given through the compound geometric tail representation of the LT of the time to ruin. Explicit expressions for the discounted joint and marginal distribution functions of the surplus prior to the time of ruin and the deficit at the time of ruin are derived. Finally, for exponential claim sizes explicit expressions and numerical examples for the ruin probability and the LT of the time to ruin are given. Journal: Scandinavian Actuarial Journal Pages: 125-158 Issue: 2 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.663730 File-URL: http://hdl.handle.net/10.1080/03461238.2012.663730 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:2:p:125-158 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_647061_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sung Chiu Author-X-Name-First: Sung Author-X-Name-Last: Chiu Author-Name: Chuancun Yin Author-X-Name-First: Chuancun Author-X-Name-Last: Yin Title: On the complete monotonicity of the compound geometric convolution with applications in risk theory Abstract: We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density. Journal: Scandinavian Actuarial Journal Pages: 116-124 Issue: 2 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.647061 File-URL: http://hdl.handle.net/10.1080/03461238.2011.647061 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:2:p:116-124 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_695748_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: S. Nadarajah Author-X-Name-First: S. Author-X-Name-Last: Nadarajah Author-Name: S.A.A. Bakar Author-X-Name-First: S.A.A. Author-X-Name-Last: Bakar Title: New composite models for the Danish fire insurance data Abstract: In recent years, several composite models based on the lognormal distribution have been developed for the Danish fire insurance data. In this note, we propose new composite models based on the lognormal distribution. At least one of the newly proposed models is shown to give a better fit to the Danish fire insurance data. Journal: Scandinavian Actuarial Journal Pages: 180-187 Issue: 2 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.695748 File-URL: http://hdl.handle.net/10.1080/03461238.2012.695748 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:2:p:180-187 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_670611_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peng Shi Author-X-Name-First: Peng Author-X-Name-Last: Shi Author-Name: Emiliano Valdez Author-X-Name-First: Emiliano Author-X-Name-Last: Valdez Title: Longitudinal modeling of insurance claim counts using jitters Abstract: Modeling insurance claim counts is a critical component in the ratemaking process for property and casualty insurance. This article explores the usefulness of copulas to model the number of insurance claims for an individual policyholder within a longitudinal context. To address the limitations of copulas commonly attributed to multivariate discrete data, we adopt a ‘jittering’ method to the claim counts which has the effect of continuitizing the data. Elliptical copulas are proposed to accommodate the intertemporal nature of the ‘jittered’ claim counts and the unobservable subject-specific heterogeneity on the frequency of claims. Observable subject-specific effects are accounted in the model by using available covariate information through a regression model. The predictive distribution together with the corresponding credibility of claim frequency can be derived from the model for ratemaking and risk classification purposes. For empirical illustration, we analyze an unbalanced longitudinal dataset of claim counts observed from a portfolio of automobile insurance policies of a general insurer in Singapore. We further establish the validity of the calibrated copula model, and demonstrate that the copula with ‘jittering’ method outperforms standard count regression models. Journal: Scandinavian Actuarial Journal Pages: 159-179 Issue: 2 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.670611 File-URL: http://hdl.handle.net/10.1080/03461238.2012.670611 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:2:p:159-179 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_636969_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lothar Breuer Author-X-Name-First: Lothar Author-X-Name-Last: Breuer Author-Name: Andrei Badescu Author-X-Name-First: Andrei Author-X-Name-Last: Badescu Title: A generalised Gerber–Shiu measure for Markov-additive risk processes with phase-type claims and capital injections Abstract: In this paper we consider a risk reserve process where the arrivals (either claims or capital injections) occur according to a Markovian point process. Both claim and capital injection sizes are phase-type distributed and the model allows for possible correlations between these and the inter-claim times. The premium income is modelled by a Markov-modulated Brownian motion which may depend on the underlying phases of the point arrival process. For this risk reserve model we derive a generalised Gerber–Shiu measure that is the joint distribution of the time to ruin, the surplus immediately before ruin, the deficit at ruin, the minimal risk reserve before ruin, and the time until this minimum is attained. Numeral examples illustrate the influence of the parameters on selected marginal distributions. Journal: Scandinavian Actuarial Journal Pages: 93-115 Issue: 2 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2011.636969 File-URL: http://hdl.handle.net/10.1080/03461238.2011.636969 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:2:p:93-115 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_683450_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jörn Sass Author-X-Name-First: Jörn Author-X-Name-Last: Sass Author-Name: Frank Seifried Author-X-Name-First: Frank Author-X-Name-Last: Seifried Title: Insurance markets and unisex tariffs: is the European Court of Justice improving or destroying welfare? Abstract: We analyze the effects of mandatory unisex tariffs in insurance contracts, such as those required by a recent ruling of the European Court of Justice, on equilibrium insurance premia and equilibrium welfare. In a unified framework, we provide a quantitative analysis of the associated insurance market equilibria in both monopolistic and competitive insurance markets. We investigate the welfare loss caused by regulatory adverse selection and show that unisex tariffs may cause market distortions that significantly reduce overall social welfare. Journal: Scandinavian Actuarial Journal Pages: 228-254 Issue: 3 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.683450 File-URL: http://hdl.handle.net/10.1080/03461238.2012.683450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:3:p:228-254 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_687697_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Adam Lenart Author-X-Name-First: Adam Author-X-Name-Last: Lenart Title: The moments of the Gompertz distribution and maximum likelihood estimation of its parameters Abstract: The Gompertz distribution is widely used to describe the distribution of adult deaths. Previous works concentrated on formulating approximate relationships to characterise it. However, using the generalised integro-exponential function, exact formulas can be derived for its moment-generating function and central moments. Based on the exact central moments, higher accuracy approximations can be defined for them. In demographic or actuarial applications, maximum likelihood estimation is often used to determine the parameters of the Gompertz distribution. By solving the maximum likelihood estimates analytically, the dimension of the optimisation problem can be reduced to one both in the case of discrete and continuous data. Monte Carlo experiments show that by ML estimation, higher accuracy estimates can be acquired than by the method of moments. Journal: Scandinavian Actuarial Journal Pages: 255-277 Issue: 3 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.687697 File-URL: http://hdl.handle.net/10.1080/03461238.2012.687697 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:3:p:255-277 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_732956_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Scollnik Author-X-Name-First: David Author-X-Name-Last: Scollnik Title: Regarding folded models and the paper by Brazauskas and Kleefeld (2011) Journal: Scandinavian Actuarial Journal Pages: 278-281 Issue: 3 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.732956 File-URL: http://hdl.handle.net/10.1080/03461238.2012.732956 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:3:p:278-281 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_760254_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jinxia Zhu Author-X-Name-First: Jinxia Author-X-Name-Last: Zhu Title: Errata for ‘Optimal dividend control for a generalized risk model with investment incomes and debit interest’ online version Journal: Scandinavian Actuarial Journal Pages: 282-282 Issue: 3 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.760254 File-URL: http://hdl.handle.net/10.1080/03461238.2012.760254 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:3:p:282-282 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_676563_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Daniel Alai Author-X-Name-First: Daniel Author-X-Name-Last: Alai Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Rethinking age-period-cohort mortality trend models Abstract: Longevity risk arising from uncertain mortality improvement is one of the major risks facing annuity providers and pension funds. In this article, we show how applying trend models from non-life claims reserving to age-period-cohort mortality trends provides new insight in estimating mortality improvement and quantifying its uncertainty. Age, period and cohort trends are modelled with distinct effects for each age, calendar year and birth year in a generalised linear models framework. The effects are distinct in the sense that they are not conjoined with age coefficients, borrowing from regression terminology, we denote them as main effects. Mortality models in this framework for age-period, age-cohort and age-period-cohort effects are assessed using national population mortality data from Norway and Australia to show the relative significance of cohort effects as compared to period effects. Results are compared with the traditional Lee–Carter model. The bilinear period effect in the Lee–Carter model is shown to resemble a main cohort effect in these trend models. However, the approach avoids the limitations of the Lee–Carter model when forecasting with the age-cohort trend model. Journal: Scandinavian Actuarial Journal Pages: 208-227 Issue: 3 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.676563 File-URL: http://hdl.handle.net/10.1080/03461238.2012.676563 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:3:p:208-227 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_676562_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mark Bebbington Author-X-Name-First: Mark Author-X-Name-Last: Bebbington Author-Name: Rebecca Green Author-X-Name-First: Rebecca Author-X-Name-Last: Green 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: Beyond the Gompertz law: exploring the late-life mortality deceleration phenomenon Abstract: Using a new distribution capable of exhibiting all the possible modes of accelerating and decelerating mortality, we conduct a systematic investigation of late-life mortality in humans. We check the insensitivity of the distribution to age cutoffs in the data relative to the logistic mortality model and propose a method to forecast evolution in the characteristic deceleration ages of the distribution. A number of data sets have been explored, with a particular emphasis on those originating from Scandinavia. Although those from Australia, Canada, and the USA are compatible with Gompertzian mortality, those from the other countries examined are not. We find in particular that the onset of mortality deceleration is being progressively delayed in Western societies but that there is evidence of mortality plateauing at earlier ages. Journal: Scandinavian Actuarial Journal Pages: 189-207 Issue: 3 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.676562 File-URL: http://hdl.handle.net/10.1080/03461238.2012.676562 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:3:p:189-207 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_690247_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Esterina Masiello Author-X-Name-First: Esterina Author-X-Name-Last: Masiello Title: On semiparametric estimation of ruin probabilities in the classical risk model Abstract: The ruin probability of an insurance company is a central topic in risk theory. We consider the classical Poisson risk model when the claim size distribution and the Poisson arrival rate are unknown. Given a sample of inter-arrival times and corresponding claims, we propose a semiparametric estimator of the ruin probability. We establish properties of strong consistency and asymptotic normality of the estimator and study bootstrap confidence bands. Further, we present a simulation example in order to investigate the finite sample properties of the proposed estimator. Journal: Scandinavian Actuarial Journal Pages: 283-308 Issue: 4 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.690247 File-URL: http://hdl.handle.net/10.1080/03461238.2012.690247 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:4:p:283-308 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_693457_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Adamic Author-X-Name-First: Peter Author-X-Name-Last: Adamic Author-Name: Sylvain Caron Author-X-Name-First: Sylvain Author-X-Name-Last: Caron Title: SC-CR Algorithms with informative masking Abstract: In this article, we present a significant improvement to the Self-Consistent, Competing Risks (SC-CR) Algorithms that have been published in the actuarial literature over the last several years. These algorithms were fairly flexible, admitting of any combination of partially masked risks and interval-censored failure times. However, we wish to show here that the SC-CR Algorithm can be further generalized to allow for each specific decrement to have its own distinct interval-censored range for any given individual observation. We have chosen to refer to this dynamic as ‘informative masking’ since additional information regarding the masking sets will be allowed to be incorporated. The enhancements will be applied to both the double-censored as well as interval-censored SC-CR Algorithms. Numerical examples that illustrate the usefulness of these enhancements will also be furnished. Journal: Scandinavian Actuarial Journal Pages: 339-351 Issue: 4 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.693457 File-URL: http://hdl.handle.net/10.1080/03461238.2012.693457 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:4:p:339-351 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_695747_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Erland Ekheden Author-X-Name-First: Erland Author-X-Name-Last: Ekheden Author-Name: Ola Hössjer Author-X-Name-First: Ola Author-X-Name-Last: Hössjer Title: Pricing catastrophe risk in life (re)insurance Abstract: What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson process of catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled, listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price. Journal: Scandinavian Actuarial Journal Pages: 352-367 Issue: 4 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.695747 File-URL: http://hdl.handle.net/10.1080/03461238.2012.695747 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:4:p:352-367 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_691427_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Author-Name: Hu Yang Author-X-Name-First: Hu Author-X-Name-Last: Yang Title: On a nonparametric estimator for ruin probability in the classical risk model Abstract: In this paper, we present a nonparametric estimator for ruin probability in the classical risk model with unknown claim size distribution. We construct the estimator by Fourier inversion and kernel density estimation method. Under some conditions imposed on the kernel, bandwidth and claim size density, we present some large sample properties of the estimator. Some simulation studies are also given to show the finite sample performance of the estimator. Journal: Scandinavian Actuarial Journal Pages: 309-338 Issue: 4 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.691427 File-URL: http://hdl.handle.net/10.1080/03461238.2012.691427 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:4:p:309-338 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_723043_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Title: First passage time for compound Poisson processes with diffusion: ruin theoretical and financial applications Abstract: In this paper, we propose to revisit Kendall’s identity (see, e.g. Kendall (1957)) related to the distribution of the first passage time for spectrally negative Lévy processes. We provide an alternative proof to Kendall’s identity for a given class of spectrally negative Lévy processes, namely compound Poisson processes with diffusion, through the application of Lagrange’s expansion theorem. This alternative proof naturally leads to an extension of this well-known identity by further examining the distribution of the number of jumps before the first passage time. In the process, we generalize some results of Gerber (1990) to the class of compound Poisson processes perturbed by diffusion. We show that this main result is particularly relevant to further our understanding of some problems of interest in actuarial science. Among others, we propose to examine the finite-time ruin probability of a dual Poisson risk model with diffusion or equally the distribution of a busy period in a specific fluid flow model. In a second example, we make use of this result to price barrier options issued on an insurer’s stock price. Journal: Scandinavian Actuarial Journal Pages: 368-382 Issue: 4 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.723043 File-URL: http://hdl.handle.net/10.1080/03461238.2012.723043 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:4:p:368-382 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_723638_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yichun Chi Author-X-Name-First: Yichun Author-X-Name-Last: Chi Author-Name: Hui Meng Author-X-Name-First: Hui Author-X-Name-Last: Meng Title: Optimal reinsurance arrangements in the presence of two reinsurers Abstract: In this paper, we investigate the optimal form of reinsurance from the perspective of an insurer when he decides to cede part of the loss to two reinsurers, where the first reinsurer calculates the premium by expected value principle while the premium principle adopted by the second reinsurer satisfies three axioms: distribution invariance, risk loading, and preserving stop-loss order. In order to exclude the moral hazard, a typical reinsurance treaty assumes that both the insurer and reinsurers are obligated to pay more for the larger loss. Under the criterion of minimizing value at risk (VaR) or conditional value at risk (CVaR) of the insurer's total risk exposure, we show that an optimal reinsurance policy is to cede two adjacent layers, where the upper layer is distributed to the first reinsurer. To further illustrate the applicability of our results, we derive explicitly the optimal layer reinsurance by assuming a generalized Wang's premium principle to the second reinsurer. Journal: Scandinavian Actuarial Journal Pages: 424-438 Issue: 5 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.723638 File-URL: http://hdl.handle.net/10.1080/03461238.2012.723638 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:5:p:424-438 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_699001_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tatiana Belkina Author-X-Name-First: Tatiana Author-X-Name-Last: Belkina Author-Name: Christian Hipp Author-X-Name-First: Christian Author-X-Name-Last: Hipp Author-Name: Shangzhen Luo Author-X-Name-First: Shangzhen Author-X-Name-Last: Luo Author-Name: Michael Taksar Author-X-Name-First: Michael Author-X-Name-Last: Taksar Title: Optimal constrained investment in the Cramer-Lundberg model Abstract: We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk-free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when short-selling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to find an optimal investment policy that minimizes the probability of ruin. The minimal ruin probability as a function of the initial surplus is characterized by a classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We study the optimal control policy and its properties. The interrelation between the parameters of the model plays a crucial role in the qualitative behavior of the optimal policy. For example, for some ratios between a and b, quite unusual and at first ostensibly counterintuitive policies may appear, like short-selling a stock with a higher rate of return to earn lower interest, or borrowing at a higher rate to invest in a stock with lower rate of return. This is in sharp contrast with the unrestricted case, first studied in Hipp and Plum, or with the case of no short-selling and no borrowing studied in Azcue and Muler. Journal: Scandinavian Actuarial Journal Pages: 383-404 Issue: 5 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.699001 File-URL: http://hdl.handle.net/10.1080/03461238.2012.699001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:5:p:383-404 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_728537_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Erengul Ozkok Author-X-Name-First: Erengul Author-X-Name-Last: Ozkok Author-Name: George Streftaris Author-X-Name-First: George Author-X-Name-Last: Streftaris Author-Name: Howard Waters Author-X-Name-First: Howard Author-X-Name-Last: Waters Author-Name: A. David Wilkie Author-X-Name-First: A. David Author-X-Name-Last: Wilkie Title: Modelling critical illness claim diagnosis rates I: methodology Abstract: In a series of two papers, this paper and the one by Ozkok et al. (Modelling critical illness claim diagnosis rates II: results), we develop statistical models to be used as a framework for estimating, and graduating, Critical Illness (CI) insurance diagnosis rates. We use UK data for 1999–2005 supplied by the Continuous Mortality Investigation (CMI) to illustrate their use. In this paper, we set out the basic methodology. In particular, we set out some models, we describe the data available to us and we discuss the statistical distribution of estimators proposed for CI diagnosis inception rates. A feature of CI insurance is the delay, on average about 6 months but in some cases much longer, between the diagnosis of an illness and the settlement of the subsequent claim. Modelling this delay, the so-called Claim Delay Distribution, is a necessary first step in the estimation of the claim diagnosis rates and this is discussed in the present paper. In the subsequent paper, we derive and discuss diagnosis rates for CI claims from ‘all causes’ and also from specific causes. Journal: Scandinavian Actuarial Journal Pages: 439-457 Issue: 5 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.728537 File-URL: http://hdl.handle.net/10.1080/03461238.2012.728537 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:5:p:439-457 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_728538_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: E. Ozkok Author-X-Name-First: E. Author-X-Name-Last: Ozkok Author-Name: G. Streftaris Author-X-Name-First: G. Author-X-Name-Last: Streftaris Author-Name: H.R. Waters Author-X-Name-First: H.R. Author-X-Name-Last: Waters Author-Name: A.D. Wilkie Author-X-Name-First: A.D. Author-X-Name-Last: Wilkie Title: Modelling critical illness claim diagnosis rates II: results Abstract: This is Paper II in a series of two papers. In Paper I we developed a methodology for estimating and graduating Critical Illness (CI) insurance diagnosis rates. In this paper we use data from the UK for 1999–2005 supplied by the Continuous Mortality Investigation (CMI) to illustrate our methodology by deriving and discussing all causes and cause specific critical illness diagnosis rates. Journal: Scandinavian Actuarial Journal Pages: 458-482 Issue: 5 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.728538 File-URL: http://hdl.handle.net/10.1080/03461238.2012.728538 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:5:p:458-482 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_723044_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Wing Yan Lee Author-X-Name-First: Wing Yan Author-X-Name-Last: Lee Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Author-Name: Jae-Kyung Woo Author-X-Name-First: Jae-Kyung Author-X-Name-Last: Woo Title: A note on deficit analysis in dependency models involving Coxian claim amounts Abstract: In this paper, we consider a fairly large class of dependent Sparre Andersen risk models where the claim sizes belong to the class of Coxian distributions. We analyze the Gerber–Shiu discounted penalty function when the penalty function depends on the deficit at ruin. We show that the system of equations needed to solve for this quantity is surprisingly simple. Various applications of this result are also considered. Journal: Scandinavian Actuarial Journal Pages: 405-423 Issue: 5 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.723044 File-URL: http://hdl.handle.net/10.1080/03461238.2012.723044 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:5:p:405-423 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_745448_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Haluk Yener Author-X-Name-First: Haluk Author-X-Name-Last: Yener Title: Minimizing the lifetime ruin under borrowing and short-selling constraints Abstract: In this paper, the optimal investment strategies for minimizing the probability of lifetime ruin under borrowing and short-selling constraints are found. The investment portfolio consists of multiple risky investments and a riskless investment. The investor withdraws money from the portfolio at a constant rate proportional to the portfolio value. In order to find the results, an auxiliary market is constructed, and the techniques of stochastic optimal control are used. Via this method, we show how the application of stochastic optimal control is possible for minimizing the probability of lifetime ruin problem defined under an auxiliary market. Journal: Scandinavian Actuarial Journal Pages: 535-560 Issue: 6 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.745448 File-URL: http://hdl.handle.net/10.1080/03461238.2012.745448 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:6:p:535-560 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_724442_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Helena Aro Author-X-Name-First: Helena Author-X-Name-Last: Aro Author-Name: Teemu Pennanen Author-X-Name-First: Teemu Author-X-Name-Last: Pennanen Title: Stochastic modelling of mortality and financial markets Abstract: The uncertain future development of mortality and financial markets affects every life insurer. In particular, the joint distribution of mortality and investment returns is crucial in determining capital requirements as well as in pricing and hedging of mortality-linked securities and other life insurance products. This paper proposes simple stochastic models that are well suited for numerical analysis of mortality-linked cash flows. The models are calibrated with a data set covering six countries and 56 years. Statistical analysis supports the known dependence of old-age mortality on GDP which, in turn, is connected to many sectors of financial markets. Our models allow for a simple quantitative description of such connections. Particular attention is paid to the long-term development of mortality rates, which is an important issue in life insurance. Journal: Scandinavian Actuarial Journal Pages: 483-509 Issue: 6 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.724442 File-URL: http://hdl.handle.net/10.1080/03461238.2012.724442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:6:p:483-509 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_729154_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: E. Vatamidou Author-X-Name-First: E. Author-X-Name-Last: Vatamidou Author-Name: I.J.B.F. Adan Author-X-Name-First: I.J.B.F. Author-X-Name-Last: Adan Author-Name: M. Vlasiou Author-X-Name-First: M. Author-X-Name-Last: Vlasiou Author-Name: B. Zwart Author-X-Name-First: B. Author-X-Name-Last: Zwart Title: On the accuracy of phase-type approximations of heavy-tailed risk models Abstract: Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations. Journal: Scandinavian Actuarial Journal Pages: 510-534 Issue: 6 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.729154 File-URL: http://hdl.handle.net/10.1080/03461238.2012.729154 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:6:p:510-534 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_749508_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sebastian Fuchs Author-X-Name-First: Sebastian Author-X-Name-Last: Fuchs Title: Consistent loss prediction for a portfolio and its subportfolios Abstract: In the present paper, we consider a portfolio of risks consisting of two subportfolios, and we study the problem of whether or not the predictors based on the subportfolios are consistent with those based on the full portfolio. We study this aggregation problem for both the chain-ladder method and the additive method (or incremental loss ratio method). In the case of the chain-ladder method we extend results of Ajne and Klemmt, using the duality of the chain-ladder method applied to incremental losses; we also give a short proof for this duality, which was first observed by Barnett, Zehnwirth & Dubossarky. In the case of the additive method the aggregation problem has not been studied before and its solution is surprisingly simple. Journal: Scandinavian Actuarial Journal Pages: 561-581 Issue: 6 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.749508 File-URL: http://hdl.handle.net/10.1080/03461238.2012.749508 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:6:p:561-581 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_750621_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jingzhen Liu Author-X-Name-First: Jingzhen Author-X-Name-Last: Liu Author-Name: Ka-Fai Cedric Yiu Author-X-Name-First: Ka-Fai Cedric Author-X-Name-Last: Yiu Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Title: Optimal investment of an insurer with regime-switching and risk constraint Abstract: We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly. Journal: Scandinavian Actuarial Journal Pages: 583-601 Issue: 7 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.750621 File-URL: http://hdl.handle.net/10.1080/03461238.2012.750621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:7:p:583-601 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_755938_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Author-Name: Richard Plat Author-X-Name-First: Richard Author-X-Name-Last: Plat Title: Micro-level stochastic loss reserving for general insurance Abstract: The vast literature on stochastic loss reserving concentrates on data aggregated in run-off triangles. However, a triangle is a summary of an underlying data-set with the development of individual claims. We refer to this data-set as ‘micro-level’ data. Using the framework of Position Dependent Marked Poisson Processes) and statistical tools for recurrent events, a data-set is analyzed with liability claims from a European insurance company. We use detailed information of the time of occurrence of the claim, the delay between occurrence and reporting to the insurance company, the occurrences of payments and their sizes, and the final settlement. Our specifications are (semi)parametric and our approach is likelihood based. We calibrate our model to historical data and use it to project the future development of open claims. An out-of-sample prediction exercise shows that we obtain detailed and valuable reserve calculations. For the case study developed in this paper, the micro-level model outperforms the results obtained with traditional loss reserving methods for aggregate data. Journal: Scandinavian Actuarial Journal Pages: 649-669 Issue: 7 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.755938 File-URL: http://hdl.handle.net/10.1080/03461238.2012.755938 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:7:p:649-669 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_755937_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yasutaka Shimizu Author-X-Name-First: Yasutaka Author-X-Name-Last: Shimizu Title: Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics Abstract: This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes. Journal: Scandinavian Actuarial Journal Pages: 620-648 Issue: 7 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.755937 File-URL: http://hdl.handle.net/10.1080/03461238.2012.755937 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:7:p:620-648 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_751674_O.xml processed with: repec_from_tfja.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: E. Gómez-Déniz Author-X-Name-First: E. Author-X-Name-Last: Gómez-Déniz Author-Name: E. Calderín-Ojeda Author-X-Name-First: E. Author-X-Name-Last: Calderín-Ojeda Title: Unconditional distributions obtained from conditional specification models with applications in risk theory Abstract: Bivariate distributions, specified in terms of their conditional distributions, provide a powerful tool to obtain flexible distributions. These distributions play an important role in specifying the conjugate prior in certain multi-parameter Bayesian settings. In this paper, the conditional specification technique is applied to look for more flexible distributions than the traditional ones used in the actuarial literature, as the Poisson, negative binomial and others. The new specification draws inferences about parameters of interest in problems appearing in actuarial statistics. Two unconditional (discrete) distributions obtained are studied and used in the collective risk model to compute the right-tail probability of the aggregate claim size distribution. Comparisons with the compound Poisson and compound negative binomial are made. Journal: Scandinavian Actuarial Journal Pages: 602-619 Issue: 7 Volume: 2014 Year: 2014 X-DOI: 10.1080/03461238.2012.751674 File-URL: http://hdl.handle.net/10.1080/03461238.2012.751674 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:7:p:602-619 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_756829_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Julia Eisenberg Author-X-Name-First: Julia Author-X-Name-Last: Eisenberg Title: Asymptotic optimal investment under interest rate for a class of subexponential distributions Abstract: We consider a classical risk model with the possibility of investment and positive interest rate for the riskless bond. The stock price movement is modelled as a geometric Brownian motion, the claim sizes are assumed to have a distribution belonging to a certain subclass of subexponential distributions. In this setting, we study the asymptotic behaviour of the optimal investment strategy under the ruin probability as a risk measure. This problem has been already considered before, but no results were obtained, for instance, for Weibull and Benktander-type-II distributions with certain parameters. We introduce a method which closes this gap. Journal: Scandinavian Actuarial Journal Pages: 671-689 Issue: 8 Volume: 2014 Year: 2014 Month: 11 X-DOI: 10.1080/03461238.2012.756829 File-URL: http://hdl.handle.net/10.1080/03461238.2012.756829 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:8:p:671-689 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_760885_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stig Rosenlund Author-X-Name-First: Stig Author-X-Name-Last: Rosenlund Title: Inference in multiplicative pricing Abstract: In multiplicative pricing of non-life insurance, we report a simulation study of mean square errors (MSEs) of point estimates by (1) the marginal totals method and (2) the Standard Generalized Linear Model (GLM) method of Poisson claim numbers and gamma distributed claim severities with constant coefficient of variation. MSEs per tariff cell are summed with insurance exposures as weights to give a total MSE. This is smallest for Standard GLM under the multiplicative assumption. But with moderate deviations from parameter multiplicativity, the study indicates that the marginal totals method is typically better in the MSE sense when there are many arguments and many claims, i.e. for mass consumer insurance. A method called MVW for confidence intervals, using only the compound Poisson model, is given for the marginal totals method. These confidence intervals are compared with the ones of Standard GLM and the Tweedie method for risk premiums in a simulation study and are found to be mostly the best. The study reports both cover probabilities, which should be close to 0.95 for 95% confidence intervals, and interval lengths, which should be small. The Tweedie method is found to be never better than Standard GLM. Journal: Scandinavian Actuarial Journal Pages: 690-713 Issue: 8 Volume: 2014 Year: 2014 Month: 11 X-DOI: 10.1080/03461238.2012.760885 File-URL: http://hdl.handle.net/10.1080/03461238.2012.760885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:8:p:690-713 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_761645_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Amin Hassan Zadeh Author-X-Name-First: Amin Author-X-Name-Last: Hassan Zadeh Author-Name: Bruce L. Jones Author-X-Name-First: Bruce L. Author-X-Name-Last: Jones Author-Name: David A. Stanford Author-X-Name-First: David A. Author-X-Name-Last: Stanford Title: The use of phase-type models for disability insurance calculations Abstract: This paper explores the use of phase-type models in actuarial calculations for disability insurance. We demonstrate that the changes in status of disability insureds can be appropriately captured by a phase-type model. Our model represents the aging process as the passage through a number of phases of decreasing vitality. When disabled, individuals additionally pass through several stages that represent duration of disability. Recovery and mortality rates from the earlier stages are greater than those in later stages. Using such a model, explicit and easily calculable expressions are obtained for relevant probabilities and actuarial present values. This facilitates the calculation of premiums and reserves. Journal: Scandinavian Actuarial Journal Pages: 714-728 Issue: 8 Volume: 2014 Year: 2014 Month: 11 X-DOI: 10.1080/03461238.2012.761645 File-URL: http://hdl.handle.net/10.1080/03461238.2012.761645 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:8:p:714-728 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_762548_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tao Jin Author-X-Name-First: Tao Author-X-Name-Last: Jin Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: Recursions and fast Fourier transforms for a new bivariate aggregate claims model Abstract: Insurance companies typically face multiple sources (types) of claims. Therefore, modelling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In this paper, we first introduce a multivariate aggregate claims model, which allows dependencies among claim numbers as well as dependencies among claim sizes. For this proposed model, we derive recursive formulas for the joint probability functions of different types of claims. In addition, we extend the concept of exponential tilting to the multivariate fast Fourier transform and use it to compute the joint probability functions of the various types of claims. We provide numerical examples to compare the accuracy and efficiency of the two computation methods. Journal: Scandinavian Actuarial Journal Pages: 729-752 Issue: 8 Volume: 2014 Year: 2014 Month: 11 X-DOI: 10.1080/03461238.2012.762548 File-URL: http://hdl.handle.net/10.1080/03461238.2012.762548 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:8:p:729-752 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_798070_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Authors’ Reply to ‘Letter to the Editor regarding folded models and the paper by Brazauskas and Kleefeld (2011)’ Journal: Scandinavian Actuarial Journal Pages: 753-757 Issue: 8 Volume: 2014 Year: 2014 Month: 11 X-DOI: 10.1080/03461238.2013.798070 File-URL: http://hdl.handle.net/10.1080/03461238.2013.798070 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2014:y:2014:i:8:p:753-757 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_773938_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Muneya Matsui Author-X-Name-First: Muneya Author-X-Name-Last: Matsui Title: Prediction in a Poisson cluster model with multiple cluster processes Abstract: We consider a simple but flexible extension of the Poisson cluster model studied in Matsui & Mikosch (2010). In the former, model only a single cluster process starts at each jump point of the Poisson process, whereas we start a randomly given number of cluster processes at each jump. This simple extension yields additional mathematical problems in prediction of future increments of the process which are based on the past observations. However, by making full use of the Poisson structure of the model, we derive reasonably explicit expressions for predictors, which is of critical importance in the insurance application. Some comparisons of predictors are also made by their mean-squared errors when the cluster process is a compound Poisson process. The result yields a natural conclusion that the finer information we use, the better predictors we obtain. Journal: Scandinavian Actuarial Journal Pages: 1-31 Issue: 1 Volume: 2015 Year: 2015 Month: 1 X-DOI: 10.1080/03461238.2013.773938 File-URL: http://hdl.handle.net/10.1080/03461238.2013.773938 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:1:p:1-31 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_774112_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Agnieszka I. Bergel Author-X-Name-First: Agnieszka I. Author-X-Name-Last: Bergel Author-Name: Alfredo D. Egídio Dos Reis Author-X-Name-First: Alfredo D. Author-X-Name-Last: Egídio Dos Reis Title: Further developments in the Erlang(n) risk process Abstract: For actuarial aplications, we consider the Sparre–Andersen risk model when the interclaim times are Erlang(n) distributed. We first address the problem of solving an integro-differential equation that is satisfied by the survival probability and other probabilities, and show an alternative and improved method to solve such equations to that presented by Li (2008).This is done by considering the roots with positive real parts of the generalized Lundberg’s equation, and establishing a one–one relation between them and the solutions of the integro-differential equation mentioned before.Afterwards, we apply our findings above in the computation of the distribution of the maximum severity of ruin. This computation depends on the non-ruin probability and on the roots of the fundamental Lundberg’s equation.We illustrate and give explicit formulae for Erlang(3) interclaim arrivals with exponentially distributed single claim amounts and Erlang(2) interclaim times with Erlang(2) claim amounts.Finally, considering an interest force, we consider the problem of calculating the expected discounted dividends prior to ruin, finding an integro-differential equation that they satisfy and solving it. Numerical examples are also provided for illustration. Journal: Scandinavian Actuarial Journal Pages: 32-48 Issue: 1 Volume: 2015 Year: 2015 Month: 1 X-DOI: 10.1080/03461238.2013.774112 File-URL: http://hdl.handle.net/10.1080/03461238.2013.774112 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:1:p:32-48 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_775665_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jelena Kočović Author-X-Name-First: Jelena Author-X-Name-Last: Kočović Author-Name: Vesna Ćojbašić Rajić Author-X-Name-First: Vesna Ćojbašić Author-X-Name-Last: Rajić Author-Name: Milan Jovanović Author-X-Name-First: Milan Author-X-Name-Last: Jovanović Title: Estimating a tail of the mixture of log-normal and inverse Gaussian distribution Abstract: In this paper, we estimate a tail of the mixture of log-normal and inverse Gaussian distribution in order to model extreme historical losses. Good estimate of the tail is essential in reinsurance for choosing or pricing high-excess layer. Method is supported by extreme value theory. We derive useful estimates of value-at-risk and expected shortfall. We apply this methodology to some fire insurance data. Journal: Scandinavian Actuarial Journal Pages: 49-58 Issue: 1 Volume: 2015 Year: 2015 Month: 1 X-DOI: 10.1080/03461238.2013.775665 File-URL: http://hdl.handle.net/10.1080/03461238.2013.775665 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:1:p:49-58 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_775964_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Morten Tolver Kronborg Author-X-Name-First: Morten Tolver Author-X-Name-Last: Kronborg Author-Name: Mogens Steffensen Author-X-Name-First: Mogens Author-X-Name-Last: Steffensen Title: Optimal consumption, investment and life insurance with surrender option guarantee Abstract: We consider an investor, with an uncertain lifetime, endowed with deterministic laboor income, who has the possibility to continuously invest in a Black–Scholes market and to buy life insurance or annuities. We solve the optimal consumption, investment and life insurance problem when the investor is restricted to fulfil an American capital guarantee. By allowing the guarantee to depend, in a very general way, on the past we include, among other possibilities, the interesting case of a minimum rate of return guarantee, commonly offered by pension companies. The optimal strategies turn out to be on option-based portfolio insurance form, but since the capital guarantee is valid at every intermediate point in time, re-calibration is needed whenever the constraint is active. Journal: Scandinavian Actuarial Journal Pages: 59-87 Issue: 1 Volume: 2015 Year: 2015 Month: 1 X-DOI: 10.1080/03461238.2013.775964 File-URL: http://hdl.handle.net/10.1080/03461238.2013.775964 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:1:p:59-87 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_779594_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Helena Aro Author-X-Name-First: Helena Author-X-Name-Last: Aro 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: Stochastic modelling of disability insurance in a multi-period framework Abstract: We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data. Journal: Scandinavian Actuarial Journal Pages: 88-106 Issue: 1 Volume: 2015 Year: 2015 Month: 1 X-DOI: 10.1080/03461238.2013.779594 File-URL: http://hdl.handle.net/10.1080/03461238.2013.779594 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:1:p:88-106 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_787367_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jonas Alm Author-X-Name-First: Jonas Author-X-Name-Last: Alm Title: A simulation model for calculating solvency capital requirements for non-life insurance risk Abstract: To stay solvent, an insurer must have enough assets to cover its liabilities towards its policy holders. In this paper, we construct a simulation model that is able to generate solvency capital requirements (SCR) for non-life insurance risk. The only input to the model is assumptions about the distributions of payment patterns and ultimate claim amounts. These assumptions should ideally be based on findings in empirical data studies. We illustrate the modelling technique by considering a specific case with motor insurance data from the Swedish insurer Folksam. The SCR values generated by the simulation model with different distributional assumptions in this specific case are analysed and compared to the SCR value calculated using the Solvency II standard model. The most important finding was that the uncertainty in prediction of the trend in ultimate claim amounts affect the SCR substantially. Insurers and supervisory authorities should be aware of the effects of this trend prediction uncertainty when building and evaluating internal models in the Solvency II or other regulatory frameworks. Journal: Scandinavian Actuarial Journal Pages: 107-123 Issue: 2 Volume: 2015 Year: 2015 Month: 2 X-DOI: 10.1080/03461238.2013.787367 File-URL: http://hdl.handle.net/10.1080/03461238.2013.787367 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:2:p:107-123 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_794436_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Matthias A. Fahrenwaldt Author-X-Name-First: Matthias A. Author-X-Name-Last: Fahrenwaldt Title: Sensitivity of life insurance reserves via Markov semigroups Abstract: Fahrenwaldt M. Sensitivity of life insurance reserves via Markov semigroups. Scandinavian Actuarial Journal. We consider Thiele’s differential equation for the reserve of a multi-state insurance contract with functional dependence on the surplus. In an analytic approach based on semigroups, we obtain existence and uniqueness results and prove growth and regularity properties. Moreover, we investigate the sensitivity of the reserves with respect to the surplus, payment rate, and transition assumptions in terms of uniform and pointwise estimates. The approach can easily be generalized. Journal: Scandinavian Actuarial Journal Pages: 124-140 Issue: 2 Volume: 2015 Year: 2015 Month: 2 X-DOI: 10.1080/03461238.2013.794436 File-URL: http://hdl.handle.net/10.1080/03461238.2013.794436 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:2:p:124-140 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_794520_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Craig Adams Author-X-Name-First: Craig Author-X-Name-Last: Adams Author-Name: Catherine Donnelly Author-X-Name-First: Catherine Author-X-Name-Last: Donnelly Author-Name: Angus Macdonald Author-X-Name-First: Angus Author-X-Name-Last: Macdonald Title: The impact of known breast cancer polygenes on critical illness insurance Abstract: Genetic studies indicate that the inherited risk of breast cancer is mediated by the well-studied major genes BRCA1 and BRCA2, and a polygenic component, probably with many genes each making a small contribution. Recently, seven polygenes have been found contributing an estimated 3.6% of all familial risk. This suggests that the polygenic component may involve well over 100 genetic loci. We extrapolate these new results into a polygenic model with 147 genetic loci and simulate lifetimes of families to calculate the premium ratings appropriate for a family history of breast or ovarian cancer. We model the adverse selection costs arising from restricting the use of genetic test information in critical illness insurance underwriting in light of new European legislation banning the use of gender for insurance underwriting. In this setting, we confirm the overall conclusion of a previous study which used a simpler model that the polygene confers higher adverse selection risk than the BRCA genes. We establish that their three-gene polygenic model does not overly inflate the insurance costs attributable to a polygenic component of breast cancer risk under a model with 147 polygenes. Journal: Scandinavian Actuarial Journal Pages: 141-171 Issue: 2 Volume: 2015 Year: 2015 Month: 2 X-DOI: 10.1080/03461238.2013.794520 File-URL: http://hdl.handle.net/10.1080/03461238.2013.794520 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:2:p:141-171 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_804002_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jinzhu Li Author-X-Name-First: Jinzhu Author-X-Name-Last: Li Title: Asymptotics for large claims reinsurance in a time-dependent renewal risk model Abstract: We study the asymptotic tail behaviour of reinsured amounts of the LCR and ECOMOR treaties under a time-dependent renewal risk model, in which a dependence structure is introduced between each claim size and the interarrival time before it. Assuming that the claim size distribution has a subexponential tail, we derive some precise asymptotic results for both treaties. Journal: Scandinavian Actuarial Journal Pages: 172-183 Issue: 2 Volume: 2015 Year: 2015 Month: 2 X-DOI: 10.1080/03461238.2013.804002 File-URL: http://hdl.handle.net/10.1080/03461238.2013.804002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:2:p:172-183 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_807299_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Igor Itskovich Author-X-Name-First: Igor Author-X-Name-Last: Itskovich Author-Name: Bradley T. Roudebush Author-X-Name-First: Bradley T. Author-X-Name-Last: Roudebush Title: A new parametric model for converting excess mortality from clinical studies to insured population Abstract: We propose a new parametric model – the generalized excess mortality (GEM) model – for converting excess mortality from clinical to insured population. The GEM model has been formulated as a generalization of the excess death rate (EDR) model in terms of a single adjustment parameter (m) that accounts for a partial elimination of a clinical study’s EDR due to the underwriting selection process. The suggested value of the parameter m depends only on the ratio of the impairment’s prevalence rate in the insured population to that in the clinical population. The model’s development has been implemented in two phases: the design phase and the validation phase. In the design phase, the data from the National Health and Nutrition Examination Survey I pertaining to three broad impairments (diabetes, coronary artery disease, and asthma) have been used. As a result, the following equation for the parameter m has been proposed: mk = (Pi,k/Pc,k)n, where Pi,k, Pc,k are the prevalence rates of impairment k under study in the insured and the clinical populations, respectively, and n a single universal parameter with its value best approximated as n = 0.5 (95% confidence interval 0.5–0.6). In the validation phase, several independent clinical studies of three other impairments (Crohn’s disease, epilepsy, and chronic obstructive pulmonary disease) were used. As it has been demonstrated in the validation phase, for a number of impairments, the GEM model can provide a better fit for observed insured population mortality than either one of the conventional EDR or mortality ratio models. Journal: Scandinavian Actuarial Journal Pages: 184-199 Issue: 2 Volume: 2015 Year: 2015 Month: 2 X-DOI: 10.1080/03461238.2013.807299 File-URL: http://hdl.handle.net/10.1080/03461238.2013.807299 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:2:p:184-199 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_807469_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David P.M. Scollnik Author-X-Name-First: David P.M. Author-X-Name-Last: Scollnik Title: A Pareto scale-inflated outlier model and its Bayesian analysis Abstract: This paper develops a Pareto scale-inflated outlier model. This model is intended for use when data from some standard Pareto distribution of interest is suspected to have been contaminated with a relatively small number of outliers from a Pareto distribution with the same shape parameter but with an inflated scale parameter. The Bayesian analysis of this Pareto scale-inflated outlier model is considered and its implementation using the Gibbs sampler is discussed. The paper contains three worked illustrative examples, two of which feature actual insurance claims data. Journal: Scandinavian Actuarial Journal Pages: 201-220 Issue: 3 Volume: 2015 Year: 2015 Month: 4 X-DOI: 10.1080/03461238.2013.807469 File-URL: http://hdl.handle.net/10.1080/03461238.2013.807469 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:3:p:201-220 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_807470_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Author-Name: Alexander Kukush Author-X-Name-First: Alexander Author-X-Name-Last: Kukush Author-Name: Daniël Linders Author-X-Name-First: Daniël Author-X-Name-Last: Linders Title: Ordered random vectors and equality in distribution Abstract: In this paper we show that under appropriate moment conditions, the supermodular ordered random vectors X¯=(X1,X2,…,Xn)$ \underline{X}=\left( X_{1},X_{2},\ldots ,X_{n}\right) $ and Y¯=(Y1,Y2,…,Yn)$ \underline{Y}=\left( Y_{1},Y_{2},\ldots ,Y_{n}\right) $ with equal expected utilities (or distorted expectations) of the sums X1+X2+…+Xn$ X_{1}+X_{2}+\ldots +X_{n} $ and Y1+Y2+…+Yn$ Y_{1}+Y_{2}+\ldots +Y_{n} $ for an appropriate utility (or distortion) function, must necessarily be equal in distribution, that is X¯=dY¯$ \underline{X}\overset{\text{ d}}{=}\underline{Y} $. The results in this paper can be considered as generalizations of some recent results on comonotonicity, where necessary conditions related to the distribution of X1+Xn+…+Xn$ X_1 + X_n+ \ldots + X_n $ are presented for the random vector X¯=(X1,X2,…,Xn)$ \underline{X}=(X_1, X_2,\ldots ,X_n) $ to be comonotonic. Journal: Scandinavian Actuarial Journal Pages: 221-244 Issue: 3 Volume: 2015 Year: 2015 Month: 4 X-DOI: 10.1080/03461238.2013.807470 File-URL: http://hdl.handle.net/10.1080/03461238.2013.807470 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:3:p:221-244 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_811096_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhong Li Author-X-Name-First: Zhong Author-X-Name-Last: Li Author-Name: Kristina P. Sendova Author-X-Name-First: Kristina P. Author-X-Name-Last: Sendova Title: On a ruin model with both interclaim times and premiums depending on claim sizes Abstract: Under the classical compound Poisson risk model and the Sparre-Andersen risk model, one crucial assumption is that the interclaim times and the claim sizes are independent. However, this assumption might be inappropriate in practice. In this paper, we consider a continuous-time risk process where the interclaim-time distribution and premium rate both depend on the size of the previous claim. Explicit solutions for the Gerber–Shiu discounted penalty function with arbitrary claim-size distribution are derived utilizing the roots of a generalized Lundberg’s equation. Applications with exponential thresholds and Kn$ K_n $-family claim sizes are presented. A numerical example is provided. Journal: Scandinavian Actuarial Journal Pages: 245-265 Issue: 3 Volume: 2015 Year: 2015 Month: 4 X-DOI: 10.1080/03461238.2013.811096 File-URL: http://hdl.handle.net/10.1080/03461238.2013.811096 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:3:p:245-265 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_819028_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: J.J. Fernández-Durán Author-X-Name-First: J.J. Author-X-Name-Last: Fernández-Durán Author-Name: M.M. Gregorio-Domínguez Author-X-Name-First: M.M. Author-X-Name-Last: Gregorio-Domínguez Title: Seasonal mortality for fractional ages in short term life insurance Abstract: Fernández-Durán, and Gregorio-Domínguez, Seasonal Mortality for Fractional Ages in Life Insurance. Scandinavian Actuarial Journal. A uniform distribution of deaths between integral ages is a widely used assumption for estimating future-lifetimes; however, this assumption does not necessarily reflect the true distribution of deaths throughout the year. We propose the use of a seasonal mortality assumption for estimating the distribution of future-lifetimes between integral ages: this assumption accounts for the number of deaths that occurs in given months of the year, including the excess mortality that is observed in winter months. The impact of this seasonal mortality assumption on short-term life insurance premium calculations is then examined by applying the proposed assumption to Mexican mortality data. Journal: Scandinavian Actuarial Journal Pages: 266-277 Issue: 3 Volume: 2015 Year: 2015 Month: 4 X-DOI: 10.1080/03461238.2013.819028 File-URL: http://hdl.handle.net/10.1080/03461238.2013.819028 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:3:p:266-277 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_821952_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: D. Kuang Author-X-Name-First: D. Author-X-Name-Last: Kuang Author-Name: B. Nielsen Author-X-Name-First: B. Author-X-Name-Last: Nielsen Author-Name: J.P. Nielsen Author-X-Name-First: J.P. Author-X-Name-Last: Nielsen Title: The geometric chain-ladder Abstract: The log normal reserving model is considered. The contribution of the paper is to derive explicit expressions for the maximum likelihood estimators. These are expressed in terms of development factors which are geometric averages. The distribution of the estimators is derived. It is shown that the analysis is invariant to traditional measures for exposure. Journal: Scandinavian Actuarial Journal Pages: 278-300 Issue: 3 Volume: 2015 Year: 2015 Month: 4 X-DOI: 10.1080/03461238.2013.821952 File-URL: http://hdl.handle.net/10.1080/03461238.2013.821952 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:3:p:278-300 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_823460_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ciyu Nie Author-X-Name-First: Ciyu Author-X-Name-Last: Nie Author-Name: David C.M. Dickson Author-X-Name-First: David C.M. Author-X-Name-Last: Dickson Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Title: The finite time ruin probability in a risk model with capital injections Abstract: We consider a risk model with capital injections. We show that in the Sparre Andersen framework the density of the time to ruin for the model with capital injections can be expressed in terms of the density of the time to ruin in an ordinary Sparre Andersen risk process. In the special case of Erlang inter-claim times and exponential claims, we show that there exists a readily computable formula for the density of the time to ruin. When the inter-claim time distribution is exponential, we obtain an explicit solution for the density of the time to ruin when the individual claim amount distribution is Erlang(2), and we explain techniques to find the moments of the time to ruin. In the final section, we consider the related problem of the distribution of the duration of negative surplus in the classical risk model, and we obtain explicit solutions for the (defective) density of the total duration of negative surplus for two individual claim amount distributions. Journal: Scandinavian Actuarial Journal Pages: 301-318 Issue: 4 Volume: 2015 Year: 2015 Month: 5 X-DOI: 10.1080/03461238.2013.823460 File-URL: http://hdl.handle.net/10.1080/03461238.2013.823460 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:4:p:301-318 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_825639_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Julia Farkas Author-X-Name-First: Julia Author-X-Name-Last: Farkas Author-Name: Enkelejd Hashorva Author-X-Name-First: Enkelejd Author-X-Name-Last: Hashorva Title: Tail approximation for reinsurance portfolios of Gaussian-like risks Abstract: We consider two different portfolios of proportional reinsurance of the same pool of risks. This contribution is concerned with Gaussian-like risks, which means that for large values the survival function of such risks is, up to a multiplier, the same as that of a standard Gaussian risk. We establish the tail asymptotic behavior of the total loss of each of the reinsurance portfolios and determine also the relation between randomly scaled Gaussian-like portfolios and unscaled ones. Further, we show that jointly two portfolios of Gaussian-like risks exhibit asymptotic independence and their weak tail dependence coefficient is nonnegative. Journal: Scandinavian Actuarial Journal Pages: 319-331 Issue: 4 Volume: 2015 Year: 2015 Month: 5 X-DOI: 10.1080/03461238.2013.825639 File-URL: http://hdl.handle.net/10.1080/03461238.2013.825639 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:4:p:319-331 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_830228_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alois Pichler Author-X-Name-First: Alois Author-X-Name-Last: Pichler Title: Premiums and reserves, adjusted by distortions Abstract: The net premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, actuarial due diligence requires additional caution in pricing of insurance contracts to avoid, for example, at least bankruptcy of the insurer. This paper addresses the distorted premium principle from various angles. Distorted premiums are typically computed by underweighting or ignoring low, but overweighting high losses. Dual characterizations, which are elaborated in a first part of the paper, support this interpretation. The main contribution consists in an opposite point of view—an alternative characterization—which leaves the probability measure unchanged, but modifies (increases) the outcomes instead in a consistent way. It turns out that this new point of view is natural in actuarial practice,as it can be used for premium calculations, but equally well to determine the reserve process in subsequent years in a time consistent way. Journal: Scandinavian Actuarial Journal Pages: 332-351 Issue: 4 Volume: 2015 Year: 2015 Month: 5 X-DOI: 10.1080/03461238.2013.830228 File-URL: http://hdl.handle.net/10.1080/03461238.2013.830228 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:4:p:332-351 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_836561_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren fiig Jarner Author-X-Name-First: Søren fiig Author-X-Name-Last: Jarner Author-Name: Thomas Møller Author-X-Name-First: Thomas Author-X-Name-Last: Møller Title: A partial internal model for longevity risk Abstract: This paper proposes a simple partial internal model for longevity risk within the Solvency 2 framework. The model is closely linked to the mechanisms associated with the so-called Danish longevity benchmark, where the underlying mortality intensity and the trend is estimated yearly based on mortality experience from the Danish life and pension insurance sector, and on current data from the entire Danish population. Within this model, we derive an estimate for the 99.5% percentile for longevity risk, which differs from the longevity stress of 20% from the standard model. The new stress explicitly reflects the risk associated with unexpected changes in the underlying population mortality intensity on a one-year horizon and with a 99.5% confidence level. In addition, the model contains a component, which quantifies the unsystematic longevity risk associated with a given insurance portfolio. This last component depends on the size of the specific portfolio. Journal: Scandinavian Actuarial Journal Pages: 352-382 Issue: 4 Volume: 2015 Year: 2015 Month: 5 X-DOI: 10.1080/03461238.2013.836561 File-URL: http://hdl.handle.net/10.1080/03461238.2013.836561 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:4:p:352-382 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_823459_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: MaríA Dolores Martínez Miranda Author-X-Name-First: MaríA Dolores Author-X-Name-Last: Martínez Miranda Author-Name: Jens Perch Nielsen Author-X-Name-First: Jens Perch Author-X-Name-Last: Nielsen Author-Name: Richard Verrall Author-X-Name-First: Richard Author-X-Name-Last: Verrall Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Double chain ladder, claims development inflation and zero-claims Abstract: Double chain ladder demonstrated how the classical chain ladder technique can be broken down into separate components. It was shown that under certain model assumptions and via one particular estimation technique, it is possible to interpret the classical chain ladder method as a model of the observed number of counts with a built-in delay function from when a claim is reported until it is paid. In this paper, we investigate the double chain ladder model further and consider the case when other knowledge is available, focusing on two specific types of prior knowledge, namely prior knowledge on the number of zero-claims for each underwriting year and prior knowledge about the relationship between the development of the claim and its mean severity. Both types of prior knowledge readily lend themselves to be included in the double chain ladder framework. Journal: Scandinavian Actuarial Journal Pages: 383-405 Issue: 5 Volume: 2015 Year: 2015 Month: 7 X-DOI: 10.1080/03461238.2013.823459 File-URL: http://hdl.handle.net/10.1080/03461238.2013.823459 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:5:p:383-405 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_838603_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Costabile Author-X-Name-First: M. Author-X-Name-Last: Costabile Author-Name: I. Massabò Author-X-Name-First: I. Author-X-Name-Last: Massabò Author-Name: E. Russo Author-X-Name-First: E. Author-X-Name-Last: Russo Title: Computing finite-time survival probabilities using multinomial approximations of risk models Abstract: We consider the problem of computing finite-time survival probabilities for various risk models. We develop an approximating discrete-time multinomial lattice that mimics the evolution of the corresponding continuous risk process. A simple recursive algorithm to compute survival probabilities is described. Numerical results show that the proposed scheme yields accurate values in all the considered cases. Journal: Scandinavian Actuarial Journal Pages: 406-422 Issue: 5 Volume: 2015 Year: 2015 Month: 7 X-DOI: 10.1080/03461238.2013.838603 File-URL: http://hdl.handle.net/10.1080/03461238.2013.838603 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:5:p:406-422 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_846277_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Author-Name: Hans W. Volkmer Author-X-Name-First: Hans W. Author-X-Name-Last: Volkmer Author-Name: Shuaiqi Zhang Author-X-Name-First: Shuaiqi Author-X-Name-Last: Zhang Author-Name: Chao Zhu Author-X-Name-First: Chao Author-X-Name-Last: Zhu Title: Optimal dividend policies for piecewise-deterministic compound Poisson risk models Abstract: This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates. Journal: Scandinavian Actuarial Journal Pages: 423-454 Issue: 5 Volume: 2015 Year: 2015 Month: 7 X-DOI: 10.1080/03461238.2013.846277 File-URL: http://hdl.handle.net/10.1080/03461238.2013.846277 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:5:p:423-454 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_849615_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lianzeng Zhang Author-X-Name-First: Lianzeng Author-X-Name-Last: Zhang Author-Name: Xiang Hu Author-X-Name-First: Xiang Author-X-Name-Last: Hu Author-Name: Baige Duan Author-X-Name-First: Baige Author-X-Name-Last: Duan Title: Optimal reinsurance under adjustment coefficient measure in a discrete risk model based on Poisson MA(1) process Abstract: In this paper, we study the retention levels for combinations of quota-share and excess of loss reinsurance by maximizing the insurer’s adjustment coefficient, which in turn minimizes the asymptotic result of ruin probability. Assuming that the premiums are determined by the expected value principle, we consider a discrete risk model, in which a dependence structure is introduced based on Poisson MA(1) process between the claim numbers for each period. The impact of dependence parameter on the adjustment coefficient is discussed and numerical examples are provided to illustrate the results obtained in this paper. Journal: Scandinavian Actuarial Journal Pages: 455-467 Issue: 5 Volume: 2015 Year: 2015 Month: 7 X-DOI: 10.1080/03461238.2013.849615 File-URL: http://hdl.handle.net/10.1080/03461238.2013.849615 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:5:p:455-467 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_850442_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Krzysztof Dȩbicki Author-X-Name-First: Krzysztof Author-X-Name-Last: Dȩbicki Author-Name: Enkelejd Hashorva Author-X-Name-First: Enkelejd Author-X-Name-Last: Hashorva Author-Name: Lanpeng Ji Author-X-Name-First: Lanpeng Author-X-Name-Last: Ji Title: Gaussian risk models with financial constraints Abstract: In this paper, we investigate Gaussian risk models which include financial elements, such as inflation and interest rates. For some general models for inflation and interest rates, we obtain an asymptotic expansion of the finite-time ruin probability for Gaussian risk models. Furthermore, we derive an approximation of the conditional ruin time by an exponential random variable as the initial capital tends to infinity. Journal: Scandinavian Actuarial Journal Pages: 469-481 Issue: 6 Volume: 2015 Year: 2015 Month: 8 X-DOI: 10.1080/03461238.2013.850442 File-URL: http://hdl.handle.net/10.1080/03461238.2013.850442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:6:p:469-481 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_852992_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Magda Schiegl Author-X-Name-First: Magda Author-X-Name-Last: Schiegl Title: A model study about the applicability of the Chain Ladder method Abstract: Loss Reserving is a major topic of actuarial sciences with a long tradition and well-established methods – both in science and in practice. With the implementation of Solvency II, stochastic methods and modelling the stochastic behaviour of individual claim portfolios will receive additional attention. The author has recently proposed a three-dimensional (3D) stochastic model of claim development. It models a reasonable claim process from first principle by integrating realistic processes of claim occurrence, claim reporting and claim settlement. This paper investigates the ability of the Chain Ladder (CL) method to adequately forecast outstanding claims within the framework of the 3D model. This allows one to find conditions under which the CL method is adequate for outstanding claim prediction, and others in which it fails. Monte Carlo (MC) simulations are performed, lending support to the theoretic results. The analysis leads to additional suggestions concerning the use of the CL method. Journal: Scandinavian Actuarial Journal Pages: 482-499 Issue: 6 Volume: 2015 Year: 2015 Month: 8 X-DOI: 10.1080/03461238.2013.852992 File-URL: http://hdl.handle.net/10.1080/03461238.2013.852992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:6:p:482-499 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_853368_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kahadawala Cooray Author-X-Name-First: Kahadawala Author-X-Name-Last: Cooray Author-Name: Chin-I Cheng Author-X-Name-First: Chin-I Author-X-Name-Last: Cheng Title: Bayesian estimators of the lognormal–Pareto composite distribution Abstract: In this paper, Bayesian methods with both Jeffreys and conjugate priors for estimating parameters of the lognormal–Pareto composite (LPC) distribution are considered. With Jeffreys prior, the posterior distributions for parameters of interest are derived and their properties are described. The conjugate priors are proposed and the conditional posterior distributions are provided. In addition, simulation studies are performed to obtain the upper percentage points of Kolmogorov–Smirnov and Anderson–Darling test statistics. Furthermore, these statistics are used to compare Bayesian and likelihood estimators. In order to clarify and advance the validity of Bayesian and likelihood estimators of the LPC distribution, well-known Danish fire insurance data-set is reanalyzed. Journal: Scandinavian Actuarial Journal Pages: 500-515 Issue: 6 Volume: 2015 Year: 2015 Month: 8 X-DOI: 10.1080/03461238.2013.853368 File-URL: http://hdl.handle.net/10.1080/03461238.2013.853368 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:6:p:500-515 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_858401_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: From ruin theory to solvency in non-life insurance Abstract: We start from ruin theory considerations in the classical Cramér–Lundberg model. We modify these considerations step by step so that finally we arrive at today’s solvency assessments for non-life insurance companies. These modifications include discussions about time horizons, risk measures, financial returns, and valuation of insurance liabilities. Journal: Scandinavian Actuarial Journal Pages: 516-526 Issue: 6 Volume: 2015 Year: 2015 Month: 8 X-DOI: 10.1080/03461238.2013.858401 File-URL: http://hdl.handle.net/10.1080/03461238.2013.858401 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:6:p:516-526 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_859634_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michael R. Powers Author-X-Name-First: Michael R. Author-X-Name-Last: Powers Author-Name: Thomas Y. Powers Author-X-Name-First: Thomas Y. Author-X-Name-Last: Powers Title: Fourier-analytic measures for heavy-tailed insurance losses Abstract: We propose a family of three ‘Fourier-analytic’ measures to extend the conventional concepts of standard deviation, variance, and coefficient of variation to insurance losses with arbitrarily heavy tails. After motivating and computing their mathematical forms, we apply the proposed measures to the case of Lévy-stable loss portfolios. Finally, the new measures are used to study the diversification properties of heavy-tailed losses. Journal: Scandinavian Actuarial Journal Pages: 527-547 Issue: 6 Volume: 2015 Year: 2015 Month: 8 X-DOI: 10.1080/03461238.2013.859634 File-URL: http://hdl.handle.net/10.1080/03461238.2013.859634 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:6:p:527-547 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_864326_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Armelle Guillou Author-X-Name-First: Armelle Author-X-Name-Last: Guillou Author-Name: Philippe Naveau Author-X-Name-First: Philippe Author-X-Name-Last: Naveau Author-Name: Alexandre You Author-X-Name-First: Alexandre Author-X-Name-Last: You Title: A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications Abstract: In this paper, the folding methodology developed in the context of univariate Extreme Value Theory (EVT) by You et al. is extended to a multivariate framework. Under the usual EVT assumption of regularly varying tails, our multivariate folding allows for the estimation of the spectral probability measure. A new weakly consistent estimator based on the classical empirical estimator is proposed. Its behaviour is illustrated through simulations and an actuarial application relative to reinsurance pricing in the case of an insurance data-set. Journal: Scandinavian Actuarial Journal Pages: 549-572 Issue: 7 Volume: 2015 Year: 2015 Month: 10 X-DOI: 10.1080/03461238.2013.864326 File-URL: http://hdl.handle.net/10.1080/03461238.2013.864326 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:7:p:549-572 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_865257_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mogens Bladt Author-X-Name-First: Mogens Author-X-Name-Last: Bladt Author-Name: Bo Friis Nielsen Author-X-Name-First: Bo Friis Author-X-Name-Last: Nielsen Author-Name: Gennady Samorodnitsky Author-X-Name-First: Gennady Author-X-Name-Last: Samorodnitsky Title: Calculation of ruin probabilities for a dense class of heavy tailed distributions Abstract: In this paper, we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions. The class of finite-dimensional phase-type distributions is dense in the class of distributions on the positive reals and may hence approximate any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase-type distributions also hold true for the infinite-dimensional case. We provide algorithms for calculating functionals of interest such as the renewal density and the ruin probability. It might be of interest to approximate a given heavy tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide a calibration procedure which works for the approximation of distributions with a slowly varying tail. An example from risk theory, comparing ruin probabilities for a classical risk process with Pareto distributed claim sizes, is presented and exact known ruin probabilities for the Pareto case are compared to the ones obtained by approximating by an infinite-dimensional hyper-exponential distribution. Journal: Scandinavian Actuarial Journal Pages: 573-591 Issue: 7 Volume: 2015 Year: 2015 Month: 10 X-DOI: 10.1080/03461238.2013.865257 File-URL: http://hdl.handle.net/10.1080/03461238.2013.865257 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:7:p:573-591 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_872174_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jinxia Zhu Author-X-Name-First: Jinxia Author-X-Name-Last: Zhu Title: Dividend optimization for general diffusions with restricted dividend payment rates Abstract: The dividend optimization problem is studied for a surplus process modeled by a general diffusion where both the drift and diffusion coefficients are functions of the surplus. The dividend payment rate is restricted. The objective is to find an optimal strategy that maximizes the total expected discounted dividends until ruin. It is shown that an optimal strategy is to pay no dividends when the surplus is below a threshold b∗$ b^* $ and to pay out dividends at the maximal possible rate when the surplus reaches or is above the threshold b∗$ b^* $. We also give a result on how to determine b∗$ b^* $ and the value function and derive some analytical properties of the value function. Journal: Scandinavian Actuarial Journal Pages: 592-615 Issue: 7 Volume: 2015 Year: 2015 Month: 10 X-DOI: 10.1080/03461238.2013.872174 File-URL: http://hdl.handle.net/10.1080/03461238.2013.872174 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:7:p:592-615 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_876927_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Løchte Jørgensen Author-X-Name-First: Peter Løchte Author-X-Name-Last: Jørgensen Author-Name: Nadine Gatzert Author-X-Name-First: Nadine Author-X-Name-Last: Gatzert Title: On risk charges and shadow account options in pension funds Abstract: This paper studies the economic implications of regulatory systems which allow equityholders of pension companies to not only charge a specific premium to compensate them for their higher risk (compared to policyholders), but also to accumulate these risk charges in a so-called shadow account in years when they are not immediately payable due to e.g. poor investment results. When surpluses are subsequently reestablished, clearance of the shadow account balance takes priority over bonus/participation transfers to policyholders. We see such a regulatory accounting rule as a valuable option to equityholders and our paper develops a model in which the influence of risk charges and shadow account options on stakeholders’ value can be quantified and studied. Our numerical results show that the value of shadow account options can be significant and thus come at the risk of expropriating policyholder wealth. However, our analysis also shows that this risk can be remedied if proper attention is given to the specific contract design and to the fixing of fair contract parameters at the outset. Journal: Scandinavian Actuarial Journal Pages: 616-639 Issue: 7 Volume: 2015 Year: 2015 Month: 10 X-DOI: 10.1080/03461238.2013.876927 File-URL: http://hdl.handle.net/10.1080/03461238.2013.876927 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:7:p:616-639 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_878853_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yang Yang Author-X-Name-First: Yang Author-X-Name-Last: Yang Author-Name: Dimitrios G. Konstantinides Author-X-Name-First: Dimitrios G. Author-X-Name-Last: Konstantinides Title: Asymptotics for ruin probabilities in a discrete-time risk model with dependent financial and insurance risks Abstract: Let us consider a discrete-time insurance risk model with insurance and financial risks, where the insurance net loss within period i$ i $ and the stochastic discount factor over the interval (i-1,i]$ (i-1, i] $ follow a certain dependence structure for each fixed i≥1$ i{} \ge 1 $. Under the assumption that the distribution of net insurance loss within one time period is consistently varying-tailed, precise estimates for finite and infinite time ruin probabilities are derived. Furthermore, these estimates are uniform on the time horizon. Journal: Scandinavian Actuarial Journal Pages: 641-659 Issue: 8 Volume: 2015 Year: 2015 Month: 11 X-DOI: 10.1080/03461238.2013.878853 File-URL: http://hdl.handle.net/10.1080/03461238.2013.878853 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:8:p:641-659 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_879919_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kristian Buchardt Author-X-Name-First: Kristian Author-X-Name-Last: Buchardt Author-Name: Thomas Møller Author-X-Name-First: Thomas Author-X-Name-Last: Møller Author-Name: Kristian Bjerre Schmidt Author-X-Name-First: Kristian Bjerre Author-X-Name-Last: Schmidt Title: Cash flows and policyholder behaviour in the semi-Markov life insurance setup Abstract: Within the setup of a semi-Markov process in a finite state space, we consider a life insurance contract. First, without the modelling of policyholder behaviour, we show how to calculate the expected cash flow associated with future payments, and to that end we present a version of Kolmogorov’s forward integro-differential equation. The semi-Markov model is then extended to include modelling of surrender and free policy behaviour, and the main result is a modification of Kolmogorov’s forward integro-differential equation, such that the cash flow can be calculated without significantly more complexity than the cash flow without policyholder modelling. The result is also demonstrated for the traditional Markov case where there is no duration dependence, and numerical examples are studied. Journal: Scandinavian Actuarial Journal Pages: 660-688 Issue: 8 Volume: 2015 Year: 2015 Month: 11 X-DOI: 10.1080/03461238.2013.879919 File-URL: http://hdl.handle.net/10.1080/03461238.2013.879919 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:8:p:660-688 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_882860_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Killian Lemoine Author-X-Name-First: Killian Author-X-Name-Last: Lemoine Title: Mortality regimes and longevity risk in a life annuity portfolio Abstract: This paper explores the presence of changes of trends or jumps in French mortality from 1947 to 2007, and assesses their implications on the longevity risk management of a life annuity portfolio. We accomplish this by extending the Poisson log-bilinear regression developed by Brouhns et al. (2002) with a regime-switching model. Estimation results show that French mortality is characterized by two distinct regimes. One refers to a strong uncertainty state, which corresponds to the longevity conditions observed during the decade following World War II. The second regime is related to the low volatility of longevity improvements observed during the last 30 years. We use these results to analyze the impact of mortality regimes on the longevity risk management of a life annuity portfolio. Simulation results suggest that the changes of trends in the mortality process have some implications for longevity risk management. Journal: Scandinavian Actuarial Journal Pages: 689-724 Issue: 8 Volume: 2015 Year: 2015 Month: 11 X-DOI: 10.1080/03461238.2014.882860 File-URL: http://hdl.handle.net/10.1080/03461238.2014.882860 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:8:p:689-724 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_883085_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bo Yi Author-X-Name-First: Bo Author-X-Name-Last: Yi Author-Name: Frederi Viens Author-X-Name-First: Frederi Author-X-Name-Last: Viens Author-Name: Zhongfei Li Author-X-Name-First: Zhongfei Author-X-Name-Last: Li Author-Name: Yan Zeng Author-X-Name-First: Yan Author-X-Name-Last: Zeng Title: Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria Abstract: In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black–Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience. Journal: Scandinavian Actuarial Journal Pages: 725-751 Issue: 8 Volume: 2015 Year: 2015 Month: 11 X-DOI: 10.1080/03461238.2014.883085 File-URL: http://hdl.handle.net/10.1080/03461238.2014.883085 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:8:p:725-751 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_967449_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Editorial Board Journal: Scandinavian Actuarial Journal Pages: (ebi)-(ebi) Issue: 8 Volume: 2015 Year: 2015 Month: 11 X-DOI: 10.1080/03461238.2014.967449 File-URL: http://hdl.handle.net/10.1080/03461238.2014.967449 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2015:y:2015:i:8:p:(ebi)-(ebi) Template-Type: ReDIF-Article 1.0 # input file: SACT_A_884017_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Haizhong Yang Author-X-Name-First: Haizhong Author-X-Name-Last: Yang Author-Name: Wei Gao Author-X-Name-First: Wei Author-X-Name-Last: Gao Author-Name: Jinzhu Li Author-X-Name-First: Jinzhu Author-X-Name-Last: Li Title: Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks Abstract: This contribution focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account and they are equipped with a wide type of dependence structure. We derive precise asymptotic formulas for the ruin probabilities when the insurance risk has a dominatedly varying tail. In the special case of regular variation, the corresponding formula is proved to be uniform for the time horizon. Journal: Scandinavian Actuarial Journal Pages: 1-17 Issue: 1 Volume: 2016 Year: 2016 Month: 1 X-DOI: 10.1080/03461238.2014.884017 File-URL: http://hdl.handle.net/10.1080/03461238.2014.884017 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:1:p:1-17 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_892899_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhibin Liang Author-X-Name-First: Zhibin Author-X-Name-Last: Liang Author-Name: Kam Chuen Yuen Author-X-Name-First: Kam Chuen Author-X-Name-Last: Yuen Title: Optimal dynamic reinsurance with dependent risks: variance premium principle Abstract: In this paper, we consider the optimal proportional reinsurance strategy in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the variance premium principle, we adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsurance strategy. Using the technique of stochastic control theory, closed-form expressions for the optimal strategy and the value function are derived for the compound Poisson risk model as well as for the Brownian motion risk model. From the numerical examples, we see that the optimal results for the compound Poisson risk model are very different from those for the diffusion model. The former depends not only on the safety loading, time, and the interest rate, but also on the claim size distributions and the claim number processes, while the latter depends only on the safety loading, time, and the interest rate. Journal: Scandinavian Actuarial Journal Pages: 18-36 Issue: 1 Volume: 2016 Year: 2016 Month: 1 X-DOI: 10.1080/03461238.2014.892899 File-URL: http://hdl.handle.net/10.1080/03461238.2014.892899 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:1:p:18-36 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_900518_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yang Shen Author-X-Name-First: Yang Author-X-Name-Last: Shen Author-Name: Jiaqin Wei Author-X-Name-First: Jiaqin Author-X-Name-Last: Wei Title: Optimal investment-consumption-insurance with random parameters Abstract: This paper discusses an optimal investment, consumption, and life insurance purchase problem for a wage earner in a complete market with Brownian information. Specifically, we assume that the parameters governing the market model and the wage earner, including the interest rate, appreciation rate, volatility, force of mortality, premium-insurance ratio, income and discount rate, are all random processes adapted to the Brownian motion filtration. Our modeling framework is very general, which allows these random parameters to be unbounded, non-Markovian functionals of the underlying Brownian motion. Suppose that the wage earner’s preference is described by a power utility. The wage earner’s problem is then to choose an optimal investment-consumption-insurance strategy so as to maximize the expected, discounted utilities from intertemporal consumption, legacy and terminal wealth over an uncertain lifetime horizon. We use a novel approach, which combines the Hamilton–Jacobi–Bellman equation and backward stochastic differential equation (BSDE) to solve this problem. In general, we give explicit expressions for the optimal investment-consumption-insurance strategy and the value function in terms of the solutions to two BSDEs. To illustrate our results, we provide closed-form solutions to the problem with stochastic income, stochastic mortality, and stochastic appreciation rate, respectively. Journal: Scandinavian Actuarial Journal Pages: 37-62 Issue: 1 Volume: 2016 Year: 2016 Month: 1 X-DOI: 10.1080/03461238.2014.900518 File-URL: http://hdl.handle.net/10.1080/03461238.2014.900518 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:1:p:37-62 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_900519_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric C.K. Cheung Author-X-Name-First: Eric C.K. Author-X-Name-Last: Cheung Author-Name: Jae-Kyung Woo Author-X-Name-First: Jae-Kyung Author-X-Name-Last: Woo Title: On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes Abstract: In this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo is considered. We study a generalization of the Gerber–Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin; and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure, where the claim severities follow a combination of exponentials, is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin. Journal: Scandinavian Actuarial Journal Pages: 63-91 Issue: 1 Volume: 2016 Year: 2016 Month: 1 X-DOI: 10.1080/03461238.2014.900519 File-URL: http://hdl.handle.net/10.1080/03461238.2014.900519 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:1:p:63-91 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1017527_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jonas Alm Author-X-Name-First: Jonas Author-X-Name-Last: Alm Title: Signs of dependence and heavy tails in non-life insurance data Abstract: In this paper, we study data from the yearly reports the four major Swedish non-life insurers have sent to the Swedish Financial Supervisory Authority (FSA). We aim at finding marginal distributions of, and dependence between, losses on the five largest lines of business (LoBs) in order to create models for solvency capital requirement (SCR) calculation. We try to use data in an optimal way by sensibly defining an accounting year loss in terms of actuarial liability predictions and by pooling observations from several companies when possible to decrease the uncertainty about the underlying distributions and their parameters. We find that dependence between LoBs is weaker in our data than what is assumed in the Solvency II standard formula. We also find dependence between companies that may affect financial stability and must be taken into account when estimating loss distribution parameters. Moreover, we discuss under what circumstances an insurer is better (or worse) off using an internal model for SCR calculation, instead of the standard formula. Journal: Scandinavian Actuarial Journal Pages: 859-875 Issue: 10 Volume: 2016 Year: 2016 Month: 11 X-DOI: 10.1080/03461238.2015.1017527 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1017527 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:10:p:859-875 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1028432_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kamille Sofie TÅgholt Gad Author-X-Name-First: Kamille Sofie TÅgholt Author-X-Name-Last: Gad Author-Name: Jeppe Woetmann Nielsen Author-X-Name-First: Jeppe Woetmann Author-X-Name-Last: Nielsen Title: Reserves and cash flows under stochastic retirement Abstract: Uncertain time of retirement and uncertain structure of retirement benefits are risk factors for life insurance companies. Nevertheless, classical life insurance models assume these are deterministic. In this paper, we include the risk from stochastic time of retirement and stochastic benefit structure in a classical finite-state Markov model for a life insurance contract. We include discontinuities in the distribution of the retirement time. First, we derive formulas for appropriate scaling of the benefits according to the time of retirement and discuss the link between the scaling and the guarantees provided. Stochastic retirement creates a need to rethink the construction of disability products for high ages and ways to handle this are discussed. We show how to calculate market reserves and how to use modified transition probabilities to calculate expected cash flows without significantly more complexity than in the traditional model. At last, we demonstrate the impact of stochastic retirement on market reserves and expected cash flow in numerical examples. Journal: Scandinavian Actuarial Journal Pages: 876-904 Issue: 10 Volume: 2016 Year: 2016 Month: 11 X-DOI: 10.1080/03461238.2015.1028432 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1028432 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:10:p:876-904 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1031165_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Shangzhen Luo Author-X-Name-First: Shangzhen Author-X-Name-Last: Luo Author-Name: Mingming Wang Author-X-Name-First: Mingming Author-X-Name-Last: Wang Title: Barrier present value maximization for a diffusion model of insurance surplus Abstract: In this paper, we study a barrier present value (BPV) maximization problem for an insurance entity whose surplus process follows an arithmetic Brownian motion. The BPV is defined as the expected discounted value of a payment made at the time when the surplus process reaches a high barrier level. The insurance entity buys proportional reinsurance and invests in a Black–Scholes market to maximize the BPV. We show that the maximal BPV function is a classical solution to the corresponding Hamilton–Jacobi–Bellman equation and is three times continuously differentiable using a novel operator. Its associated optimal reinsurance-investment control policy is determined by verification techniques. Journal: Scandinavian Actuarial Journal Pages: 905-931 Issue: 10 Volume: 2016 Year: 2016 Month: 11 X-DOI: 10.1080/03461238.2015.1031165 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1031165 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:10:p:905-931 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1054302_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ilie-Radu Mitric Author-X-Name-First: Ilie-Radu Author-X-Name-Last: Mitric Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Title: On a risk measure inspired from the ruin probability and the expected deficit at ruin Abstract: In this paper, we study a risk measure derived from ruin theory defined as the amount of capital needed to cope in expectation with the first occurrence of a ruin event. Specifically, within the compound Poisson model, we investigate some properties of this risk measure with respect to the stochastic ordering of claim severities. Particular situations where combining risks yield diversification benefits are identified. Closed form expressions and upper bounds are also provided for certain claim severities. Journal: Scandinavian Actuarial Journal Pages: 932-951 Issue: 10 Volume: 2016 Year: 2016 Month: 11 X-DOI: 10.1080/03461238.2015.1054302 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1054302 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:10:p:932-951 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_908411_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bowen Yang Author-X-Name-First: Bowen Author-X-Name-Last: Yang 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 Title: Cohort extensions of the Poisson common factor model for modelling both genders jointly Abstract: The earlier work on mortality modelling and forecasting has largely focused on the study of a single population. Recently, there is an emerging strand of literature that emphasises the interrelationship between multiple populations. In this paper, we examine some cohort extensions of the Poisson common factor model for modelling both genders jointly. The cohort effect is specified in six alternatives which are applied to data-sets from five developed regions. We find that direct parameterisation of cohort effect could improve model fitting, reduce the need for additional period factors, and produce consistent mortality forecasts for females and males. Furthermore, we find that the cohort effect appears to be gender indifferent for the populations examined and has an interaction effect with age in certain cases. Journal: Scandinavian Actuarial Journal Pages: 93-112 Issue: 2 Volume: 2016 Year: 2016 Month: 2 X-DOI: 10.1080/03461238.2014.908411 File-URL: http://hdl.handle.net/10.1080/03461238.2014.908411 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:2:p:93-112 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_910833_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Matias Leppisaari Author-X-Name-First: Matias Author-X-Name-Last: Leppisaari Title: Modeling catastrophic deaths using EVT with a microsimulation approach to reinsurance pricing Abstract: Recently, a marked Poisson process (MPP) model for life catastrophe risk was proposed in Ekheden & Hössjer (2014). We provide a justification and further support for the model by considering more general Poisson point processes in the context of extreme value theory (EVT), and basing the choice of model on statistical tests and model comparisons. A case study examining accidental deaths in the Finnish population is provided. We further extend the applicability of the catastrophe risk model by considering small and big accidents separately; the resulting combined MPP model can flexibly capture the whole range of accidental death counts. Using the proposed model, we present a simulation framework for pricing (life) catastrophe reinsurance, based on modeling the underlying policies at individual contract level. The accidents are first simulated at population level, and their effect on a specific insurance company is then determined by explicitly simulating the resulting insured deaths. The proposed microsimulation approach can potentially lead to more accurate results than the traditional methods, and to a better view of risk, as it can make use of all the information available to the re/insurer and can explicitly accommodate even complex re/insurance terms and product features. As an example, we price several excess reinsurance contracts. The proposed simulation model is also suitable for solvency assessment. Journal: Scandinavian Actuarial Journal Pages: 113-145 Issue: 2 Volume: 2016 Year: 2016 Month: 2 X-DOI: 10.1080/03461238.2014.910833 File-URL: http://hdl.handle.net/10.1080/03461238.2014.910833 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:2:p:113-145 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_916228_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Pauline M. Barrieu Author-X-Name-First: Pauline M. Author-X-Name-Last: Barrieu Author-Name: Luitgard A.M. Veraart Author-X-Name-First: Luitgard A.M. Author-X-Name-Last: Veraart Title: Pricing q-forward contracts: an evaluation of estimation window and pricing method under different mortality models Abstract: The aim of this paper is to study the impact of various sources of uncertainty on the pricing of a special longevity–based instrument: a q$ q $-forward contract. At the expiry of a q$ q $-forward contract, the realized mortality rate for a given population is exchanged in return for a fixed (mortality) rate that is agreed at the initiation of the contract. Pricing a q$ q $-forward involves determining this fixed rate. In our study, we disentangle three main sources of uncertainty and consider their impact on pricing: model choice for the underlying mortality rate, time-window used for estimation and the pricing method itself. Journal: Scandinavian Actuarial Journal Pages: 146-166 Issue: 2 Volume: 2016 Year: 2016 Month: 2 X-DOI: 10.1080/03461238.2014.916228 File-URL: http://hdl.handle.net/10.1080/03461238.2014.916228 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:2:p:146-166 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_917360_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Esbjörn Ohlsson Author-X-Name-First: Esbjörn Author-X-Name-Last: Ohlsson Title: Unallocated loss adjustment expense reserving Abstract: In non-life insurance, the provision for outstanding claims (the claims reserve) should include future loss adjustment expenses, i.e. administrative expenses to settle the claims, and therefore we have to estimate the expected Unallocated Loss Adjustment Expenses (ULAE) – expenses that are not attributable to individual claims, such as salaries at the claims handling department. The ULAE reserve has received little attention from European actuaries in the literature, supposedly because of the lack of detailed data for estimation and evaluation. Having good estimation procedures will, however, become even more important with the introduction of the Solvency II regulations, which require unbiased estimation of future cash flows for all expenses. We present a model for ULAE at the individual claim level that includes both fixed and variable costs. This model leads to an estimate of the ULAE reserve at the aggregate (line-of-business) level, as demonstrated in a numerical example from a Swedish non-life insurer. Journal: Scandinavian Actuarial Journal Pages: 167-180 Issue: 2 Volume: 2016 Year: 2016 Month: 2 X-DOI: 10.1080/03461238.2014.917360 File-URL: http://hdl.handle.net/10.1080/03461238.2014.917360 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:2:p:167-180 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_918696_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: A.Y. Golubin Author-X-Name-First: A.Y. Author-X-Name-Last: Golubin Title: Optimal insurance and reinsurance policies chosen jointly in the individual risk model Abstract: The paper studies the so-called individual risk model where both a policy of per-claim insurance and a policy of reinsurance are chosen jointly by the insurer in order to maximize his/her expected utility. The insurance and reinsurance premiums are defined by the expected value principle. The problem is solved under additional constraints on the reinsurer’s risk and the residual risk of the insured. It is shown that the solution to the problem is the following: The optimal reinsurance is a modification of stop-loss reinsurance policy, so-called stop-loss reinsurance with an upper limit; the optimal insurer’s indemnity is a combination of stop-loss- and deductible policies. The results are illustrated by a numerical example for the case of exponential utility function. The effects of changing model parameters on optimal insurance and reinsurance policies are considered. Journal: Scandinavian Actuarial Journal Pages: 181-197 Issue: 3 Volume: 2016 Year: 2016 Month: 3 X-DOI: 10.1080/03461238.2014.918696 File-URL: http://hdl.handle.net/10.1080/03461238.2014.918696 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:3:p:181-197 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_921639_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peng Shi Author-X-Name-First: Peng Author-X-Name-Last: Shi Title: Insurance ratemaking using a copula-based multivariate Tweedie model Abstract: The Tweedie distribution, featured with a mass probability at zero, is a convenient tool for insurance claims modeling and pure premium determination in general insurance. Motivated by the fact that an insurance policy typically provides multiple types of coverage, we propose a copula-based multivariate Tweedie regression for modeling the semi-continuous claims while accommodating the association among different types. The proposed approach also allows for dispersion modeling, resulting in a multivariate version of the double generalized linear model. We demonstrate the application in insurance ratemaking using a portfolio of policyholders of automobile insurance from the state of Massachusetts in the United States. Journal: Scandinavian Actuarial Journal Pages: 198-215 Issue: 3 Volume: 2016 Year: 2016 Month: 3 X-DOI: 10.1080/03461238.2014.921639 File-URL: http://hdl.handle.net/10.1080/03461238.2014.921639 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:3:p:198-215 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_921640_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tao Jin Author-X-Name-First: Tao Author-X-Name-Last: Jin Author-Name: Serge B. Provost Author-X-Name-First: Serge B. Author-X-Name-Last: Provost Author-Name: Jiandong Ren Author-X-Name-First: Jiandong Author-X-Name-Last: Ren Title: Moment-based density approximations for aggregate losses Abstract: The determination of the distribution of aggregate losses is of crucial importance for an insurer. In this paper, we propose a technique for approximating the distribution of univariate and bivariate aggregate losses, which is solely based on their moments. Accordingly, this methodology can be implemented without any specific knowledge of the claim number or size distributions. The numerical examples presented herein indicate that the proposed approach constitutes a viable alternative to the commonly used recursive and FFT methods. Journal: Scandinavian Actuarial Journal Pages: 216-245 Issue: 3 Volume: 2016 Year: 2016 Month: 3 X-DOI: 10.1080/03461238.2014.921640 File-URL: http://hdl.handle.net/10.1080/03461238.2014.921640 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:3:p:216-245 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_924433_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Paolo De Angelis Author-X-Name-First: Paolo Author-X-Name-Last: De Angelis Author-Name: Antonio Luciano Martire Author-X-Name-First: Antonio Luciano Author-X-Name-Last: Martire Author-Name: Emilio Russo Author-X-Name-First: Emilio Author-X-Name-Last: Russo Title: A bivariate model for evaluating equity-linked policies with surrender option Abstract: This article proposes a bivariate lattice model for evaluating equity-linked policies embedding a surrender option when the underlying equity dynamics is described by a geometric Brownian motion with stochastic interest rate. The main advantage of the model stays in that the original processes for the reference fund and the interest rate are directly discretized by means of lattice approximations, without resorting to any additional transformation. Then, the arising lattices are combined in order to establish a bivariate tree where equity-linked policy premiums are computed by discounting the policy payoff over the lattice branches, and allowing early exercise at each premium payment date to model the surrender decision. Journal: Scandinavian Actuarial Journal Pages: 246-261 Issue: 3 Volume: 2016 Year: 2016 Month: 3 X-DOI: 10.1080/03461238.2014.924433 File-URL: http://hdl.handle.net/10.1080/03461238.2014.924433 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:3:p:246-261 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_924434_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lazhar Benkhelifa Author-X-Name-First: Lazhar Author-X-Name-Last: Benkhelifa Title: Kernel-type estimators for the distortion risk premiums of heavy-tailed distributions Abstract: A new kernel-type estimator for the distortion risk premiums of heavy-tailed losses is introduced. Using a least-squares approach, a bias-reduced version of this estimator is proposed. Under suitable assumptions, the asymptotic normality of the given estimators is established. A small simulation study, to illustrate the performance of our method, is carried out. Journal: Scandinavian Actuarial Journal Pages: 262-278 Issue: 3 Volume: 2016 Year: 2016 Month: 3 X-DOI: 10.1080/03461238.2014.924434 File-URL: http://hdl.handle.net/10.1080/03461238.2014.924434 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:3:p:262-278 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_925496_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Frédéric Planchet Author-X-Name-First: Frédéric Author-X-Name-Last: Planchet Author-Name: Julien Tomas Author-X-Name-First: Julien Author-X-Name-Last: Tomas Title: Uncertainty on survival probabilities and solvency capital requirement: application to long-term care insurance Abstract: In this paper, we focus on uncertainty issues on disabled lives survival probabilities of LTC insurance policyholders and its consequences on solvency capital requirement. Among the risks affecting long-term care portfolios, special attention is addressed to the table risk, i.e. the risk of unanticipated aggregate mortality, arising from the uncertainty in modeling LTC claimants survival law. The table risk can be thought as the risk of systematic deviations referring not only to a parameter risk but, as well, to any other sources leading to a misinterpretation of the life table resulting for example from an evolution of medical techniques or a change in rules of acceptance. In fine, the idea is to introduce the risk of systematic deviations arising from the uncertainty on the disabled lives death probabilities directly. We analyze the consequences of an error of appreciation on the disabled lives survival probabilities in terms of level of reserves and describe a framework in an Own Risk and Solvency Assessment perspective to measure the gap between the risk profile from the standard formula to the risk analysis specific to the organism. Journal: Scandinavian Actuarial Journal Pages: 279-292 Issue: 4 Volume: 2016 Year: 2016 Month: 4 X-DOI: 10.1080/03461238.2014.925496 File-URL: http://hdl.handle.net/10.1080/03461238.2014.925496 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:279-292 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_925967_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Chou-Wen Wang Author-X-Name-First: Chou-Wen Author-X-Name-Last: Wang Author-Name: Hong-Chih Huang Author-X-Name-First: Hong-Chih Author-X-Name-Last: Huang Author-Name: Yung-Tsung Lee Author-X-Name-First: Yung-Tsung Author-X-Name-Last: Lee Title: On the valuation of reverse mortgage insurance Abstract: This article presents a closed-form formula for calculating the loan-to-value (LTV) ratio in an adjusted-rate reverse mortgage (RM) with a lump sum payment. Previous literatures consider the pricing of RM in a constant interest rate assumption and price it on fixed-rate loans. This paper successfully considers the dynamic of interest rate and the adjustable-rate RM simultaneously. This paper also considers the housing price shock into the valuation model. Assuming that house prices follow a jump diffusion process with a stochastic interest rate and that the loan interest rate is adjusted instantaneously according to the short rate, we demonstrate that the LTV ratio is independent of the term structure of interest rates. This argument holds even when housing prices follow a general process: an exponential Lévy process. In addition, the HECM (Home Equity Conversion Mortgage) program may be not sustainable, especially for a higher level of housing price volatility. Finally, when the loan interest rate is adjusted periodically according to the LIBOR rate, our finding reveals that the LTV ratio is insensitive to the parameters characterizing the CIR model. Journal: Scandinavian Actuarial Journal Pages: 293-318 Issue: 4 Volume: 2016 Year: 2016 Month: 4 X-DOI: 10.1080/03461238.2014.925967 File-URL: http://hdl.handle.net/10.1080/03461238.2014.925967 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:293-318 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_926288_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Irmina Czarna Author-X-Name-First: Irmina Author-X-Name-Last: Czarna Title: Parisian ruin probability with a lower ultimate bankrupt barrier Abstract: The paper deals with a ruin problem, where there is a Parisian delay and a lower ultimate bankrupt barrier. In this problem, we will say that a risk process get ruined when it stays below zero longer than a fixed amount of time ζ > 0 or goes below a fixed level −a. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we identify the Laplace transform of the ruin probability in terms of so-called q-scale functions. We find its Cramér-type and convolution-equivalent asymptotics when reserves tends to infinity. Finally, we analyze few explicit examples. Journal: Scandinavian Actuarial Journal Pages: 319-337 Issue: 4 Volume: 2016 Year: 2016 Month: 4 X-DOI: 10.1080/03461238.2014.926288 File-URL: http://hdl.handle.net/10.1080/03461238.2014.926288 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:319-337 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_926977_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Amin Hassan Zadeh Author-X-Name-First: Amin Author-X-Name-Last: Hassan Zadeh Author-Name: David A. Stanford Author-X-Name-First: David A. Author-X-Name-Last: Stanford Title: Bayesian and Bühlmann credibility for phase-type distributions with a univariate risk parameter Abstract: Credibility theory is a statistical tool to calculate the premium for the next period based on past claims experience and the manual rate. Each contract is characterized by a risk parameter. A phase-type (or PH) random variable, which is defined as the time until absorption in a continuous-time Markov chain, is fully characterized by two sets of parameters from that Markov chain: the initial probability vector and transition intensity matrix. In this article, we identify an interpretable univariate risk parameter from amongst the many candidate parameters, by means of uniformization. The resulting density form is then expressed as an infinite mixture of Erlang distributions. These results are used to obtain a tractable likelihood function by a recursive formula. Then the best estimator for the next premium, i.e. the Bayesian premium, as well as its approximation by the Bühlmann credibility premium are calculated. Finally, actuarial calculations for the Bühlmann and Bayesian premiums are investigated in the context of a gamma prior, and illustrated by simulated data in a series of examples. Journal: Scandinavian Actuarial Journal Pages: 338-355 Issue: 4 Volume: 2016 Year: 2016 Month: 4 X-DOI: 10.1080/03461238.2014.926977 File-URL: http://hdl.handle.net/10.1080/03461238.2014.926977 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:338-355 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_928230_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Iain D. Currie Author-X-Name-First: Iain D. Author-X-Name-Last: Currie Title: On fitting generalized linear and non-linear models of mortality Abstract: Many common models of mortality can be expressed compactly in the language of either generalized linear models or generalized non-linear models. The R language provides a description of these models which parallels the usual algebraic definitions but has the advantage of a transparent and flexible model specification. We compare eight model structures for mortality. For each structure, we consider (a) the Poisson models for the force of mortality with both log and logit link functions and (b) the binomial models for the rate of mortality with logit and complementary log–log link functions. Part of this work shows how to extend the usual smooth two-dimensional P-spline model for the force of mortality with Poisson error and log link to the other smooth two-dimensional P-spline models with Poisson and binomial errors defined in (a) and (b). Our comments are based on the results of fitting these models to data from six countries: Australia, France, Japan, Sweden, UK and USA. We also discuss the possibility of forecasting with these models; in particular, the introduction of cohort terms generally leads to an improvement in overall fit, but can also make forecasting with these models problematic. Journal: Scandinavian Actuarial Journal Pages: 356-383 Issue: 4 Volume: 2016 Year: 2016 Month: 4 X-DOI: 10.1080/03461238.2014.928230 File-URL: http://hdl.handle.net/10.1080/03461238.2014.928230 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:356-383 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_936972_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Wuyuan Jiang Author-X-Name-First: Wuyuan Author-X-Name-Last: Jiang Author-Name: Zhaojun Yang Author-X-Name-First: Zhaojun Author-X-Name-Last: Yang Title: The maximum surplus before ruin for dependent risk models through Farlie–Gumbel–Morgenstern copula Abstract: We extend the classical compound Poisson risk model to consider the distribution of the maximum surplus before ruin where the claim sizes depend on inter-claim times via the Farlie–Gumbel–Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for this distribution, of which the Laplace transform is provided. We obtain the renewal equation and explicit expressions for this distribution are derived when the claim amounts are exponentially distributed. Finally, we present numerical examples. Journal: Scandinavian Actuarial Journal Pages: 385-397 Issue: 5 Volume: 2016 Year: 2016 Month: 5 X-DOI: 10.1080/03461238.2014.936972 File-URL: http://hdl.handle.net/10.1080/03461238.2014.936972 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:385-397 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_954606_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Minsuk Kwak Author-X-Name-First: Minsuk Author-X-Name-Last: Kwak Title: Dynamic preferences for popular investment strategies in pension funds Abstract: In this paper, we characterize dynamic investment strategies that are consistent with the expected utility setting and more generally with the forward utility setting. Two popular dynamic strategies in the pension funds industry are used to illustrate our results: a constant proportion portfolio insurance (CPPI) strategy and a life-cycle strategy. For the CPPI strategy, we are able to infer preferences of the pension fund’s manager from her investment strategy, and to exhibit the specific expected utility maximization that makes this strategy optimal at any given time horizon. In the Black–Scholes market with deterministic parameters, we are able to show that traditional life-cycle funds are not optimal to any expected utility maximizers. We also prove that a CPPI strategy is optimal for a fund manager with HARA utility function, while an investor with a SAHARA utility function will choose a time-decreasing allocation to risky assets in the same spirit as the life-cycle funds strategy. Finally, we suggest how to modify these strategies if the financial market follows a more general diffusion process than in the Black–Scholes market. Journal: Scandinavian Actuarial Journal Pages: 398-419 Issue: 5 Volume: 2016 Year: 2016 Month: 5 X-DOI: 10.1080/03461238.2014.954606 File-URL: http://hdl.handle.net/10.1080/03461238.2014.954606 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:398-419 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_954607_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: On the time and the number of claims when the surplus drops below a certain level Abstract: In this paper, we define Tz(u)$ T_{z}(u) $ to be the first time that the surplus process drops below a certain level z$ z $ from the initial surplus u(>z)$ u({>}z) $ for a risk model with interest. A generalized Gerber–Shiu-type function is then defined based on the first time and the number of claims that the surplus drops below z$ z $ from u$ u $, and other Tz(u)$ T_{z}(u) $-related random variables. Explicit expressions for this function, when u=z$ u=z $, and when u>z$ u>z $ under exponential claims, are obtained. We then obtain the moments and probability function (with numerical examples) of the number of claims until Tz(u)$ T_{z}(u) $. We also investigate a joint transform function of the two-sided first exit time and the number of claims until then, and obtain the probability of the surplus hitting an upper level from the initial surplus without having dropped below a lower level with Erlang(2)$ (2) $ claims. Journal: Scandinavian Actuarial Journal Pages: 420-445 Issue: 5 Volume: 2016 Year: 2016 Month: 5 X-DOI: 10.1080/03461238.2014.954607 File-URL: http://hdl.handle.net/10.1080/03461238.2014.954607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:420-445 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_954608_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anna Rita Bacinello Author-X-Name-First: Anna Rita Author-X-Name-Last: Bacinello Author-Name: Pietro Millossovich Author-X-Name-First: Pietro Author-X-Name-Last: Millossovich Author-Name: Alvaro Montealegre Author-X-Name-First: Alvaro Author-X-Name-Last: Montealegre Title: The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours Abstract: In this paper, we present a dynamic programming algorithm for pricing variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) under a general Lévy processes framework. The GMWB gives the policyholder the right to make periodical withdrawals from her policy account even when the value of this account is exhausted. Typically, the total amount guaranteed for withdrawals coincides with her initial investment, providing then a protection against downside market risk. At each withdrawal date, the policyholder has to decide whether, and how much, to withdraw, or to surrender the contract. We show how different policyholder’s withdrawal behaviours can be modelled. We perform a sensitivity analysis comparing the numerical results obtained for different contractual and market parameters, policyholder behaviours and different types of Lévy processes. Journal: Scandinavian Actuarial Journal Pages: 446-465 Issue: 5 Volume: 2016 Year: 2016 Month: 5 X-DOI: 10.1080/03461238.2014.954608 File-URL: http://hdl.handle.net/10.1080/03461238.2014.954608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:446-465 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_955048_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sun-Yong Choi Author-X-Name-First: Sun-Yong Author-X-Name-Last: Choi Author-Name: Jeong-Hoon Kim Author-X-Name-First: Jeong-Hoon Author-X-Name-Last: Kim Title: Equity-linked annuities with multiscale hybrid stochastic and local volatility Abstract: In recent times, hybrid underlying models have become an industry standard for the pricing of derivatives and other problems in finance. This paper chooses a hybrid stochastic and local volatility model to evaluate an equity-linked annuity (ELA), which is a sort of tax-deferred annuity whose credited interest is linked to an equity index. The stochastic volatility component of the hybrid model is driven by a fast mean-reverting diffusion process while the local volatility component is given by the constant elasticity of variance (CEV) model. Since contracts of the ELA usually have long maturities over 10 years, a slowly moving factor in the stochastic volatility of stock index is expected to play a significant role in the valuation of the ELA, and thus, it is added to the aforementioned model. Based on this multiscale hybrid model, an analytic approximate formula is obtained for the price of a European option in terms of the CEV probability density function and then the result is applied to the value of the point-to-point ELA. The formula leads to the dependence structure of the ELA price on the fast and slow scale stochastic volatility and the elasticity of variance. Journal: Scandinavian Actuarial Journal Pages: 466-487 Issue: 5 Volume: 2016 Year: 2016 Month: 5 X-DOI: 10.1080/03461238.2014.955048 File-URL: http://hdl.handle.net/10.1080/03461238.2014.955048 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:466-487 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_963886_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marion Haugen Author-X-Name-First: Marion Author-X-Name-Last: Haugen Author-Name: Tron Anders Moger Author-X-Name-First: Tron Anders Author-X-Name-Last: Moger Title: Frailty modelling of time-to-lapse of single policies for customers holding multiple car contracts Abstract: Corporate customers often hold multiple contracts and this might give dependence between the lapsing times of the single policies. We present a shared gamma frailty model in order to study the time-to-lapse of single car policies for customers holding multiple car contracts with the same insurance company, accounting for measured and time-dependent covariates. Customers with the highest frailty value tend to leave the company earlier than the others and finding these is a central aspect within a company’s customer relationship management strategy. We estimate conditional survival curves which illustrate the decreased survival probability of a customer after a lapse in a single car insurance policy. The individual survival curves are overestimated if the underlying association for cars with the same customer is ignored. Fitting misspecified Cox’s proportional hazards model also results in an underestimation of the standard error of the parameter estimates. Journal: Scandinavian Actuarial Journal Pages: 489-501 Issue: 6 Volume: 2016 Year: 2016 Month: 7 X-DOI: 10.1080/03461238.2014.963886 File-URL: http://hdl.handle.net/10.1080/03461238.2014.963886 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:6:p:489-501 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_971860_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marcus Christian Christiansen Author-X-Name-First: Marcus Christian Author-X-Name-Last: Christiansen Author-Name: Lars Frederik Brandt Henriksen Author-X-Name-First: Lars Frederik Brandt Author-X-Name-Last: Henriksen Author-Name: Kristian Juul Schomacker Author-X-Name-First: Kristian Juul Author-X-Name-Last: Schomacker Author-Name: Mogens Steffensen Author-X-Name-First: Mogens Author-X-Name-Last: Steffensen Title: Stress scenario generation for solvency and risk management Abstract: We derive worst-case scenarios in a life insurance model in the case where the interest rate and the various transition intensities are mutually dependent. Examples of this dependence are that (a) surrender intensities and interest rates are high at the same time, (b) mortality intensities of a policyholder as active and disabled, respectively, are low at the same time, and (c) mortality intensities of the policyholders in a portfolio are low at the same time. The set from which the worst-case scenario is taken reflects the dependence structure and allows us to relate the worst-case scenario-based reserve, qualitatively, to a Value-at-Risk-based calculation of solvency capital requirements. This brings out perspectives for our results in relation to qualifying the standard formula of Solvency II or using a scenario-based approach in internal models. Our results are powerful for various applications and the techniques are non-standard in control theory, exactly because our worst-case scenario is deterministic and not adapted to the stochastic development of the portfolio. The formalistic results are exemplified in a series of numerical studies. Journal: Scandinavian Actuarial Journal Pages: 502-529 Issue: 6 Volume: 2016 Year: 2016 Month: 7 X-DOI: 10.1080/03461238.2014.971860 File-URL: http://hdl.handle.net/10.1080/03461238.2014.971860 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:6:p:502-529 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_977817_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrew Luong Author-X-Name-First: Andrew Author-X-Name-Last: Luong Title: Cramér–Von Mises distance estimation for some positive infinitely divisible parametric families with actuarial applications Abstract: Cramér–Von Mises (CVM) inference techniques are developed for some positive flexible infinitely divisible parametric families generalizing the compound Poisson family. These larger families appear to be useful for parametric inference for positive data. The methods are based on inverting the characteristic functions. They are numerically implementable whenever the characteristic function has a closed form. In general, likelihood methods based on density functions are more difficult to implement. CVM methods also lead to model testing, with test statistics asymptotically following a chi-square distribution. The methods are for continuous models, but they can also handle models with a discontinuity point at the origin such as the case of compound Poisson models. Simulation studies seem to suggest that CVM estimators are more efficient than moment estimators for the common range of the compound Poisson gamma family. Actuarial applications include estimation of the stop loss premium, and estimation of the present value of cash flows when interest rates are assumed to be driven by a corresponding Lévy process. Journal: Scandinavian Actuarial Journal Pages: 530-549 Issue: 6 Volume: 2016 Year: 2016 Month: 7 X-DOI: 10.1080/03461238.2014.977817 File-URL: http://hdl.handle.net/10.1080/03461238.2014.977817 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:6:p:530-549 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_979227_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Wing Yan Lee Author-X-Name-First: Wing Yan Author-X-Name-Last: Lee Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Title: The moments of the time to ruin in dependent Sparre Andersen models with Coxian claim sizes Abstract: A very general class of dependent Sparre Andersen models with Coxian claim sizes (e.g. Landriault et al. 2014) is considered in this paper. The moments of the time to ruin are studied under this class. An analytical form is provided for the moments, which involves solving linear systems of equations. Numerical examples are then considered to further study the properties of the mean and variance of the time to ruin. Journal: Scandinavian Actuarial Journal Pages: 550-564 Issue: 6 Volume: 2016 Year: 2016 Month: 7 X-DOI: 10.1080/03461238.2014.979227 File-URL: http://hdl.handle.net/10.1080/03461238.2014.979227 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:6:p:550-564 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1004802_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yang Yang Author-X-Name-First: Yang Author-X-Name-Last: Yang Author-Name: Kam C. Yuen Author-X-Name-First: Kam C. Author-X-Name-Last: Yuen Title: Asymptotics for a discrete-time risk model with Gamma-like insurance risks Abstract: Consider a discrete-time insurance risk model with insurance and financial risks. Within period i$ i $, the net insurance loss is denoted by Xi$ X_i $ and the stochastic discount factor over the same time period is denoted by Yi$ Y_i $. Assume that {Xi,i≥1}$ \{X_i,\ i \ge 1\} $ form a sequence of independent and identically distributed real-valued random variables with common distribution F$ F $; {Yi,i≥1}$ \{Y_i,\ i \ge 1\} $ are another sequence of independent and identically distributed positive random variables with common distribution G$ G $; and the two sequences are mutually independent. Under the assumptions that F$ F $ is Gamma-like tailed and G$ G $ has a finite upper endpoint, we derive some precise formulas for the tail probability of the present value of aggregate net losses and the finite-time and infinite-time ruin probabilities. As an extension, a dependent risk model is considered, where each random pair of the net loss and the discount factor follows a bivariate Sarmanov distribution. Journal: Scandinavian Actuarial Journal Pages: 565-579 Issue: 6 Volume: 2016 Year: 2016 Month: 7 X-DOI: 10.1080/03461238.2015.1004802 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1004802 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:6:p:565-579 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_987807_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Frank van Berkum Author-X-Name-First: Frank Author-X-Name-Last: van Berkum Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Author-Name: Michel Vellekoop Author-X-Name-First: Michel Author-X-Name-Last: Vellekoop Title: The impact of multiple structural changes on mortality predictions Abstract: Most mortality models proposed in recent literature rely on the standard ARIMA framework (in particular: a random walk with drift) to project mortality rates. As a result the projections are highly sensitive to the calibration period. We therefore analyse the impact of allowing for multiple structural changes on a large collection of mortality models. We find that this may lead to more robust projections for the period effect but that there is only a limited effect on the ranking of the models based on backtesting criteria, since there is often not yet sufficient statistical evidence for structural changes. However, there are cases for which we do find improvements in estimates and we therefore conclude that one should not exclude on beforehand that structural changes may have occurred. Journal: Scandinavian Actuarial Journal Pages: 581-603 Issue: 7 Volume: 2016 Year: 2016 Month: 8 X-DOI: 10.1080/03461238.2014.987807 File-URL: http://hdl.handle.net/10.1080/03461238.2014.987807 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:7:p:581-603 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_991423_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ulrich Riegel Author-X-Name-First: Ulrich Author-X-Name-Last: Riegel Title: Bifurcation of attritional and large losses in an additive IBNR environment Abstract: In certain segments, IBNR calculations on paid triangles are more stable than on incurred triangles. However, calculations on payments often do not adequately take large losses into account. An IBNR method which separates large and attritional losses and thus allows to use payments for the attritional and incurred amounts for the large losses has been introduced by Riegel (see Riegel, U. (2014). A bifurcation approach for attritional and large losses in chain ladder calculations. Astin Bulletin 44, 127–172). The method corresponds to a stochastic model that is based on Mack’s chain ladder model. In this paper, we analyse a quasi-additive version of this model, i.e. a version which is in essence based on the assumptions of the additive (or incremental loss ratio) method. We describe the corresponding IBNR method and derive formulas for the mean squared error of prediction. Journal: Scandinavian Actuarial Journal Pages: 604-623 Issue: 7 Volume: 2016 Year: 2016 Month: 8 X-DOI: 10.1080/03461238.2014.991423 File-URL: http://hdl.handle.net/10.1080/03461238.2014.991423 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:7:p:604-623 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_994025_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Title: Optimal reinsurance with expectile Abstract: In this paper, we study optimal reinsurance treaties that minimize the liability of an insurer. The liability is defined as the actuarial reserve on an insurer’s risk exposure plus the risk margin required for the risk exposure. The risk margin is determined by the risk measure of expectile. Among a general class of reinsurance premium principles, we prove that a two-layer reinsurance treaty is optimal. Furthermore, if a reinsurance premium principle in the class is translation invariant or is the expected value principle, we show that a one-layer reinsurance treaty is optimal. Moreover, we use the expected value premium principle and Wang’s premium principle to demonstrate how the parameters in an optimal reinsurance treaty can be determined explicitly under a given premium principle. Journal: Scandinavian Actuarial Journal Pages: 624-645 Issue: 7 Volume: 2016 Year: 2016 Month: 8 X-DOI: 10.1080/03461238.2014.994025 File-URL: http://hdl.handle.net/10.1080/03461238.2014.994025 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:7:p:624-645 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1048710_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xiang Lin Author-X-Name-First: Xiang Author-X-Name-Last: Lin Author-Name: Yiping Qian Author-X-Name-First: Yiping Author-X-Name-Last: Qian Title: Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model Abstract: We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk 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 stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary. Journal: Scandinavian Actuarial Journal Pages: 646-671 Issue: 7 Volume: 2016 Year: 2016 Month: 8 X-DOI: 10.1080/03461238.2015.1048710 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1048710 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:7:p:646-671 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_996248_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vsevolod K. Malinovskii Author-X-Name-First: Vsevolod K. Author-X-Name-Last: Malinovskii Title: How an aggressively expanding insurance company becomes insolvent Abstract: This paper aims to model a rational firm expanding on a regulated competitive insurance market. While the market is profitable, an aggressive price cut makes the firm’s market shares and revenue climb due to immigration of insureds. But the revenue’s growth may be slower than the growth in reserves needed to maintain the annual probabilities of ruin equal to a legally predetermined value. It will result in a progressive run-out of the funds allocated for the company’s strategic growth and is fraught with inability to meet the legal solvency requirements. Journal: Scandinavian Actuarial Journal Pages: 673-691 Issue: 8 Volume: 2016 Year: 2016 Month: 9 X-DOI: 10.1080/03461238.2014.996248 File-URL: http://hdl.handle.net/10.1080/03461238.2014.996248 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:8:p:673-691 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1007891_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Daniel H. Alai Author-X-Name-First: Daniel H. Author-X-Name-Last: Alai 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: Multivariate Tweedie lifetimes: the impact of dependence Abstract: Systematic longevity risk is increasingly relevant for public pension schemes and insurance companies that provide life benefits. In view of this, mortality models should incorporate dependence between lives. However, the independent lifetime assumption is still heavily relied upon in the risk management of life insurance and annuity portfolios. This paper applies a multivariate Tweedie distribution to incorporate dependence, which it induces through a common shock component. Model parameter estimation is developed based on the method of moments and generalized to allow for truncated observations. The estimation procedure is explicitly developed for various important distributions belonging to the Tweedie family, and finally assessed using simulation. Journal: Scandinavian Actuarial Journal Pages: 692-712 Issue: 8 Volume: 2016 Year: 2016 Month: 9 X-DOI: 10.1080/03461238.2015.1007891 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1007891 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:8:p:692-712 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1012223_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Edgars Jakobsons Author-X-Name-First: Edgars Author-X-Name-Last: Jakobsons Author-Name: Xiaoying Han Author-X-Name-First: Xiaoying Author-X-Name-Last: Han Author-Name: Ruodu Wang Author-X-Name-First: Ruodu Author-X-Name-Last: Wang Title: General convex order on risk aggregation Abstract: Using a general notion of convex order, we derive general lower bounds for risk measures of aggregated positions under dependence uncertainty, and this in arbitrary dimensions and for heterogeneous models. We also prove sharpness of the bounds obtained when each marginal distribution has a decreasing density. The main result answers a long-standing open question and yields an insight in optimal dependence structures. A numerical algorithm provides bounds for quantities of interest in risk management. Furthermore, our numerical results suggest that the bounds obtained in this paper are generally sharp for a broader class of models. Journal: Scandinavian Actuarial Journal Pages: 713-740 Issue: 8 Volume: 2016 Year: 2016 Month: 9 X-DOI: 10.1080/03461238.2015.1012223 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1012223 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:8:p:713-740 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1015161_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Shangzhen Luo Author-X-Name-First: Shangzhen Author-X-Name-Last: Luo Author-Name: Mingming Wang Author-X-Name-First: Mingming Author-X-Name-Last: Wang Author-Name: Xudong Zeng Author-X-Name-First: Xudong Author-X-Name-Last: Zeng Title: Optimal reinsurance: minimize the expected time to reach a goal Abstract: In this paper, we consider an optimal reinsurance problem. The surplus model of the insurance company is approximated by a diffusion model with the drift coefficient μ$ \mu $. The insurance company employs reinsurance to reduce the risk. π$ \pi $ is the proportion of each claim paid by the company and the remainder proportion of the claim is paid by the reinsurer. λ(1-π)$ \lambda (1-\pi ) $ is the rate at which the premiums are diverted to the reinsurer, thus it holds λ≥μ>0$ \lambda \ge \mu >0 $ in general. We discuss two cases: (i) non-cheap reinsurance (when λ>μ$ \lambda >\mu $), (ii) cheap reinsurance (when λ=μ$ \lambda =\mu $). The objective of the insurance company is to make an optimal decision on reinsurance to reach a goal (a given surplus level) in minimal expected time. We disclose that for some case it is not suitable to search optimal decisions by minimizing the expected time to reach a goal. In order to deal with this case, we study two other methodologies (ruin probability minimization and expected discount factor maximization) for the optimal strategy selection problem in reinsurance decision. Journal: Scandinavian Actuarial Journal Pages: 741-762 Issue: 8 Volume: 2016 Year: 2016 Month: 9 X-DOI: 10.1080/03461238.2015.1015161 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1015161 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:8:p:741-762 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1020856_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M.C. Christiansen Author-X-Name-First: M.C. Author-X-Name-Last: Christiansen Author-Name: M.A. Fahrenwaldt Author-X-Name-First: M.A. Author-X-Name-Last: Fahrenwaldt Title: Dynamics of solvency risk in life insurance liabilities Abstract: We describe the time dynamics of the solvency level of life insurance contracts by representing the solvency level and the underlying risk sources as the solution of a forward–backward system. This leads to an additive decomposition of the total solvency level with respect to time and different risk sources. The decomposition turns out to be an intuitive tool to study risk sensitivities. We study the forward–backward system and discuss two methods to obtain explicit representations: via linear partial differential equations and via a Monte Carlo method based on Malliavin calculus. Journal: Scandinavian Actuarial Journal Pages: 763-792 Issue: 9 Volume: 2016 Year: 2016 Month: 10 X-DOI: 10.1080/03461238.2015.1020856 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1020856 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:9:p:763-792 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1025822_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xudong Zeng Author-X-Name-First: Xudong Author-X-Name-Last: Zeng Author-Name: James M. Carson Author-X-Name-First: James M. Author-X-Name-Last: Carson Author-Name: Qihong Chen Author-X-Name-First: Qihong Author-X-Name-Last: Chen Author-Name: Yuling Wang Author-X-Name-First: Yuling Author-X-Name-Last: Wang Title: Optimal life insurance with no-borrowing constraints: duality approach and example Abstract: We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT. Journal: Scandinavian Actuarial Journal Pages: 793-816 Issue: 9 Volume: 2016 Year: 2016 Month: 10 X-DOI: 10.1080/03461238.2015.1025822 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1025822 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:9:p:793-816 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1034763_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Enrique Calderín-Ojeda Author-X-Name-First: Enrique Author-X-Name-Last: Calderín-Ojeda Author-Name: Chun Fung Kwok Author-X-Name-First: Chun Fung Author-X-Name-Last: Kwok Title: Modeling claims data with composite Stoppa models Abstract: In this paper, a new class of composite model is proposed for modeling actuarial claims data of mixed sizes. The model is developed using the Stoppa distribution and a mode-matching procedure. The use of the Stoppa distribution allows for more flexibility over the thickness of the tail, and the mode-matching procedure gives a simple derivation of the model compositing with a variety of distributions. In particular, the Weibull–Stoppa and the Lognormal–Stoppa distributions are investigated. Their performance is compared with existing composite models in the context of the well-known Danish fire insurance data-set. The results suggest the composite Weibull–Stoppa model outperforms the existing composite models in all seven goodness-of-fit measures considered. Journal: Scandinavian Actuarial Journal Pages: 817-836 Issue: 9 Volume: 2016 Year: 2016 Month: 10 X-DOI: 10.1080/03461238.2015.1034763 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1034763 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:9:p:817-836 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1046087_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Løchte Jørgensen Author-X-Name-First: Peter Løchte Author-X-Name-Last: Jørgensen Author-Name: Søren Kærgaard Slipsager Author-X-Name-First: Søren Kærgaard Author-X-Name-Last: Slipsager Title: An analysis of a three-factor model proposed by the Danish Society of Actuaries for forecasting and risk analysis Abstract: This paper provides the explicit solution to the three-factor diffusion model recently proposed by the Danish Society of Actuaries to the Danish industry of life insurance and pensions. The solution is obtained by use of the known general solution to multidimensional linear stochastic differential equation systems. With offset in the explicit solution, we establish the conditional distribution of the future state variables which allows for exact simulation. Using exact simulation, we illustrate how simulation of the system can be improved compared to a standard Euler scheme. In order to analyze the effect of choosing the exact simulation scheme over the traditional Euler approximation scheme frequently applied by practitioners, we carry out a simulation study. We show that due to its recursive nature, the Euler scheme becomes computationally expensive as it requires a small step size in order to minimize discretization errors. Using our exact simulation scheme, one is able to cut these computational costs significantly and obtain even better forecasts. As probability density tail behavior is key to expected investment portfolio performance, we further conduct a risk analysis in which we compare well-known risk measures under both schemes. Finally, we conduct a sensitivity analysis and find that the relative performance of the two schemes depends on the chosen model parameter estimates. Journal: Scandinavian Actuarial Journal Pages: 837-857 Issue: 9 Volume: 2016 Year: 2016 Month: 10 X-DOI: 10.1080/03461238.2015.1046087 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1046087 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2016:y:2016:i:9:p:837-857 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1054303_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Author-Name: Ambrose Lo Author-X-Name-First: Ambrose Author-X-Name-Last: Lo Title: Characterizations of optimal reinsurance treaties: a cost-benefit approach Abstract: This article investigates optimal reinsurance treaties minimizing an insurer’s risk-adjusted liability, which encompasses a risk margin quantified by distortion risk measures. Via the introduction of a transparent cost-benefit argument, we extend the results in Cui et al. [Cui, W., Yang, J. & Wu, L. (2013). Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles. Insurance: Mathematics and Economics 53, 74–85] and provide full characterizations on the set of optimal reinsurance treaties within the class of non-decreasing, 1-Lipschitz functions. Unlike conventional studies, our results address the issue of (non-)uniqueness of optimal solutions and indicate that ceded loss functions beyond the traditional insurance layers can be optimal in some cases. The usefulness of our novel cost-benefit approach is further demonstrated by readily solving the dual problem of minimizing the reinsurance premium while maintaining the risk-adjusted liability below a fixed tolerance level. Journal: Scandinavian Actuarial Journal Pages: 1-28 Issue: 1 Volume: 2017 Year: 2017 Month: 1 X-DOI: 10.1080/03461238.2015.1054303 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1054303 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:1:p:1-28 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1058854_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Franck Adékambi Author-X-Name-First: Franck Author-X-Name-Last: Adékambi Author-Name: Marcus C. Christiansen Author-X-Name-First: Marcus C. Author-X-Name-Last: Christiansen Title: Integral and differential equations for the moments of multistate models in health insurance Abstract: The moments of the random future liabilities of health insurance policies are key quantities for studying distributional properties of the future liabilities. Assuming that the randomness of the future health status of individual policyholders can be described by a semi-Markovian multistate model, integral and differential equations are derived for moments of any order and for the moment generating function. Different representations are derived and discussed with a view to numerical solution methods. Journal: Scandinavian Actuarial Journal Pages: 29-50 Issue: 1 Volume: 2017 Year: 2017 Month: 1 X-DOI: 10.1080/03461238.2015.1058854 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1058854 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:1:p:29-50 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1062042_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Author-Name: Eric C.K. Cheung Author-X-Name-First: Eric C.K. Author-X-Name-Last: Cheung Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Lévy insurance risk process with Poissonian taxation Abstract: The idea of taxation in risk process was first introduced by Albrecher, H. & Hipp, C. Lundberg’s risk process with tax. Blätter der DGVFM 28(1), 13–28, who suggested that a certain proportion of the insurer’s income is paid immediately as tax whenever the surplus process is at its running maximum. In this paper, a spectrally negative Lévy insurance risk model under taxation is studied. Motivated by the concept of randomized observations proposed by Albrecher, H., Cheung, E.C.K. & Thonhauser, S. Randomized observation periods for the compound Poisson risk model: Dividends. ASTIN Bulletin 41(2), 645–672, we assume that the insurer’s surplus level is only observed at a sequence of Poisson arrival times, at which the event of ruin is checked and tax may be collected from the tax authority. In particular, if the observed (pre-tax) level exceeds the maximum of the previously observed (post-tax) values, then a fraction of the excess will be paid as tax. Analytic expressions for the Gerber–Shiu expected discounted penalty function and the expected discounted tax payments until ruin are derived. The Cramér-Lundberg asymptotic formula is shown to hold true for the Gerber–Shiu function, and it differs from the case without tax by a multiplicative constant. Delayed start of tax payments will be discussed as well. We also take a look at the case where solvency is monitored continuously (while tax is still paid at Poissonian time points), as many of the above results can be derived in a similar manner. Some numerical examples will be given at the end. Journal: Scandinavian Actuarial Journal Pages: 51-87 Issue: 1 Volume: 2017 Year: 2017 Month: 1 X-DOI: 10.1080/03461238.2015.1062042 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1062042 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:1:p:51-87 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1084945_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Title: Tail mutual exclusivity and Tail-VaR lower bounds Abstract: In this paper, we extend the concept of mutual exclusivity proposed by [Dhaene, J. & Denuit, M. (1999). The safest dependence structure among risks. Insurance: Mathematics and Economics 25, 11–21] to its tail counterpart and baptize this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency structure, at most one exceedance over the corresponding Value-at-Risks (VaRs) is possible, the other components being zero in such a case. No condition is imposed when all components stay below the VaRs. Several properties of this new negative dependence concept are derived. We show that this dependence structure gives rise to the smallest value of Tail-VaR (TVaR) of a sum of risks within a given Fréchet space, provided that the probability level of the TVaR is close enough to one. Journal: Scandinavian Actuarial Journal Pages: 88-104 Issue: 1 Volume: 2017 Year: 2017 Month: 1 X-DOI: 10.1080/03461238.2015.1084945 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1084945 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:1:p:88-104 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1258370_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Javier Pla-Porcel Author-X-Name-First: Javier Author-X-Name-Last: Pla-Porcel Author-Name: Manuel Ventura-Marco Author-X-Name-First: Manuel Author-X-Name-Last: Ventura-Marco Author-Name: Carlos Vidal-Meliá Author-X-Name-First: Carlos Author-X-Name-Last: Vidal-Meliá Title: Converting retirement benefit into a life care annuity with graded benefits Abstract: This paper deals with life care annuities, i.e. bundled products comprising a life annuity and long-term care insurance. It aims to assess the cost of converting retirement benefit into a life care annuity with graded benefits using a pre-existing public pay-as-you-go pension scheme. With this objective in mind, we present an actuarial method based on array calculus for valuing this type of life care annuity. The health dynamics of the annuitant rely on a reversible illness-death multistate framework. The paper contains a numerical example in which mortality and disability assumptions are based on data from the USA and Australia, although this should be viewed simply as an illustration. In addition, in order to check the coherence of these data, we compute life expectancy for both healthy and dependent persons, and then for dependent persons in each of the states of dependence. The effect of ruling out the recovery assumption on the annuity’s cost is also assessed. The analysis provides valuable insights into how much it would cost to introduce these annuities and enables us to make some policy recommendations to help ensure that this combined pension scheme has a good actuarial design. Journal: Scandinavian Actuarial Journal Pages: 829-853 Issue: 10 Volume: 2017 Year: 2017 Month: 11 X-DOI: 10.1080/03461238.2016.1258370 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1258370 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:10:p:829-853 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1261734_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Irmina Czarna Author-X-Name-First: Irmina Author-X-Name-Last: Czarna Author-Name: Zbigniew Palmowski Author-X-Name-First: Zbigniew Author-X-Name-Last: Palmowski Author-Name: Przemysław Świa̧tek Author-X-Name-First: Przemysław Author-X-Name-Last: Świa̧tek Title: Discrete time ruin probability with Parisian delay Abstract: In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time d>0$ d>0 $. We identify expressions for the ruin probabilities within finite and infinite-time horizon. We also find their light and heavy-tailed asymptotics when initial reserves approach infinity. Finally, we calculate these probabilities for a few explicit examples. Journal: Scandinavian Actuarial Journal Pages: 854-869 Issue: 10 Volume: 2017 Year: 2017 Month: 11 X-DOI: 10.1080/03461238.2016.1261734 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1261734 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:10:p:854-869 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1263236_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kris Peremans Author-X-Name-First: Kris Author-X-Name-Last: Peremans Author-Name: Pieter Segaert Author-X-Name-First: Pieter Author-X-Name-Last: Segaert Author-Name: Stefan Van Aelst Author-X-Name-First: Stefan Author-X-Name-Last: Van Aelst Author-Name: Tim Verdonck Author-X-Name-First: Tim Author-X-Name-Last: Verdonck Title: Robust bootstrap procedures for the chain-ladder method Abstract: Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures. Journal: Scandinavian Actuarial Journal Pages: 870-897 Issue: 10 Volume: 2017 Year: 2017 Month: 11 X-DOI: 10.1080/03461238.2016.1263236 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1263236 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:10:p:870-897 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1268541_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Title: Estimating the Gerber–Shiu function by Fourier–Sinc series expansion Abstract: In this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier–Sinc series expansion. Our estimator is easily computed and has a faster convergence rate. Some simulation examples are provided to show that the estimator performs well when the sample size is finite. Journal: Scandinavian Actuarial Journal Pages: 898-919 Issue: 10 Volume: 2017 Year: 2017 Month: 11 X-DOI: 10.1080/03461238.2016.1268541 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1268541 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:10:p:898-919 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1090476_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghobad Barmalzan Author-X-Name-First: Ghobad Author-X-Name-Last: Barmalzan Author-Name: Amir T. Payandeh Najafabadi Author-X-Name-First: Amir T. Author-X-Name-Last: Payandeh Najafabadi Author-Name: Narayanaswamy Balakrishnan Author-X-Name-First: Narayanaswamy Author-X-Name-Last: Balakrishnan Title: Ordering properties of the smallest and largest claim amounts in a general scale model Abstract: Suppose Xλ1,…,Xλn$ X_{\lambda _1},\ldots ,X_{\lambda _n} $ is a set of non-negative random variables with Xλi$ X_{\lambda _i} $ having the distribution function G(λit)$ G(\lambda _i\, t) $, λi>0$ \lambda _i>0 $ for i=1,…,n,$ i=1,\ldots ,n, $ and Ip1,…,Ipn$ I_{p_1},\ldots ,I_{p_n} $ are independent Bernoulli random variables, independent of the Xλi$ X_{\lambda _i} $’s, with E(Ipi)=pi$ E(I_{p_i})=p_i $, i=1,…,n$ i=1,\ldots ,n $. Let Yi=IpiXλi$ Y_{i}=I_{p_i} X_{\lambda _i} $, for i=1,…,n$ i=1, \ldots , n $. It is of interest to note that in actuarial science, Yi$ Y_{i} $ corresponds to the claim amount in a portfolio of risks. In this paper, under certain conditions, by using the concept of vector majorization and related orders, we discuss stochastic comparison between the smallest claim amount in the sense of the usual stochastic and hazard rate orders. We also obtain the usual stochastic order between the largest claim amounts when the matrix of parameters (h(p),λ)$ ({\boldsymbol{h(p)}}, {\boldsymbol{\lambda }}) $ changes to another matrix in a mathematical sense. We then apply the results for three special cases of the scale model: generalized gamma, Marshall–Olkin extended exponential and exponentiated Weibull distributions with possibly different scale parameters to illustrate the established results. Journal: Scandinavian Actuarial Journal Pages: 105-124 Issue: 2 Volume: 2017 Year: 2017 Month: 2 X-DOI: 10.1080/03461238.2015.1090476 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1090476 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:2:p:105-124 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1092168_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Joelle H. Fong Author-X-Name-First: Joelle H. Author-X-Name-Last: Fong Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: James Yap Author-X-Name-First: James Author-X-Name-Last: Yap Title: Forecasting disability: application of a frailty model Abstract: Random changes in individual frailty occur due to the stochastic processes of physical deterioration or environmental influences. This paper implements a stochastic ageing model using maximum likelihood methods and calibrates the model to more than 30 years of historical Australian mortality data in order to examine cohort and gender differences in health-state distributions among older adults. We find that frailty levels have declined over time for both male and female cohorts. Nonetheless, patterns of frailty are different between genders. Older females experience a faster pace of health deterioration than their male counterparts causing them to move quicker into worse states of health. Health states are also more heterogeneous among women than men. Population-level estimates suggest that the number of elderly Australians requiring aged care services will exceed that projected under governmental assumptions by 2050. Journal: Scandinavian Actuarial Journal Pages: 125-147 Issue: 2 Volume: 2017 Year: 2017 Month: 2 X-DOI: 10.1080/03461238.2015.1092168 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1092168 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:2:p:125-147 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1094403_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lluís Bermúdez Author-X-Name-First: Lluís Author-X-Name-Last: Bermúdez Author-Name: Dimitris Karlis Author-X-Name-First: Dimitris Author-X-Name-Last: Karlis Title: A posteriori ratemaking using bivariate Poisson models Abstract: Recently, different bivariate Poisson regression models have been used in the actuarial literature to make an a priori ratemaking taking into account the dependence between two types of claims. A natural extension for these models is to consider a posteriori ratemaking (i.e. experience rating models) that also relaxes the independence assumption. We introduce here two bivariate experience rating models that integrate the a priori ratemaking based on the bivariate Poisson regression models, extending the existing literature for the univariate case to the bivariate case. These bivariate experience rating models are applied to an automobile insurance claims data-set to analyse the consequences for posterior premiums when the independence assumption is relaxed. The main finding is that the a posteriori risk factors obtained with the bivariate experience rating models are significantly lower than those factors derived under the independence assumption. Journal: Scandinavian Actuarial Journal Pages: 148-158 Issue: 2 Volume: 2017 Year: 2017 Month: 2 X-DOI: 10.1080/03461238.2015.1094403 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1094403 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:2:p:148-158 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1094404_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ionica Cojocaru Author-X-Name-First: Ionica Author-X-Name-Last: Cojocaru Title: Ruin probabilities in multivariate risk models with periodic common shock Abstract: We propose a multidimensional risk model where the common shock affecting all classes of insurance business is arriving according to a non-homogeneous periodic Poisson process. In this multivariate setting, we derive upper bounds of Lundberg-type for the probability that ruin occurs in all classes simultaneously using the martingale approach via piecewise deterministic Markov processes theory. These results are numerically illustrated in a bivariate risk model, where the beta-shape periodic claim intensity function is considered. Under the assumption of dependent heavy-tailed claims, asymptotic bounds for the finite-time ruin probabilities associated to three types of ruin in this multivariate framework are investigated. Journal: Scandinavian Actuarial Journal Pages: 159-174 Issue: 2 Volume: 2017 Year: 2017 Month: 2 X-DOI: 10.1080/03461238.2015.1094404 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1094404 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:2:p:159-174 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1095793_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: Joelle H. Fong Author-X-Name-First: Joelle H. Author-X-Name-Last: Fong Title: Product pricing and solvency capital requirements for long-term care insurance Abstract: This paper presents a comprehensive assessment of premiums, reserves and solvency capital requirements (SCRs) for long-term care (LTC) insurance policies using Activities of Daily Living and US data. We compare stand-alone policies, whole life insurance policies with LTC benefit riders (LTC insurance combined with whole life insurance), life care annuities (LTC insurance combined with annuities) and shared LTC insurance in terms of net premium cost and SCRs. Net premiums and best-estimate reserves for base LTC insurance policies are determined using Thiele’s differential equation. Product features such as the elimination period and the maximum benefit period are compared using a simulation-based model. We show how a maximum benefit period can reduce costs and risks for LTC insurance products. SCRs for longevity risk and disability risk are based on the Solvency II standard formula. We quantify the extent to which whole life insurance policies with LTC benefit riders and life care annuities provide lower SCRs than stand-alone LTC insurance policies. Journal: Scandinavian Actuarial Journal Pages: 175-208 Issue: 2 Volume: 2017 Year: 2017 Month: 2 X-DOI: 10.1080/03461238.2015.1095793 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1095793 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:2:p:175-208 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1102167_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: José Da Fonseca Author-X-Name-First: José Author-X-Name-Last: Da Fonseca Author-Name: Jonathan Ziveyi Author-X-Name-First: Jonathan Author-X-Name-Last: Ziveyi Title: Valuing variable annuity guarantees on multiple assets Abstract: Guarantees embedded variable annuity contracts exhibit option-like payoff features and the pricing of such instruments naturally leads to risk neutral valuation techniques. This paper considers the pricing of two types of guarantees; namely, the Guaranteed Minimum Maturity Benefit and the Guaranteed Minimum Death Benefit riders written on several underlying assets whose dynamics are given by affine stochastic processes. Within the standard affine framework for the underlying mortality risk, stochastic volatility and correlation risk, we develop the key ingredients to perform the pricing of such guarantees. The model implies that the corresponding characteristic function for the state variables admits a closed form expression. We illustrate the methodology for two possible payoffs for the guarantees leading to prices that can be obtained through numerical integration. Using typical values for the parameters, an implementation of the model is provided and underlines the significant impact of the assets’ correlation structure on the guarantee prices. Journal: Scandinavian Actuarial Journal Pages: 209-230 Issue: 3 Volume: 2017 Year: 2017 Month: 3 X-DOI: 10.1080/03461238.2015.1102167 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1102167 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:3:p:209-230 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1119716_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Costabile Author-X-Name-First: M. Author-X-Name-Last: Costabile Title: A lattice-based model to evaluate variable annuities with guaranteed minimum withdrawal benefits under a regime-switching model Abstract: We consider the problem of evaluating variable annuities with a guaranteed minimum withdrawal benefit under a regime-switching model. We propose a trinomial lattice model to approximate the evolution of the investment fund value and the policy value at inception is computed through a backward induction scheme. Finally, the insurance fee is computed as the solution of the equation that makes the contract actuarially fair. Numerical results are reported to illustrate the consistency of the proposed model. Journal: Scandinavian Actuarial Journal Pages: 231-244 Issue: 3 Volume: 2017 Year: 2017 Month: 3 X-DOI: 10.1080/03461238.2015.1119716 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1119716 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:3:p:231-244 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1119717_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Giovanni Puccetti Author-X-Name-First: Giovanni Author-X-Name-Last: Puccetti Author-Name: Ludger Rüschendorf Author-X-Name-First: Ludger Author-X-Name-Last: Rüschendorf Author-Name: Daniel Small Author-X-Name-First: Daniel Author-X-Name-Last: Small Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Title: Reduction of Value-at-Risk bounds via independence and variance information Abstract: We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and independence among (some) subgroups of the marginal components is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. When the variance of the joint portfolio loss is small enough, further improvements can be obtained. Journal: Scandinavian Actuarial Journal Pages: 245-266 Issue: 3 Volume: 2017 Year: 2017 Month: 3 X-DOI: 10.1080/03461238.2015.1119717 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1119717 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:3:p:245-266 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1123174_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Bin Li Author-X-Name-First: Bin Author-X-Name-Last: Li Author-Name: Shu Li Author-X-Name-First: Shu Author-X-Name-Last: Li Title: Drawdown analysis for the renewal insurance risk process Abstract: In this paper, we study some drawdown-related quantities in the context of the renewal insurance risk process with general interarrival times and phase-type distributed jump sizes. We make use of some recent results on the two-sided exit problem for the spectrally negative Markov additive process and a fluid flow analogy between certain queues and risk processes to solve for the two-sided exit problem of the renewal insurance risk process. The two-sided exit quantities are later shown to be central to the analysis of drawdown quantities including the drawdown time, the drawdown size, the running maximum (minimum) at the drawdown time, the last running maximum time prior to drawdown, the number of jumps before drawdown and the number of excursions from running maximum before drawdown. Finally, we consider another application of our methodology for the study of the expected discounted dividend payments until ruin. Journal: Scandinavian Actuarial Journal Pages: 267-285 Issue: 3 Volume: 2017 Year: 2017 Month: 3 X-DOI: 10.1080/03461238.2015.1123174 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1123174 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:3:p:267-285 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1126343_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Pierre Devolder Author-X-Name-First: Pierre Author-X-Name-Last: Devolder Author-Name: Adrien Lebègue Author-X-Name-First: Adrien Author-X-Name-Last: Lebègue Title: Iterated VaR or CTE measures: A false good idea? Abstract: The purpose of this paper is twofold. Firstly, we consider different risk measures in order to determine the solvency capital requirement of a pension fund. Secondly, we illustrate the impact of the time horizon of long-term guarantee products on these capital. We consider a financial market modelled by a common Black–Scholes–Merton model. We neglect the mortality and underwriting risks by assuming that the pension fund is fully hedged against these risks, which allows us to keep understandable and tractable formulæ (the longevity risk will be a part of future researches). A portfolio is built in this market according to different strategies and the pension fund offers a fixed guaranteed rate on a certain time horizon. We begin with well-known static risk measures (value at risk and conditional tail expectation measures) and then we consider their natural dynamic generalization. In order to be time consistent, we consider their iterated versions by a backward iterations scheme. Within the dynamic setting, we show that solvency capital can be expensive and that attention must be paid to the safety level considered. Journal: Scandinavian Actuarial Journal Pages: 287-318 Issue: 4 Volume: 2017 Year: 2017 Month: 4 X-DOI: 10.1080/03461238.2015.1126343 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1126343 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:4:p:287-318 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1133450_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vasil Enchev Author-X-Name-First: Vasil Author-X-Name-Last: Enchev 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: Multi-population mortality models: fitting, forecasting and comparisons Abstract: We review a number of multi-population mortality models: variations of the Li & Lee model, and the common-age-effect (CAE) model of Kleinow. Model parameters are estimated using maximum likelihood. Although this introduces some challenging identifiability problems and complicates the estimation process it allows a fair comparison of the different models. We propose to solve these identifiability problems by applying two-dimensional constraints over the parameters. Using data from six countries, we compare and rank, both visually and numerically, the models’ fitting qualities and develop forecasting models that produce non-diverging, joint mortality rate scenarios. It is found that the CAE model fits best. But we also find that the Li and Lee model potentially suffers from robustness problems when calibrated using maximum likelihood. Journal: Scandinavian Actuarial Journal Pages: 319-342 Issue: 4 Volume: 2017 Year: 2017 Month: 4 X-DOI: 10.1080/03461238.2015.1133450 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1133450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:4:p:319-342 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1134636_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Clemente De Rosa Author-X-Name-First: Clemente Author-X-Name-Last: De Rosa Author-Name: Elisa Luciano Author-X-Name-First: Elisa Author-X-Name-Last: Luciano Author-Name: Luca Regis Author-X-Name-First: Luca Author-X-Name-Last: Regis Title: Basis risk in static versus dynamic longevity-risk hedging Abstract: This paper provides a tractable, parsimonious model for assessing basis risk in longevity and its effect on the hedging strategies of Pension Funds and annuity providers. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population’s longevity. The paper sets out the static, full and customized swap-hedge for an annuity, and compares it with a dynamic, partial, and index-based hedge. We calibrate our model to the UK and Scottish populations. The effectiveness of static versus dynamic strategies depends on the rebalancing frequency of the second, on the relative costs, and on basis risk, which does not affect fully-customized, static hedges. We show that appropriately calibrated dynamic hedging strategies can still be reasonably effective, even at low rebalancing frequencies. Journal: Scandinavian Actuarial Journal Pages: 343-365 Issue: 4 Volume: 2017 Year: 2017 Month: 4 X-DOI: 10.1080/03461238.2015.1134636 File-URL: http://hdl.handle.net/10.1080/03461238.2015.1134636 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:4:p:343-365 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1148627_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nicolino Ettore D’Ortona Author-X-Name-First: Nicolino Ettore Author-X-Name-Last: D’Ortona Author-Name: Gabriella Marcarelli Author-X-Name-First: Gabriella Author-X-Name-Last: Marcarelli Title: Optimal proportional reinsurance from the point of view of cedent and reinsurer Abstract: In the reinsurance market, the cedent and the reinsurer make their subjective evaluations of the utility and riskiness of the financial operations covered by a treaty by deriving preference rankings of the different kinds of agreements. If both the cedent and the reinsurer evaluate the operation underlying the treaty by means of their utility functions and adopt the criterion based on the comparison between the expected utilities in order to take into account the subjective attitude toward risk, then the indifference prices play a crucial role because they define the preference thresholds of the exchange, thus restricting the range of variability of the reinsurance price. By using an analytical approach, this paper examines the above problem identifying the margins for achieving Pareto-optimal solutions in trading insurance risks. Journal: Scandinavian Actuarial Journal Pages: 366-375 Issue: 4 Volume: 2017 Year: 2017 Month: 4 X-DOI: 10.1080/03461238.2016.1148627 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1148627 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:4:p:366-375 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1160255_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kristian Buchardt Author-X-Name-First: Kristian Author-X-Name-Last: Buchardt Title: Kolmogorov’s forward PIDE and forward transition rates in life insurance Abstract: We consider a doubly stochastic Markov chain, where the transition intensities are modelled as diffusion processes. Here we present a forward partial integro-differential equation (PIDE) for the transition probabilities. This is a generalisation of Kolmogorov’s forward differential equation. In this set-up, we define forward transition rates, generalising the concept of forward rates, e.g. the forward mortality rate. These models are applicable in e.g. life insurance mathematics, which is treated in the paper. The results presented follow from the general forward PIDE for stochastic processes, of which the Fokker–Planck differential equation and Kolmogorov’s forward differential equation are the two most known special cases. We end the paper by considering the semi-Markov case, which can also be considered a special case of a general forward partial integro-differential equation. Journal: Scandinavian Actuarial Journal Pages: 377-394 Issue: 5 Volume: 2017 Year: 2017 Month: 5 X-DOI: 10.1080/03461238.2016.1160255 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1160255 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:5:p:377-394 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1167114_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Chengguo Weng Author-X-Name-First: Chengguo Author-X-Name-Last: Weng Author-Name: Sheng Chao Zhuang Author-X-Name-First: Sheng Chao Author-X-Name-Last: Zhuang Title: CDF formulation for solving an optimal reinsurance problem Abstract: An innovative cumulative distribution function (CDF)-based method is proposed for deriving optimal reinsurance contracts to maximize an insurer’s survival probability. The optimal reinsurance model is a non-concave constrained stochastic maximization problem, and the CDF-based method transforms it into a functional concave programming problem of determining an optimal CDF over a corresponding feasible set. Compared to the existing literature, our proposed CDF formulation provides a more transparent derivation of the optimal solutions, and more interestingly, it enables us to study a further complex model with an extra background risk and more sophisticated premium principle. Journal: Scandinavian Actuarial Journal Pages: 395-418 Issue: 5 Volume: 2017 Year: 2017 Month: 5 X-DOI: 10.1080/03461238.2016.1167114 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1167114 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:5:p:395-418 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1167115_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Incorporating the Bühlmann credibility into mortality models to improve forecasting performances Abstract: In this paper, we incorporate the Bühlmann credibility into three mortality models (the Lee–Carter model, the Cairns–Blake–Dowd model, and a linear relational model) to improve their forecasting performances, as measured by the MAPE (mean absolute percentage error), using mortality data for the UK. The results show that the MAPE reduction ratios for the three mortality models with the Bühlmann credibility are all significant. More importantly, the MAPEs under the three mortality models with the Bühlmann credibility are very close to each other for each age and forecast year. Thus, by incorporating the Bühlmann credibility we are able to converge the forecasting MAPEs resulting from the three different mortality models to a lower and more consistent level. Moreover, we provide a credibility interpretation with an individual time trend for age x and a group time trend for all ages. Finally, we apply the forecasted mortality rates both with and without the Bühlmann credibility to the net single premiums of life insurance products, and compare the corresponding MAPEs. Journal: Scandinavian Actuarial Journal Pages: 419-440 Issue: 5 Volume: 2017 Year: 2017 Month: 5 X-DOI: 10.1080/03461238.2016.1167115 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1167115 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:5:p:419-440 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1174731_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anişoara Maria Răducan Author-X-Name-First: Anişoara Maria Author-X-Name-Last: Răducan Author-Name: Raluca Vernic Author-X-Name-First: Raluca Author-X-Name-Last: Vernic Author-Name: Gheorghiţă Zbăganu Author-X-Name-First: Gheorghiţă Author-X-Name-Last: Zbăganu Title: On a conjecture related to the ruin probability for nonhomogeneous exponentially distributed claims Abstract: Recently, some recursive formulas have been obtained for the ruin probability evaluated at or before claim instants for a surplus process under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim revenues, which are assumed to be independent, identically distributed, following an arbitrary distribution. Based on numerical examples, a conjecture has also been stated relating the order in which the claims arrive to the magnitude of the corresponding ruin probability. In this paper, we prove this conjecture in the particular case when the claims are all exponentially distributed with different parameters. Journal: Scandinavian Actuarial Journal Pages: 441-451 Issue: 5 Volume: 2017 Year: 2017 Month: 5 X-DOI: 10.1080/03461238.2016.1174731 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1174731 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:5:p:441-451 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1174876_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Title: Nonparametric estimation of the finite time ruin probability in the classical risk model Abstract: In this paper, we consider the nonparametric estimation of the finite time ruin probability in the classical risk model. Suppose that the individual claim size distribution is unknown, but a random sample of claims is available. We construct the estimator by double Fourier transform. The asymptotic properties of the estimator are studied under large sample setting, and show that an almost n$ \sqrt{n} $ convergence rate can be obtained. Some simulation examples are also provided to illustrate the performance of the estimator under finite sample size setting. Journal: Scandinavian Actuarial Journal Pages: 452-469 Issue: 5 Volume: 2017 Year: 2017 Month: 5 X-DOI: 10.1080/03461238.2016.1174876 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1174876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:5:p:452-469 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1174732_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren Fiig Jarner Author-X-Name-First: Søren Fiig Author-X-Name-Last: Jarner Author-Name: Michael Preisel Author-X-Name-First: Michael Author-X-Name-Last: Preisel Title: Long guarantees with short duration: the rolling annuity Abstract: We present a new type of with-profits annuities which offer lifelong, yet hedgeable, guarantees. The rolling annuity gives a minimum lifelong guarantee at the time of contribution complemented with a series of guaranteed increases prior to retirement. Importantly, the initial guarantee and the subsequent increases are all set at prevailing market rates and hence are not known in advance. The structure of the guarantee implies that, prior to the last increase, the liability is equivalent to a zero-coupon bond maturing at the next increase and can therefore easily be hedged in the financial markets. Furthermore, the short duration implies that the financial and regulatory value will (essentially) coincide. We show financial fairness and we derive the reserve and thereby the hedging strategy. We also consider longevity risk, the duration profile, and report on a simulation study of the real value of the final payout. Journal: Scandinavian Actuarial Journal Pages: 471-494 Issue: 6 Volume: 2017 Year: 2017 Month: 7 X-DOI: 10.1080/03461238.2016.1174732 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1174732 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:6:p:471-494 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1177585_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Josep Lledó Author-X-Name-First: Josep Author-X-Name-Last: Lledó 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 Title: Assessing implicit hypotheses in life table construction Abstract: Mortality figures are of capital importance for policy-making and public planning, as in forecasting financial provisions in public pension systems. General population life tables are constructed from aggregated statistics, an issue that usually entails adopting some (implicit) assumptions in their construction, such as the hypothesis of closed demographic system or the hypotheses of uniform distributions of death counts (and migration events) by age and calendar year. As microdata have become more abundant and reliable, these hypotheses could be assessed and more assumption-free estimators employed. Using a real database from Spain, we show that the above hypotheses are not appropriate in general and that the more efficient estimators proposed in this paper should be promoted, as differences persist depending on the estimator computed. Journal: Scandinavian Actuarial Journal Pages: 495-518 Issue: 6 Volume: 2017 Year: 2017 Month: 7 X-DOI: 10.1080/03461238.2016.1177585 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1177585 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:6:p:495-518 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1182064_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Frank Y. Feng Author-X-Name-First: Frank Y. Author-X-Name-Last: Feng Author-Name: Michael R. Powers Author-X-Name-First: Michael R. Author-X-Name-Last: Powers Author-Name: Rui’an Xiao Author-X-Name-First: Rui’an Author-X-Name-Last: Xiao Author-Name: Lin Zhao Author-X-Name-First: Lin Author-X-Name-Last: Zhao Title: Berry-Esseen bounds for compound-Poisson loss percentiles Abstract: The Berry–Esseen (BE) theorem of probability theory is employed to establish bounds on percentile estimates for compound-Poisson loss portfolios. We begin by arguing that these bounds should not be based upon the exact BE constant, but rather upon a possibly lower, asymptotic counterpart for which the Lyapunov fraction converges uniformly to zero. We use this constant to construct two bounds – one approximate, and the other exact – and then propose a simple numerical criterion for determining whether the Gaussian approximation affords sufficient accuracy for a given Poisson mean and individual-loss distribution. Applying this criterion to the cases of gamma and lognormal individual losses, we find there exists a positive lower bound for the minimum Poisson mean necessary to achieve a fixed degree of accuracy for losses generated by the ‘best-case’ individual-loss distribution. Further investigation of this ‘best case’ reveals that large minimum Poisson means (i.e. >$ > $700) are required to achieve reasonable accuracy for the 99th percentile associated with these losses. Finally, we consider how the upper BE bound of a tail percentile may be applied to a common practical problem: selecting excess-of-loss reinsurance retentions. Journal: Scandinavian Actuarial Journal Pages: 519-534 Issue: 6 Volume: 2017 Year: 2017 Month: 7 X-DOI: 10.1080/03461238.2016.1182064 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1182064 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:6:p:519-534 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1184710_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sheng Chao Zhuang Author-X-Name-First: Sheng Chao Author-X-Name-Last: Zhuang Author-Name: Tim J. Boonen Author-X-Name-First: Tim J. Author-X-Name-Last: Boonen Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Zuo Quan Xu Author-X-Name-First: Zuo Quan Author-X-Name-Last: Xu Title: Optimal insurance in the presence of reinsurance Abstract: This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution. Journal: Scandinavian Actuarial Journal Pages: 535-554 Issue: 6 Volume: 2017 Year: 2017 Month: 7 X-DOI: 10.1080/03461238.2016.1184710 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1184710 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:6:p:535-554 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1329161_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Title: Jan M. Hoem, 1939–2017 Journal: Scandinavian Actuarial Journal Pages: 555-557 Issue: 6 Volume: 2017 Year: 2017 Month: 7 X-DOI: 10.1080/03461238.2017.1329161 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1329161 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:6:p:555-557 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1193557_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Brett Shanahan Author-X-Name-First: Brett Author-X-Name-Last: Shanahan Author-Name: Farzad Alavi Fard Author-X-Name-First: Farzad Author-X-Name-Last: Alavi Fard Author-Name: John van der Hoek Author-X-Name-First: John Author-X-Name-Last: van der Hoek Title: Pricing participating policies under the Meixner process and stochastic volatility Abstract: We propose a model for the valuation of participating life insurance products under the Meixner process, which belongs to the family of semi-heavy tailed processes. This particular model assumption is extremely desirable as it captures the stylised features of the return distribution, with existing moment generating functions. The highlight of the paper is the analytical solution derived for minimising the relative entropy between the historical and risk-neutral measures, when driving a pricing kernel. Further, we capture the stochastic volatility effect using an accurate polynomial approximation technique. Finally, to highlight the practical applications, we conduct a simulation experiment. Journal: Scandinavian Actuarial Journal Pages: 559-583 Issue: 7 Volume: 2017 Year: 2017 Month: 8 X-DOI: 10.1080/03461238.2016.1193557 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1193557 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:7:p:559-583 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1193558_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ambrose Lo Author-X-Name-First: Ambrose Author-X-Name-Last: Lo Title: A unifying approach to risk-measure-based optimal reinsurance problems with practical constraints Abstract: The design of optimal reinsurance treaties in the presence of multifarious practical constraints is a substantive but underdeveloped topic in modern risk management. To examine the influence of these constraints on the contract design systematically, this article formulates a generic constrained reinsurance problem where the objective and constraint functions take the form of Lebesgue integrals whose integrands involve the unit-valued derivative of the ceded loss function to be chosen. Such a formulation provides a unifying framework to tackle a wide body of existing and novel distortion-risk-measure-based optimal reinsurance problems with constraints that reflect diverse practical considerations. Prominent examples include insurers’ budgetary, regulatory and reinsurers’ participation constraints. An elementary and intuitive solution scheme based on an extension of the cost–benefit technique in Cheung and Lo [Cheung, K.C. & Lo, A. (2015, in press). Characterizations of optimal reinsurance treaties: a cost–benefit approach Scandinavian Actuarial Journal. doi:10.1080/03461238.2015.1054303.] is proposed and illuminated by analytically identifying the optimal risk-sharing schemes in several concrete optimal reinsurance models of practical interest. Particular emphasis is placed on the economic implications of the above constraints in terms of stimulating or curtailing the demand for reinsurance, and how these constraints serve to reconcile the possibly conflicting objectives of different parties. Journal: Scandinavian Actuarial Journal Pages: 584-605 Issue: 7 Volume: 2017 Year: 2017 Month: 8 X-DOI: 10.1080/03461238.2016.1193558 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1193558 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:7:p:584-605 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1209549_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. C. López-Díaz Author-X-Name-First: M. C. Author-X-Name-Last: López-Díaz Author-Name: M. López-Díaz Author-X-Name-First: M. Author-X-Name-Last: López-Díaz Author-Name: S. Martínez-Fernández Author-X-Name-First: S. Author-X-Name-Last: Martínez-Fernández Title: A stochastic comparison of customer classifiers with an application to customer attrition in commercial banking Abstract: The classification of clients is an essential matter in commercial banking, insurance companies, electrical corporations, communication business, etc. Those companies frequently classify their customers by means of the information provided by the so-called classifier. Motivated by the need to compare systems of classification, we introduce a new stochastic order which permits the comparison of classifiers. The stochastic order is analysed in detail, providing characterizations and properties as well as connections with other stochastic orders and other classification systems. Such an order is applied to compare some classifiers used by a Spanish commercial banking to analyse the key problem of customer churn, obtaining conclusive results by means of real databases. Namely, the optimal classifier among them in the new stochastic order is obtained. Journal: Scandinavian Actuarial Journal Pages: 606-627 Issue: 7 Volume: 2017 Year: 2017 Month: 8 X-DOI: 10.1080/03461238.2016.1209549 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1209549 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:7:p:606-627 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1225265_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Author-Name: Di Xu Author-X-Name-First: Di Author-X-Name-Last: Xu Title: Analysis of IBNR claims in renewal insurance models Abstract: Incurred but not reported (IBNR) claims, which arise naturally in insurance contexts, are of central importance to insurers for risk management and financial reporting purposes. In this paper, we first examine the moments of the total discounted IBNR claim amount at a given time t≥0$ t \ge 0 $ when claim events occur according to a compound renewal process. Under the same claim arrival dynamic, we later consider the joint moments of the total discounted IBNR claim amount and the total incurred and reported claim amount at possibly different time points, a quantity of much interest for claim reserving purposes. In the second part of this article, we examine in more detail properties of the IBNR claim number under specific distributional assumptions for the reporting lags and the interarrival times. Among others, the self-decomposability of the IBNR claim number process is considered when claim events occur according to a compound Poisson process. Journal: Scandinavian Actuarial Journal Pages: 628-650 Issue: 7 Volume: 2017 Year: 2017 Month: 8 X-DOI: 10.1080/03461238.2016.1225265 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1225265 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:7:p:628-650 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1225592_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Author-Name: Johannes M. Schumacher Author-X-Name-First: Johannes M. Author-X-Name-Last: Schumacher Title: Financial fairness and conditional indexation Abstract: Collective pension contracts can generate advantages for their participants by implementing forms of risk sharing. To ensure the continuity of a collective scheme, it has to be monitored whether the contracts offered to participants are financially fair in terms of their market value. When risk sharing is implemented by means of optionalities such as conditional indexation, the analysis of financial fairness is not straightforward. In this paper, we use a stylised overlapping generations model to study financial fairness for a conditional indexation scheme. We find that financial fairness for all participants at all times is not feasible within a scheme of this type, unless the nature of indexation is such that the scheme is reduced to DC. However, financial fairness for incoming generations at the moment of entry can be realised. We show how to compute the fair contribution rate as a function of the current nominal asset/liability ratio for a given level of nominal entitlements. At low levels of the ratio, the fair contribution for incoming generations is also relatively low; nevertheless, the joining of a new generation still has a positive effect on the asset/liability ratio. Journal: Scandinavian Actuarial Journal Pages: 651-669 Issue: 8 Volume: 2017 Year: 2017 Month: 9 X-DOI: 10.1080/03461238.2016.1225592 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1225592 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:8:p:651-669 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1228542_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Chi Chung Siu Author-X-Name-First: Chi Chung Author-X-Name-Last: Siu Author-Name: Sheung Chi Phillip Yam Author-X-Name-First: Sheung Chi Phillip Author-X-Name-Last: Yam Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Author-Name: Hui Zhao Author-X-Name-First: Hui Author-X-Name-Last: Zhao Title: A class of nonzero-sum investment and reinsurance games subject to systematic risks Abstract: Recently, there have been numerous insightful applications of zero-sum stochastic differential games in insurance, as discussed in Liu et al. [Liu, J., Yiu, C. K.-F. & Siu, T. K. (2014). Optimal investment of an insurer with regime-switching and risk constraint. Scandinavian Actuarial Journal 2014(7), 583–601]. While there could be some practical situations under which nonzero-sum game approach is more appropriate, the development of such approach within actuarial contexts remains rare in the existing literature. In this article, we study a class of nonzero-sum reinsurance-investment stochastic differential games between two competitive insurers subject to systematic risks described by a general compound Poisson risk model. Each insurer can purchase the excess-of-loss reinsurance to mitigate both systematic and idiosyncratic jump risks of the inter-arrival claims; and can invest in one risk-free asset and one risky asset whose price dynamics follows the famous Heston stochastic volatility model [Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6, 327–343]. The main objective of each insurer is to maximize the expected utility of his terminal surplus relative to that of his competitor. Dynamic programming principle for this class of nonzero-sum game problems leads to a non-canonical fixed-point problem of coupled non-linear integral-typed equations. Despite the complex structure, we establish the unique existence of the Nash equilibrium reinsurance-investment strategies and the corresponding value functions of the insurers in a representative example of the constant absolute risk aversion insurers under a mild, time-independent condition. Furthermore, Nash equilibrium strategies and value functions admit closed forms. Numerical studies are also provided to illustrate the impact of the systematic risks on the Nash equilibrium strategies. Finally, we connect our results to that under the diffusion-approximated model by proving explicitly that the Nash equilibrium under the diffusion-approximated model is an ϵ$ \epsilon $-Nash equilibrium under the general Poisson risk model, thereby establishing that the analogous Nash equilibrium in Bensoussan et al. [Bensoussan, A., Siu, C. C., Yam, S. C. P. & Yang, H. (2014). A class of nonzero-sum stochastic differential investment and reinsurance games. Automatica 50(8), 2025–2037] serves as an interesting complementary case of the present framework. Journal: Scandinavian Actuarial Journal Pages: 670-707 Issue: 8 Volume: 2017 Year: 2017 Month: 9 X-DOI: 10.1080/03461238.2016.1228542 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1228542 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:8:p:670-707 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1240709_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Hiabu Author-X-Name-First: M. Author-X-Name-Last: Hiabu Title: On the relationship between classical chain ladder and granular reserving Abstract: We connect classical chain ladder to granular reserving. This is done by defining explicitly how the classical run-off triangles are generated from individual iid observations in continuous time. One important result is that the development factors have a one to one correspondence to a histogram estimator of a hazard running in reversed development time. A second result is that chain ladder has a systematic bias if the row effect has not the same distribution when conditioned on any of the aggregated periods. This means that the chain ladder assumptions on one level of aggregation, say yearly, are different from the chain ladder assumptions when aggregated in quarters and the optimal level of aggregation is a classical bias variance trade-off depending on the data-set. We introduce smooth development factors arising from non-parametric hazard kernel smoother improving the estimation significantly. Journal: Scandinavian Actuarial Journal Pages: 708-729 Issue: 8 Volume: 2017 Year: 2017 Month: 9 X-DOI: 10.1080/03461238.2016.1240709 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1240709 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:8:p:708-729 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1243574_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Enkelejd Hashorva Author-X-Name-First: Enkelejd Author-X-Name-Last: Hashorva Author-Name: Gildas Ratovomirija Author-X-Name-First: Gildas Author-X-Name-Last: Ratovomirija Author-Name: Maissa Tamraz Author-X-Name-First: Maissa Author-X-Name-Last: Tamraz Title: On some new dependence models derived from multivariate collective models in insurance applications Abstract: Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes (Xi,Yi),i≥1$ (X_i,Y_i), i \ge 1 $ and a claim counting random variable N. In this paper, we are concerned with the joint distribution function (df) F of the largest claim sizes (XN:N,YN:N)$ (X_{N:N}, Y_{N:N}) $. By allowing N to depend on some parameter, say θ$ \theta $, then F=F(θ)$ F=F(\theta ) $ is for various choices of N a tractable parametric family of bivariate dfs. We investigate both distributional and extremal properties of (XN:N,YN:N)$ (X_{N:N}, Y_{N:N}) $. Furthermore, we present several applications of the implied parametric models to some data from the literature and a new data-set from a Swiss insurance company (Data-set can be downloaded here http://dx.doi.org/10.13140/RG.2.1.3082.9203.) Journal: Scandinavian Actuarial Journal Pages: 730-750 Issue: 8 Volume: 2017 Year: 2017 Month: 9 X-DOI: 10.1080/03461238.2016.1243574 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1243574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:8:p:730-750 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1248480_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: On capital injections and dividends with tax in a diffusion approximation Abstract: We consider a diffusion approximation to a risk process with dividends and capital injections. Tax has to be paid on dividends, but capital injections lead to an exemption from tax. That is, tax is only paid for the aggregate excess of dividends over the capital injections. The value of a strategy is the expected value of the discounted dividend payments after tax minus the discounted capital injections. We solve the problem and show that the optimal dividend strategy is a barrier strategy. Journal: Scandinavian Actuarial Journal Pages: 751-760 Issue: 9 Volume: 2017 Year: 2017 Month: 10 X-DOI: 10.1080/03461238.2016.1248480 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1248480 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:9:p:751-760 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1252944_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Agnieszka I. Bergel Author-X-Name-First: Agnieszka I. Author-X-Name-Last: Bergel Author-Name: Eugenio V. Rodríguez-Martínez Author-X-Name-First: Eugenio V. Author-X-Name-Last: Rodríguez-Martínez Author-Name: Alfredo D. Egídio dos Reis Author-X-Name-First: Alfredo D. Author-X-Name-Last: Egídio dos Reis Title: On dividends in the phase–type dual risk model Abstract: The dual risk model assumes that the surplus of a company decreases at a constant rate over time, and grows by means of upward jumps which occur at random times with random sizes. In the present work, we study the dual risk renewal model when the waiting times are phase-type distributed. Using the roots of the fundamental and the generalized Lundberg’s equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Then, we address the calculation of expected discounted future dividends particularly when the individual common gains follow a phase-type distribution. We further show that the optimal dividend barrier does not depend on the initial reserve. As far as the roots of the Lundberg equations and the time of ruin are concerned, we address the existing formulae in the corresponding Sparre-Andersen insurance risk model for the first hitting time, and we generalize them to cover also the situations where we have multiple roots. We do that working a new approach and technique, approach we also use for working the dividends, unlike others, it can be also applied for every situation. Journal: Scandinavian Actuarial Journal Pages: 761-784 Issue: 9 Volume: 2017 Year: 2017 Month: 10 X-DOI: 10.1080/03461238.2016.1252944 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1252944 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:9:p:761-784 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1255249_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Harrie Hendriks Author-X-Name-First: Harrie Author-X-Name-Last: Hendriks Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Title: A generalization of multivariate Pareto distributions: tail risk measures, divided differences and asymptotics Abstract: We consider a multivariate distribution of the form P(X1>x1,…,Xn>xn)=h∑i=1nλixi$ { \mathbb P }(X_{1}>x_{1},\ldots ,X_{n}>x_{n})=h\left( \sum _{i=1}^{n}\lambda _{i}x_{i}\right) $, where the survival function h is a multiply monotonic function of order (n-1)$ (n-1) $ such that h(0)=1$ h(0)=1 $, λi>0$ \lambda _{i}>0 $ for all i and λi≠λj$ \lambda _{i}\ne \lambda _{j} $ for i≠j$ i\ne j $. This generalizes work by Chiragiev and Landsman on completely monotonic survival functions. We show that the considered dependence structure is more flexible in the sense that the correlation coefficient between two components may attain negative values. We demonstrate that the tool of divided difference is very convenient for evaluation of tail risk measures and their allocations. In terms of divided differences, formulas for tail conditional expectation (tce), tail conditional variance and tce-based capital allocation are obtained. We obtain a closed form for the capital allocation of aggregate risk. Special attention is paid to survival functions h that are regularly or rapidly varying. Journal: Scandinavian Actuarial Journal Pages: 785-803 Issue: 9 Volume: 2017 Year: 2017 Month: 10 X-DOI: 10.1080/03461238.2016.1255249 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1255249 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:9:p:785-803 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1255655_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Author-Name: Stephen J. Richards Author-X-Name-First: Stephen J. Author-X-Name-Last: Richards Title: Parameter risk in time-series mortality forecasts Abstract: The projection of mortality rates is an essential part of valuing liabilities in life insurance portfolios and pension schemes. An important tool for risk management and solvency purposes is a stochastic projection model. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the issue of parameter risk in time-series models from the point of view of an insurer using them for regulatory risk reporting – formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Particular attention is given to the contrasts in how academic researchers might view these models and how insurance regulators and practitioners in life offices might use them. Using a bootstrap method we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. We also find that an objective model selection criterion, such as goodness of fit to past data, can result in the selection of a model with unstable parameter values. While this aspect of the model is superficially undesirable, it also leads to slightly higher capital requirements and thus makes the model of keen interest to regulators. Our conclusions have relevance to insurers using value-at-risk capital assessments in the European Union under Solvency II, but also territories using conditional tail expectations such as Australia, Canada and Switzerland. Journal: Scandinavian Actuarial Journal Pages: 804-828 Issue: 9 Volume: 2017 Year: 2017 Month: 10 X-DOI: 10.1080/03461238.2016.1255655 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1255655 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2017:y:2017:i:9:p:804-828 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1274270_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Duni Hu Author-X-Name-First: Duni Author-X-Name-Last: Hu Author-Name: Shou Chen Author-X-Name-First: Shou Author-X-Name-Last: Chen Author-Name: Hailong Wang Author-X-Name-First: Hailong Author-X-Name-Last: Wang Title: Robust reinsurance contracts in continuous time Abstract: We investigate reinsurance contract problems in a continuous-time principal-agent framework, where the reinsurer (principal) is concerned about potential model ambiguity in the claims process, but the insurer (agent) trusts the claims process, or vice versa. The reinsurer designs a robust reinsurance contract that maximizes his exponential utility of terminal wealth under the worst-case distribution, subject to the insurer’s incentive constraint. Optimal reinsurance contracts are explicitly derived in different ambiguity situations. We first show that the reinsurer’s robustness preference makes him become more conservative, which induces him to raise the reinsurance price, which then decreases the demand for reinsurance. However, the insurer’s robustness preference increases both the reinsurance price and the demand. Furthermore, the reinsurer continuously adjusts the reinsurance price, leading the insurer to always purchase a constant proportion of reinsurance, no matter who faces ambiguity, or whether ambiguity exists. Finally, the economic implications of model ambiguity are illustrated using numerical examples. Journal: Scandinavian Actuarial Journal Pages: 1-22 Issue: 1 Volume: 2018 Year: 2018 Month: 1 X-DOI: 10.1080/03461238.2016.1274270 File-URL: http://hdl.handle.net/10.1080/03461238.2016.1274270 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:1:p:1-22 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1278717_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Narayanaswamy Balakrishnan Author-X-Name-First: Narayanaswamy Author-X-Name-Last: Balakrishnan Author-Name: Yiying Zhang Author-X-Name-First: Yiying Author-X-Name-Last: Zhang Author-Name: Peng Zhao Author-X-Name-First: Peng Author-X-Name-Last: Zhao Title: Ordering the largest claim amounts and ranges from two sets of heterogeneous portfolios Abstract: This paper investigates the ordering properties of the largest claim amounts and sample ranges arising from two sets of heterogeneous portfolios. First, some sufficient conditions are provided in the sense of the usual stochastic ordering to compare the largest claim amounts from two sets of independent or interdependent claims. Second, comparison results on the largest claim amounts in the sense of the reversed hazard rate and hazard rate orderings are established for two batches of heterogeneous independent claims. Finally, we present sufficient conditions to stochastically compare sample ranges from two sets of heterogeneous claims by means of the usual stochastic ordering. Some numerical examples are also given to illustrate the theoretical findings. The results established here not only extend and generalize those known in the literature, but also provide insight that will be useful to lay down the annual premiums of policyholders. Journal: Scandinavian Actuarial Journal Pages: 23-41 Issue: 1 Volume: 2018 Year: 2018 Month: 1 X-DOI: 10.1080/03461238.2017.1278717 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1278717 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:1:p:23-41 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1280527_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nonhle Channon Mdziniso Author-X-Name-First: Nonhle Channon Author-X-Name-Last: Mdziniso Author-Name: Kahadawala Cooray Author-X-Name-First: Kahadawala Author-X-Name-Last: Cooray Title: Odd Pareto families of distributions for modeling loss payment data Abstract: A three-parameter generalization of the Pareto distribution is presented with density function having a flexible upper tail in modeling loss payment data. This generalized Pareto distribution will be referred to as the Odd Pareto distribution since it is derived by considering the distributions of the odds of the Pareto and inverse Pareto distributions. Basic properties of the Odd Pareto distribution (OP) are studied. Model parameters are estimated using both modified and regular maximum likelihood methods. Simulation studies are conducted to compare the OP with the exponentiated Pareto, Burr, and Kumaraswamy distributions using two different test statistics based on the ml method. Furthermore, two examples from the Norwegian fire insurance claims data-set are provided to illustrate the upper tail flexibility of the distribution. Extensions of the Odd Pareto distribution are also considered to improve the fitting of data. Journal: Scandinavian Actuarial Journal Pages: 42-63 Issue: 1 Volume: 2018 Year: 2018 Month: 1 X-DOI: 10.1080/03461238.2017.1280527 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1280527 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:1:p:42-63 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1284152_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Patryk Miziuła Author-X-Name-First: Patryk Author-X-Name-Last: Miziuła Author-Name: Radek Solnický Author-X-Name-First: Radek Author-X-Name-Last: Solnický Title: Sharp bounds on change in expected values and variances for single risk analysis in the flood catastrophe model Abstract: In the paper we propose a method how to assess sharp bounds on change in the expected value and variance of the individual loss distributions of the risks in the flood catastrophe model. The method does not involve the use of the whole model, only the river discharge distributions and above mentioned loss distribution moments are required. We present the method on a case study inspired by floods in Poland. Journal: Scandinavian Actuarial Journal Pages: 64-75 Issue: 1 Volume: 2018 Year: 2018 Month: 1 X-DOI: 10.1080/03461238.2017.1284152 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1284152 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:1:p:64-75 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1300605_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Jevgenijs Ivanovs Author-X-Name-First: Jevgenijs Author-X-Name-Last: Ivanovs Title: Linking dividends and capital injections – a probabilistic approach Abstract: In the context of collective risk theory, we give a sample path identity relating capital injections in the original model and dividend payments in the time-reversed counterpart. We exploit this duality to provide an alternative view on some of the known results on the expected discounted capital injections and dividend payments for risk models driven by spectrally negative Lévy processes. Furthermore, we present a probabilistic analysis and simple resulting expressions for a model with two dividend barriers, which was recently shown by Schmidli to be optimal in various Lévy risk models when maximizing the difference of dividend payments and injections in the presence of tax exemptions. Journal: Scandinavian Actuarial Journal Pages: 76-83 Issue: 1 Volume: 2018 Year: 2018 Month: 1 X-DOI: 10.1080/03461238.2017.1300605 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1300605 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:1:p:76-83 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1469098_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xia Han Author-X-Name-First: Xia Author-X-Name-Last: Han Author-Name: Zhibin Liang Author-X-Name-First: Zhibin Author-X-Name-Last: Liang Author-Name: Kam Chuen Yuen Author-X-Name-First: Kam Chuen Author-X-Name-Last: Yuen Title: Optimal proportional reinsurance to minimize the probability of drawdown under thinning-dependence structure Abstract: In this paper, we consider the optimal proportional reinsurance problem in a risk model with the thinning-dependence structure, and the criterion is to minimize the probability that the value of the surplus process drops below some fixed proportion of its maximum value to date which is known as the probability of drawdown. The thinning dependence assumes that stochastic sources related to claim occurrence are classified into different groups, and that each group may cause a claim in each insurance class with a certain probability. By the technique of stochastic control theory and the corresponding Hamilton–Jacobi–Bellman equation, the optimal reinsurance strategy and the corresponding minimum probability of drawdown are derived not only for the expected value principle but also for the variance premium principle. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results. Journal: Scandinavian Actuarial Journal Pages: 863-889 Issue: 10 Volume: 2018 Year: 2018 Month: 11 X-DOI: 10.1080/03461238.2018.1469098 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1469098 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:10:p:863-889 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1470562_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hyunju Lee Author-X-Name-First: Hyunju Author-X-Name-Last: Lee Author-Name: Ji Hwan Cha Author-X-Name-First: Ji Hwan Author-X-Name-Last: Cha Title: A dynamic bivariate common shock model with cumulative effect and its actuarial application Abstract: Standard actuarial theory of multiple life insurance traditionally postulates independence for the remaining lifetimes mainly due to computational convenience rather than realism. In this paper, we propose a general common shock model for modelling dependent coupled lives and apply it to a life insurance model. In the proposed shock model, we consider not only simultaneous deaths of the coupled members due to a single shock (e.g. a critical accident), but also cumulative effect in the mortality rate when they survive shocks. Under the model, we derive a bivariate lifetime distribution and its marginal distributions in closed forms. We study the bivariate ageing property, dependence structure and the dependence orderings of the lifetime distribution. Based on it, we investigate the influence of dependence on the pricings of insurance policies involving multiple lives which are subject to common shocks. Furthermore, we discuss relevant useful stochastic bounds. Journal: Scandinavian Actuarial Journal Pages: 890-906 Issue: 10 Volume: 2018 Year: 2018 Month: 11 X-DOI: 10.1080/03461238.2018.1470562 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1470562 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:10:p:890-906 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1471001_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michele Antonello Author-X-Name-First: Michele Author-X-Name-Last: Antonello Author-Name: Luca Cipani Author-X-Name-First: Luca Author-X-Name-Last: Cipani Author-Name: Wolfgang J. Runggaldier Author-X-Name-First: Wolfgang J. Author-X-Name-Last: Runggaldier Title: Minimizing capital injections by investment and reinsurance for a piecewise deterministic reserve process model Abstract: We consider the possibility for an insurance company to rely on capital injections to bring the reserve back to a given level if it has fallen below it and study the problem of dynamically choosing the reinsurance level and the investment in the financial market in order to minimize the expected discounted total amount of capital injection. The reserve process is described by a piecewise deterministic process, where the random discontinuities are triggered by the arrival of a claim or by a change in the prices of the risky assets in which the company invests. The capital injections, combined with the specific model, make the problem non-linear and difficult to solve via an HJB approach. The emphasis here is on making the actual computation of a solution possible by value iteration combined with an approximation based on discretization. This leads to a nearly optimal solution with an approximation that can be made arbitrarily precise. Numerical results show the feasibility of the proposed approach. Journal: Scandinavian Actuarial Journal Pages: 907-932 Issue: 10 Volume: 2018 Year: 2018 Month: 11 X-DOI: 10.1080/03461238.2018.1471001 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1471001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:10:p:907-932 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1475300_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xingchun Peng Author-X-Name-First: Xingchun Author-X-Name-Last: Peng Author-Name: Fenge Chen Author-X-Name-First: Fenge Author-X-Name-Last: Chen Author-Name: Wenyuan Wang Author-X-Name-First: Wenyuan Author-X-Name-Last: Wang Title: Optimal investment and risk control for an insurer with partial information in an anticipating environment Abstract: This paper considers an optimal investment and risk control problem under the criterion of logarithm utility maximization. The risky asset process and the insurance risk process are described by stochastic differential equations with jumps and anticipating coefficients. The insurer invests in the financial assets and controls the number of policies based on some partial information about the financial market and the insurance claims. The forward integral and Malliavin calculus for Lévy processes are used to obtain a characterization of the optimal strategy. Some special cases are discussed and the closed-form expressions for the optimal strategies are derived. Journal: Scandinavian Actuarial Journal Pages: 933-952 Issue: 10 Volume: 2018 Year: 2018 Month: 11 X-DOI: 10.1080/03461238.2018.1475300 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1475300 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:10:p:933-952 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1304984_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jennifer Alonso-García Author-X-Name-First: Jennifer Author-X-Name-Last: Alonso-García Author-Name: María del Carmen Boado-Penas Author-X-Name-First: María del Carmen Author-X-Name-Last: Boado-Penas Author-Name: Pierre Devolder Author-X-Name-First: Pierre Author-X-Name-Last: Devolder Title: Automatic balancing mechanisms for notional defined contribution accounts in the presence of uncertainty Abstract: The notional defined contribution model combines pay-as-you-go financing and a defined contribution pension formula. This paper aims to demonstrate the extent to which liquidity and solvency indicators are affected by fluctuations in economic and demographic conditions and to explore the introduction of an automatic balancing mechanism (ABM) into the pension scheme. We demonstrate that the introduction of an ABM reduces the volatility of the buffer fund and that, in most cases, the automatic mechanism that re-establishes solvency produces the highest value of the risk-adjusted notional factor. Journal: Scandinavian Actuarial Journal Pages: 85-108 Issue: 2 Volume: 2018 Year: 2018 Month: 2 X-DOI: 10.1080/03461238.2017.1304984 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1304984 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:2:p:85-108 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1306795_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nicola Loperfido Author-X-Name-First: Nicola Author-X-Name-Last: Loperfido Author-Name: Stepan Mazur Author-X-Name-First: Stepan Author-X-Name-Last: Mazur Author-Name: Krzysztof Podgórski Author-X-Name-First: Krzysztof Author-X-Name-Last: Podgórski Title: Third cumulant for multivariate aggregate claim models Abstract: The third cumulant for the aggregated multivariate claims is considered. A formula is presented for the general case when the aggregating variable is independent of the multivariate claims. Two important special cases are considered. In the first one, multivariate skewed normal claims are considered and aggregated by a Poisson variable. The second case is dealing with multivariate asymmetric generalized Laplace and aggregation is made by a negative binomial variable. Due to the invariance property the latter case can be derived directly, leading to the identity involving the cumulant of the claims and the aggregated claims. There is a well-established relation between asymmetric Laplace motion and negative binomial process that corresponds to the invariance principle of the aggregating claims for the generalized asymmetric Laplace distribution. We explore this relation and provide multivariate continuous time version of the results. It is discussed how these results that deal only with dependence in the claim sizes can be used to obtain a formula for the third cumulant for more complex aggregate models of multivariate claims in which the dependence is also in the aggregating variables. Journal: Scandinavian Actuarial Journal Pages: 109-128 Issue: 2 Volume: 2018 Year: 2018 Month: 2 X-DOI: 10.1080/03461238.2017.1306795 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1306795 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:2:p:109-128 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1307267_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Dimitris Karlis Author-X-Name-First: Dimitris Author-X-Name-Last: Karlis Author-Name: George Tzougas Author-X-Name-First: George Author-X-Name-Last: Tzougas Author-Name: Nicholas Frangos Author-X-Name-First: Nicholas Author-X-Name-Last: Frangos Title: Confidence intervals of the premiums of optimal bonus malus systems Abstract: In view of the economic importance of motor third-party liability insurance in developed countries the construction of optimal BMS has been given considerable interest. However, a major drawback in the construction of optimal BMS is that they fail to account for the variability on premium calculations which are treated as point estimates. The present study addresses this issue. Specifically, nonparametric mixtures of Poisson laws are used to construct an optimal BMS with a finite number of classes. The mixing distribution is estimated by nonparametric maximum likelihood (NPML). The main contribution of this paper is the use of the NPML estimator for the construction of confidence intervals for the premium rates derived by updating the posterior mean claim frequency. Furthermore, we advance one step further by improving the performance of the confidence intervals based on a bootstrap procedure where the estimated mixture is used for resampling. The construction of confidence intervals for the individual premiums based on the asymptotic maximum likelihood theory is beneficial for the insurance company as it can result in accurate and effective adjustments to the premium rating policies from a practical point of view. Journal: Scandinavian Actuarial Journal Pages: 129-144 Issue: 2 Volume: 2018 Year: 2018 Month: 2 X-DOI: 10.1080/03461238.2017.1307267 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1307267 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:2:p:129-144 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1309679_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Danping Li Author-X-Name-First: Danping Author-X-Name-Last: Li Author-Name: Yan Zeng Author-X-Name-First: Yan Author-X-Name-Last: Zeng Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps Abstract: This paper considers a robust optimal excess-of-loss reinsurance-investment problem in a model with jumps for an ambiguity-averse insurer (AAI), who worries about ambiguity and aims to develop a robust optimal reinsurance-investment strategy. The AAI’s surplus process is assumed to follow a diffusion model, which is an approximation of the classical risk model. The AAI is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion for maximizing the expected exponential utility of terminal wealth, optimal strategy and optimal value function are derived by applying the stochastic dynamic programming approach. Our model and results extend some of the existing results in the literature, and the economic implications of our findings are illustrated. Numerical examples show that considering ambiguity and reinsurance brings utility enhancements. Journal: Scandinavian Actuarial Journal Pages: 145-171 Issue: 2 Volume: 2018 Year: 2018 Month: 2 X-DOI: 10.1080/03461238.2017.1309679 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1309679 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:2:p:145-171 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1328370_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ayşe Arık Author-X-Name-First: Ayşe Author-X-Name-Last: Arık Author-Name: Yeliz Yolcu-Okur Author-X-Name-First: Yeliz Author-X-Name-Last: Yolcu-Okur Author-Name: Şule Şahin Author-X-Name-First: Şule Author-X-Name-Last: Şahin Author-Name: Ömür Uğur Author-X-Name-First: Ömür Author-X-Name-Last: Uğur Title: Pricing pension buy-outs under stochastic interest and mortality rates Abstract: Pension buy-out is a special financial asset issued to offload the pension liabilities holistically in exchange for an upfront premium. In this paper, we concentrate on the pricing of pension buy-outs under dependence between interest and mortality rates risks with an explicit correlation structure in a continuous time framework. Change of measure technique is invoked to simplify the valuation. We also present how to obtain the buy-out price for a hypothetical benefit pension scheme using stochastic models to govern the dynamics of interest and mortality rates. Besides employing a non-mean reverting specification of the Ornstein–Uhlenbeck process and a continuous version of Lee–Carter setting for modeling mortality rates, we prefer Vasicek and Cox–Ingersoll–Ross models for short rates. We provide numerical results under various scenarios along with the confidence intervals using Monte Carlo simulations. Journal: Scandinavian Actuarial Journal Pages: 173-190 Issue: 3 Volume: 2018 Year: 2018 Month: 3 X-DOI: 10.1080/03461238.2017.1328370 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1328370 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:3:p:173-190 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1329160_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fengyang Cheng Author-X-Name-First: Fengyang Author-X-Name-Last: Cheng Author-Name: Dongya Cheng Author-X-Name-First: Dongya Author-X-Name-Last: Cheng Title: Randomly weighted sums of dependent subexponential random variables with applications to risk theory Abstract: For any fixed integer n≥1$ n \ge 1 $, let X1,…,Xn$ X_1,\ldots ,X_n $ be real-valued random variables with a common subexponential distribution, and let θ1,…,θn$ \theta _1,\ldots ,\theta _n $ be positive random variables which are bounded above and independent of X1,…,Xn$ X_1,\ldots ,X_n $. Under some rather loose conditional dependence assumptions on the primary random variables X1,…,Xn$ X_1,\ldots ,X_n $, this paper proves that the asymptotic relationsP∑i=1nθiXi>x∼Pmax1≤m≤n∑i=1mθiXi>x∼Pmax1≤i≤nθiXi>x∼∑i=1nPθiXi>x$$ \begin{aligned} P\left(\sum _{i=1}^n \theta _iX_i >x\right)&\sim P\left( \max _{1\le m\le n}\sum _{i=1}^m \theta _iX_i>x\right)\sim P\left(\max _{1\le i\le n}\theta _iX_i>x\right)\\&\sim \sum _{i=1}^n {P\left( \theta _iX_i>x\right)} \end{aligned} $$hold as x→∞$ x\rightarrow \infty $, where θ1,…,θn$ \theta _1,\ldots ,\theta _n $ are arbitrarily dependent. In particular, it is shown that the above results hold true for X1,…,Xn$ X_1,\ldots ,X_n $ with certain Samarnov distributions. The obtained results on randomly weighted sums are applied to estimating the finite-time ruin probability in a discrete-time risk model with both insurance and financial risks. Journal: Scandinavian Actuarial Journal Pages: 191-202 Issue: 3 Volume: 2018 Year: 2018 Month: 3 X-DOI: 10.1080/03461238.2017.1329160 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1329160 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:3:p:191-202 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1332679_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kjersti Aas Author-X-Name-First: Kjersti Author-X-Name-Last: Aas Author-Name: Linda R. Neef Author-X-Name-First: Linda R. Author-X-Name-Last: Neef Author-Name: Lloyd Williams Author-X-Name-First: Lloyd Author-X-Name-Last: Williams Author-Name: Dag Raabe Author-X-Name-First: Dag Author-X-Name-Last: Raabe Title: Interest rate model comparisons for participating products under Solvency II Abstract: Under the Solvency II regulatory framework it is essential for life insurers to have an adequate interest rate model. In this paper, we investigate whether the choice of the interest rate model has an impact on the valuation of the best estimate of the liabilities. We use three well-known interest rate models; the CIR++-model, the G2++-model and the Libor Market model. Our numerical results show that for low to medium durations of the liabilities and a relatively low proportion of credit bonds in the asset portfolio, the three interest rate models produce quite similar values for the best estimate liabilities. However, for large durations of the liabilities, or a large bond proportion, or both, the differences can be quite large. There is no easy answer to the question of which model should be used in cases where the choice of interest rate model has a significant impact. Based on the study described in this paper, our advice is to use the G2++-model, which seems to represent an appropriate trade-off between accuracy and complexity. Journal: Scandinavian Actuarial Journal Pages: 203-224 Issue: 3 Volume: 2018 Year: 2018 Month: 3 X-DOI: 10.1080/03461238.2017.1332679 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1332679 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:3:p:203-224 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1339634_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: An Chen Author-X-Name-First: An Author-X-Name-Last: Chen Author-Name: Felix Hentschel Author-X-Name-First: Felix Author-X-Name-Last: Hentschel Author-Name: Xian Xu Author-X-Name-First: Xian Author-X-Name-Last: Xu Title: Optimal retirement time under habit persistence: what makes individuals retire early? Abstract: As the effective labor market exit observed in most OECD countries is lower than the corresponding official retirement age, the question concerning the driving factors for an early retirement decision arises. This paper incorporates the optimal retirement decision in an optimal consumption and asset allocation problem in order to analyze, among others, the effect of habit forming preferences and diverse leisure preferences for earlier retirement. We compare two possible situations for the retirement phase: (a) the individual is allowed to freely consume and invest; (b) he annuitizes his wealth at retirement and consumes the annuity income. We find that early retirement is optimal if leisure gain through earlier retirement is highly appreciated or the standard of living (habit level) is low. Additionally, our numerical results show that high initial wealth or low labor income lead to early retirement, confirming observations of Fields & Mitchell. Journal: Scandinavian Actuarial Journal Pages: 225-249 Issue: 3 Volume: 2018 Year: 2018 Month: 3 X-DOI: 10.1080/03461238.2017.1339634 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1339634 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:3:p:225-249 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1341847_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren Kærgaard Slipsager Author-X-Name-First: Søren Kærgaard Author-X-Name-Last: Slipsager Title: The real risk in pension forecasting Abstract: The purpose of this paper is to shed light on some of the flaws in the forecasting approach undertaken by the pension industry. Specifically, it considers the treatment of inflation and shows that the current modeling framework is too simplistic. I identify the flaws of the existing regulatory framework and provide an alternative full model framework constructed around the three-factor diffusion model recently proposed by the Danish Society of Actuaries. By use of a simulation study I compare the deterministic inflation scheme applied in the industry to a stochastic scheme and show that the real value of the pension saver’s investment portfolio at retirement is highly dependent on the inflation scheme. As the deterministic scheme does not take state variable correlations into account it overestimates the expected portfolio value in real terms compared to the stochastic scheme. Moreover, the deterministic scheme gives rise to a more heavy-tailed distribution implying a misestimation of downside risk and upside potential. Finally, it is shown in a realistic case study that the pension saver’s expected retirement payout profile is heavily affected. Journal: Scandinavian Actuarial Journal Pages: 250-273 Issue: 3 Volume: 2018 Year: 2018 Month: 3 X-DOI: 10.1080/03461238.2017.1341847 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1341847 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:3:p:250-273 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1343748_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xiaoqing Liang Author-X-Name-First: Xiaoqing Author-X-Name-Last: Liang Author-Name: Zbigniew Palmowski Author-X-Name-First: Zbigniew Author-X-Name-Last: Palmowski Title: A note on optimal expected utility of dividend payments with proportional reinsurance Abstract: In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company that controls risk exposure by purchasing proportional reinsurance. We assume the preference of the insurer is of CRRA form. By solving the corresponding Hamilton–Jacobi–Bellman equation, we identify the value function and the corresponding optimal strategy. We also analyze the asymptotic behavior of the value function for large initial reserves. Finally, we provide some numerical examples to illustrate the results and analyze the sensitivity of the parameters. Journal: Scandinavian Actuarial Journal Pages: 275-293 Issue: 4 Volume: 2018 Year: 2018 Month: 4 X-DOI: 10.1080/03461238.2017.1343748 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1343748 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:4:p:275-293 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1343749_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yang Shen Author-X-Name-First: Yang Author-X-Name-Last: Shen Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Lifetime asset allocation with idiosyncratic and systematic mortality risks Abstract: This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long. Journal: Scandinavian Actuarial Journal Pages: 294-327 Issue: 4 Volume: 2018 Year: 2018 Month: 4 X-DOI: 10.1080/03461238.2017.1343749 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1343749 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:4:p:294-327 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1350203_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Oliver Kley Author-X-Name-First: Oliver Author-X-Name-Last: Kley Author-Name: Claudia Klüppelberg Author-X-Name-First: Claudia Author-X-Name-Last: Klüppelberg Author-Name: Gesine Reinert Author-X-Name-First: Gesine Author-X-Name-Last: Reinert Title: Conditional risk measures in a bipartite market structure Abstract: In this paper, we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional risk measures. For large markets, Poisson approximations of the relevant constants are provided. Differences of the conditional risk measures for an underlying homogeneous and inhomogeneous random graph are illustrated by simulations. Journal: Scandinavian Actuarial Journal Pages: 328-355 Issue: 4 Volume: 2018 Year: 2018 Month: 4 X-DOI: 10.1080/03461238.2017.1350203 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1350203 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:4:p:328-355 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1350876_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hiroaki Hata Author-X-Name-First: Hiroaki Author-X-Name-Last: Hata Author-Name: Kazuhiro Yasuda Author-X-Name-First: Kazuhiro Author-X-Name-Last: Yasuda Title: Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model Abstract: In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy. Journal: Scandinavian Actuarial Journal Pages: 357-378 Issue: 5 Volume: 2018 Year: 2018 Month: 5 X-DOI: 10.1080/03461238.2017.1350876 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1350876 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:357-378 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1357654_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Enkelejd Hashorva Author-X-Name-First: Enkelejd Author-X-Name-Last: Hashorva Author-Name: Gildas Ratovomirija Author-X-Name-First: Gildas Author-X-Name-Last: Ratovomirija Author-Name: Maissa Tamraz Author-X-Name-First: Maissa Author-X-Name-Last: Tamraz Author-Name: Yizhou Bai Author-X-Name-First: Yizhou Author-X-Name-Last: Bai Title: Some mathematical aspects of price optimisation Abstract: Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely (a) construction of an optimal renewal tariff subject to business and technical constraints, and (b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic suboptimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach. Journal: Scandinavian Actuarial Journal Pages: 379-403 Issue: 5 Volume: 2018 Year: 2018 Month: 5 X-DOI: 10.1080/03461238.2017.1357654 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1357654 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:379-403 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1365758_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Liang Hong Author-X-Name-First: Liang Author-X-Name-Last: Hong Title: A note on Mossin’s theorem for deductible insurance given random initial wealth Abstract: Mossin’s theorem for deductible insurance given random initial wealth is re-examined. For a fair premium, it is shown that a necessary and sufficient condition, in the spirit of the Generalized Mossin Theorem for coinsurance, is impossible using the notion of expectation dependence. Next, it is established that for a fair premium, full insurance will be optimal for a risk-averse individual if the random loss and the random initial wealth are negative quadrant dependent, improving upon an extant result in the literature. In view of a set of examples given in this paper, such a sufficient condition cannot be obtained using the notion of expectation dependence. Finally, for an unfair premium, it is shown that partial insurance will always be optimal, irrespective of the risk preference of the individual as well as the dependence structure between the random loss and the random initial wealth. Journal: Scandinavian Actuarial Journal Pages: 404-411 Issue: 5 Volume: 2018 Year: 2018 Month: 5 X-DOI: 10.1080/03461238.2017.1365758 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1365758 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:404-411 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1371067_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xiang Hu Author-X-Name-First: Xiang Author-X-Name-Last: Hu Author-Name: Lianzeng Zhang Author-X-Name-First: Lianzeng Author-X-Name-Last: Zhang Author-Name: Weiwei Sun Author-X-Name-First: Weiwei Author-X-Name-Last: Sun Title: Risk model based on the first-order integer-valued moving average process with compound Poisson distributed innovations Abstract: This paper considers a discrete-time risk model by introducing a temporal dependence structure between the number of claims for each period. The risk model is based on the first-order integer-valued moving average (INMA(1)) process with compound Poisson distributed innovations. We derive the explicit expression for the moment generating function of the aggregate claim amount, which can be used for the calculation of some related quantities. We examine the properties of the adjustment coefficient for measuring the dangerousness of an insurance portfolio. Some special cases are included and numerical examples are provided to illustrate the results obtained in the paper. Journal: Scandinavian Actuarial Journal Pages: 412-425 Issue: 5 Volume: 2018 Year: 2018 Month: 5 X-DOI: 10.1080/03461238.2017.1371067 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1371067 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:412-425 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1371068_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Author-Name: Wen Su Author-X-Name-First: Wen Author-X-Name-Last: Su Title: A new efficient method for estimating the Gerber–Shiu function in the classical risk model Abstract: In this paper, we propose a new efficient method for estimating the Gerber–Shiu discounted penalty function in the classical risk model. We develop the Gerber–Shiu function on the Laguerre basis, and then estimate the unknown coefficients based on sample information on claim numbers and individual claim sizes. The convergence rate of the estimate is derived. Some simulation examples are illustrated to show that the estimate performs very well when the sample size is finite. We also show that the proposed estimate outperforms other estimates in the simulation studies. Journal: Scandinavian Actuarial Journal Pages: 426-449 Issue: 5 Volume: 2018 Year: 2018 Month: 5 X-DOI: 10.1080/03461238.2017.1371068 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1371068 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:426-449 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1377106_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Qiuying Zhang Author-X-Name-First: Qiuying Author-X-Name-Last: Zhang Author-Name: Fengyang Cheng Author-X-Name-First: Fengyang Author-X-Name-Last: Cheng Title: Precise local large deviations for heavy-tailed random sums with applications to risk models Abstract: In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common heavy-tailed distribution F, where F(x+Δ)=F((x,x+T])$ F(x+\Delta )=F((x, x+T]) $ is an O$ \mathcal O $-regularly varying function for some fixed constant T>0$ T>0 $(finite or infinite). We also obtain some results on precise local large deviation probabilities for the claim surplus process of generalized risk models in which the premium income until time t is simply assumed to be a nondecreasing and nonnegative stochastic process. In particular, the results we obtained are also valid for the global case, i.e. case T=∞$ T=\infty $. Journal: Scandinavian Actuarial Journal Pages: 450-463 Issue: 5 Volume: 2018 Year: 2018 Month: 5 X-DOI: 10.1080/03461238.2017.1377106 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1377106 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:450-463 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1428681_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Machine learning in individual claims reserving Abstract: Machine learning techniques make it feasible to calculate claims reserves on individual claims data. This paper illustrates how these techniques can be used by providing an explicit example in individual claims reserving. Journal: Scandinavian Actuarial Journal Pages: 465-480 Issue: 6 Volume: 2018 Year: 2018 Month: 7 X-DOI: 10.1080/03461238.2018.1428681 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1428681 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:6:p:465-480 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1388273_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jan Natolski Author-X-Name-First: Jan Author-X-Name-Last: Natolski Author-Name: Ralf Werner Author-X-Name-First: Ralf Author-X-Name-Last: Werner Title: Mathematical foundation of the replicating portfolio approach Abstract: In the last few years, the first theoretical foundations for replicating portfolios – probably the most prevailing technique for risk capital calculation in life insurance – have been given in a series of papers by Beutner, Pelsser and Schweizer. In these papers, the asymptotic behaviour of replicating portfolios concerning the approximation of the terminal value (TVL) and the fair value distribution of the liabilities (FVL) has been investigated in detail. We complement this line of research by providing results on approximations based on a finite number of replicating instruments. We do so by providing the link between the approximation error of the TVL distribution, the FVL distribution and the error in the resulting risk capital figure, either value at risk or some coherent risk measure. We further allow for a variety of practically relevant formulations of the replication problem, including cash flow matching approaches. In contrast to the existing literature, all our results apply to approaches both under the risk-neutral and the real-world measure. Our strongest bounds are due to the observation that in discrete time, the measure change from the real-world to the risk-neutral measure can be both bounded below and above by a suitable constant in the first period. Journal: Scandinavian Actuarial Journal Pages: 481-504 Issue: 6 Volume: 2018 Year: 2018 Month: 7 X-DOI: 10.1080/03461238.2017.1388273 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1388273 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:6:p:481-504 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1391114_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Matija Vidmar Author-X-Name-First: Matija Author-X-Name-Last: Vidmar Title: Ruin under stochastic dependence between premium and claim arrivals Abstract: We investigate, focusing on the ruin probability, an adaptation of the Cramér–Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of the premiums and of the claims respectively, are independent. Such a model exhibits a stochastic dependence between the aggregate premium and claim amount processes. An explicit expression for the ruin probability is obtained when the claim and premium sizes are exponentially distributed. Journal: Scandinavian Actuarial Journal Pages: 505-513 Issue: 6 Volume: 2018 Year: 2018 Month: 7 X-DOI: 10.1080/03461238.2017.1391114 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1391114 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:6:p:505-513 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1391872_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Long Bai Author-X-Name-First: Long Author-X-Name-Last: Bai Title: Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon Abstract: Let B(t),t≥0$ B(t), t \ge 0 $ be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (0.1)Ruδ(t)=eδtu+c∫0te-δvdv-σ∫0te-δvdB(v),t≥0,$$ \begin{aligned} R_u^{\delta }(t)=e^{\delta t}\left(u+c\int ^{t}_{0}e^{-\delta v}\mathrm{d} v-\sigma \int _{0}^{t}e^{-\delta v}\mathrm{d} B(v)\right),\quad t \ge 0, \end{aligned} $$where u≥0$ u \ge 0 $ is the initial reserve, δ≥0$ \delta \ge 0 $ is the force of interest, c>0$ c>0 $ is the rate of premium and σ>0$ \sigma >0 $ is a volatility factor. It turns out that the Parisian ruin probability decays exponentially as u tends to infinity and is a decreasing function of the force of interest for u large. Moreover, we obtain the approximations of Parisian ruin time. Journal: Scandinavian Actuarial Journal Pages: 514-528 Issue: 6 Volume: 2018 Year: 2018 Month: 7 X-DOI: 10.1080/03461238.2017.1391872 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1391872 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:6:p:514-528 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1394364_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tobias Gütschow Author-X-Name-First: Tobias Author-X-Name-Last: Gütschow Author-Name: Klaus Th. Hess Author-X-Name-First: Klaus Th. Author-X-Name-Last: Hess Author-Name: Klaus D. Schmidt Author-X-Name-First: Klaus D. Author-X-Name-Last: Schmidt Title: Separation of small and large claims on the basis of collective models Abstract: This paper is inspired by two papers of Riegel who proposed to consider the paid and incurred loss development of the individual claims and to use a filter in order to separate small and large claims and to construct loss development squares for the paid or incurred small or large claims and for the numbers of large claims. We show that such loss development squares can be constructed from collective models for the accident years. Moreover, under certain assumptions on these collective models, we show that a development pattern exists for each of these loss development squares, which implies that various methods of loss reserving can be used for prediction and that the chain ladder method is a natural method for the prediction of future numbers of large claims. Journal: Scandinavian Actuarial Journal Pages: 529-544 Issue: 6 Volume: 2018 Year: 2018 Month: 7 X-DOI: 10.1080/03461238.2017.1394364 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1394364 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:6:p:529-544 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1402086_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Dirichlet process mixture models for insurance loss data Abstract: In the recent insurance literature, a variety of finite-dimensional parametric models have been proposed for analyzing the hump-shaped, heavy-tailed, and highly skewed loss data often encountered in applications. These parametric models are relatively simple, but they lack flexibility in the sense that an actuary analyzing a new data-set cannot be sure that any one of these parametric models will be appropriate. As a consequence, the actuary must make a non-trivial choice among a collection of candidate models, putting him/herself at risk for various model misspecification biases. In this paper, we argue that, at least in cases where prediction of future insurance losses is the ultimate goal, there is reason to consider a single but more flexible nonparametric model. We focus here on Dirichlet process mixture models, and we reanalyze several of the standard insurance data-sets to support our claim that model misspecification biases can be avoided by taking a nonparametric approach, with little to no cost, compared to existing parametric approaches. Journal: Scandinavian Actuarial Journal Pages: 545-554 Issue: 6 Volume: 2018 Year: 2018 Month: 7 X-DOI: 10.1080/03461238.2017.1402086 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1402086 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:6:p:545-554 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1402817_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Corina Constantinescu Author-X-Name-First: Corina Author-X-Name-Last: Constantinescu Author-Name: Gennady Samorodnitsky Author-X-Name-First: Gennady Author-X-Name-Last: Samorodnitsky Author-Name: Wei Zhu Author-X-Name-First: Wei Author-X-Name-Last: Zhu Title: Ruin probabilities in classical risk models with gamma claims Abstract: In this paper, we provide three equivalent expressions for ruin probabilities in a Cramér–Lundberg model with gamma distributed claims. The results are solutions of integro-differential equations, derived by means of (inverse) Laplace transforms. All the three formulas have infinite series forms, two involving Mittag–Leffler functions and the third one involving moments of the claims distribution. This last result applies to any other claim size distributions that exhibits finite moments. Journal: Scandinavian Actuarial Journal Pages: 555-575 Issue: 7 Volume: 2018 Year: 2018 Month: 8 X-DOI: 10.1080/03461238.2017.1402817 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1402817 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:7:p:555-575 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1405840_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Daniel H. Alai Author-X-Name-First: Daniel H. Author-X-Name-Last: Alai Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Title: Lifetime dependence models generated by multiply monotone functions Abstract: We study a family of distributions generated from multiply monotone functions that includes a multivariate Pareto and, previously unidentified, exponential-Pareto distribution. We utilize an established link with Archimedean survival copulas to provide further examples, including a multivariate Weibull distribution, that may be used to fit light, or heavy-tailed phenomena, and which exhibit various forms of dependence, ranging from positive to negative. Because the model is intended for the study of joint lifetimes, we consider the effect of truncation and formulate properties required for a number of parameter estimation procedures based on moments and quantiles. For the quantile-based estimation procedure applied to the multivariate Weibull distribution, we also address the problem of optimal quantile selection. Journal: Scandinavian Actuarial Journal Pages: 576-604 Issue: 7 Volume: 2018 Year: 2018 Month: 8 X-DOI: 10.1080/03461238.2017.1405840 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1405840 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:7:p:576-604 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1418420_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Title: A Bayesian non-parametric model for small population mortality Abstract: This paper proposes a Bayesian non-parametric mortality model for a small population, when a benchmark mortality table is also available and serves as part of the prior information. In particular, we extend the Poisson-gamma model of Hardy and Panjer to incorporate correlated and age-specific mortality coefficients. These coefficients, which measure the difference in mortality levels between the small and the benchmark population, follow an age-indexed autoregressive gamma process, and can be stochastically extrapolated to ages where the small population has no historical exposure. Our model substantially improves the computation efficiency of existing two-population Bayesian mortality models by allowing for closed form posterior mean and variance of the future number of deaths, and an efficient sampling algorithm for the entire posterior distribution. We illustrate the proposed model with a life insurance portfolio from a French insurance company. Journal: Scandinavian Actuarial Journal Pages: 605-628 Issue: 7 Volume: 2018 Year: 2018 Month: 8 X-DOI: 10.1080/03461238.2017.1418420 File-URL: http://hdl.handle.net/10.1080/03461238.2017.1418420 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:7:p:605-628 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1426038_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Klaus Herrmann Author-X-Name-First: Klaus Author-X-Name-Last: Herrmann Author-Name: Marius Hofert Author-X-Name-First: Marius Author-X-Name-Last: Hofert Author-Name: Mélina Mailhot Author-X-Name-First: Mélina Author-X-Name-Last: Mailhot Title: Multivariate geometric expectiles Abstract: A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample version is shown to be a consistent estimator. We exemplify their usage as risk measures in a number of multivariate settings, highlighting the influence of varying margins and dependence structures. Journal: Scandinavian Actuarial Journal Pages: 629-659 Issue: 7 Volume: 2018 Year: 2018 Month: 8 X-DOI: 10.1080/03461238.2018.1426038 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1426038 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:7:p:629-659 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1429299_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xing Wang Author-X-Name-First: Xing Author-X-Name-Last: Wang Author-Name: Qing Liu Author-X-Name-First: Qing Author-X-Name-Last: Liu Author-Name: Yanxi Hou Author-X-Name-First: Yanxi Author-X-Name-Last: Hou Author-Name: Liang Peng Author-X-Name-First: Liang Author-X-Name-Last: Peng Title: Nonparametric inference for sensitivity of Haezendonck–Goovaerts risk measure Abstract: Recently Haezendonck–Goovaerts (H-G) risk measure has been popular in actuarial science. When it is applied to an insurance or a financial portfolio with several loss variables, sensitivity analysis becomes useful in managing the portfolio, and the assumption of independent observations may not be reasonable. This paper first derives an expression for computing the sensitivity of the H-G risk measure, which enables us to estimate the sensitivity nonparametrically via the H-G risk measure. Further, we derive the asymptotic distributions of the nonparametric estimators for the H-G risk measure and the sensitivity by assuming that loss variables in the portfolio follow from a strictly stationary α$ \alpha $-mixing sequence. A simulation study is provided to examine the finite sample performance of the proposed nonparametric estimators. Finally, the method is applied to a real data set. Journal: Scandinavian Actuarial Journal Pages: 661-680 Issue: 8 Volume: 2018 Year: 2018 Month: 9 X-DOI: 10.1080/03461238.2018.1429299 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1429299 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:8:p:661-680 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1429300_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Roel Henckaerts Author-X-Name-First: Roel Author-X-Name-Last: Henckaerts Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Author-Name: Maxime Clijsters Author-X-Name-First: Maxime Author-X-Name-Last: Clijsters Author-Name: Roel Verbelen Author-X-Name-First: Roel Author-X-Name-Last: Verbelen Title: A data driven binning strategy for the construction of insurance tariff classes Abstract: We present a fully data driven strategy to incorporate continuous risk factors and geographical information in an insurance tariff. A framework is developed that aligns flexibility with the practical requirements of an insurance company, the policyholder and the regulator. Our strategy is illustrated with an example from property and casualty (P&C) insurance, namely a motor insurance case study. We start by fitting generalized additive models (GAMs) to the number of reported claims and their corresponding severity. These models allow for flexible statistical modeling in the presence of different types of risk factors: categorical, continuous, and spatial risk factors. The goal is to bin the continuous and spatial risk factors such that categorical risk factors result which captures the effect of the covariate on the response in an accurate way, while being easy to use in a generalized linear model (GLM). This is in line with the requirement of an insurance company to construct a practical and interpretable tariff that can be explained easily to stakeholders. We propose to bin the spatial risk factor using Fisher’s natural breaks algorithm and the continuous risk factors using evolutionary trees. GLMs are fitted to the claims data with the resulting categorical risk factors. We find that the resulting GLMs approximate the original GAMs closely, and lead to a very similar premium structure. Journal: Scandinavian Actuarial Journal Pages: 681-705 Issue: 8 Volume: 2018 Year: 2018 Month: 9 X-DOI: 10.1080/03461238.2018.1429300 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1429300 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:8:p:681-705 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1431805_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Piotr S̀liwka Author-X-Name-First: Piotr Author-X-Name-Last: S̀liwka Author-Name: Lesław Socha Author-X-Name-First: Lesław Author-X-Name-Last: Socha Title: A proposition of generalized stochastic Milevsky–Promislov mortality models Abstract: The aim of this article is to propose a new approach to the estimation of the mortality rates based on two extended Milevsky and Promislov models: the first one with colored excitations modeled by Gaussian linear filters and the second one with excitations modeled by a continuous non-Gaussian process. The exact analytical formulas for theoretical mortality rates based on Gaussian linear scalar filter models have been derived. The theoretical values obtained in both cases were compared with theoretical mortality rates based on a classical Lee–Carter model, and verified on the basis of empirical Polish mortality data. The obtained results confirm the usefulness of the switched model based on the continuous non-Gaussian process for modeling mortality rates. Journal: Scandinavian Actuarial Journal Pages: 706-726 Issue: 8 Volume: 2018 Year: 2018 Month: 9 X-DOI: 10.1080/03461238.2018.1431805 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1431805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:8:p:706-726 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1452285_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jiwook Jang Author-X-Name-First: Jiwook Author-X-Name-Last: Jang Author-Name: Angelos Dassios Author-X-Name-First: Angelos Author-X-Name-Last: Dassios Author-Name: Hongbiao Zhao Author-X-Name-First: Hongbiao Author-X-Name-Last: Zhao Title: Moments of renewal shot-noise processes and their applications Abstract: In this paper, we study the family of renewal shot-noise processes. The Feynmann–Kac formula is obtained based on the piecewise deterministic Markov process theory and the martingale methodology. We then derive the Laplace transforms of the conditional moments and asymptotic moments of the processes. In general, by inverting the Laplace transforms, the asymptotic moments and the first conditional moments can be derived explicitly; however, other conditional moments may need to be estimated numerically. As an example, we develop a very efficient and general algorithm of Monte Carlo exact simulation for estimating the second conditional moments. The results can be then easily transformed to the counterparts of discounted aggregate claims for insurance applications, and we apply the first two conditional moments for the actuarial net premium calculation. Similarly, they can also be applied to credit risk and reliability modelling. Numerical examples with four distribution choices for interarrival times are provided to illustrate how the models can be implemented. Journal: Scandinavian Actuarial Journal Pages: 727-752 Issue: 8 Volume: 2018 Year: 2018 Month: 9 X-DOI: 10.1080/03461238.2018.1452285 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1452285 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:8:p:727-752 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1452786_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Antonio Heras Author-X-Name-First: Antonio Author-X-Name-Last: Heras Author-Name: Ignacio Moreno Author-X-Name-First: Ignacio Author-X-Name-Last: Moreno Author-Name: José L. Vilar-Zanón Author-X-Name-First: José L. Author-X-Name-Last: Vilar-Zanón Title: An application of two-stage quantile regression to insurance ratemaking Abstract: Two-part models based on generalized linear models are widely used in insurance rate-making for predicting the expected loss. This paper explores an alternative method based on quantile regression which provides more information about the loss distribution and can be also used for insurance underwriting. Quantile regression allows estimating the aggregate claim cost quantiles of a policy given a number of covariates. To do so, a first stage is required, which involves fitting a logistic regression to estimate, for every policy, the probability of submitting at least one claim. The proposed methodology is illustrated using a portfolio of car insurance policies. This application shows that the results of the quantile regression are highly dependent on the claim probability estimates. The paper also examines an application of quantile regression to premium safety loading calculation, the so-called Quantile Premium Principle (QPP). We propose a premium calculation based on quantile regression which inherits the good properties of the quantiles. Using the same insurance portfolio data-set, we find that the QPP captures the riskiness of the policies better than the expected value premium principle. Journal: Scandinavian Actuarial Journal Pages: 753-769 Issue: 9 Volume: 2018 Year: 2018 Month: 10 X-DOI: 10.1080/03461238.2018.1452786 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1452786 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:9:p:753-769 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1455153_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stig Rosenlund Author-X-Name-First: Stig Author-X-Name-Last: Rosenlund Title: Credibility pseudo-estimators Abstract: We treat a model with independent claim numbers and claim amounts, conditional on stochastic parameters. Groups are categorized into a smaller number of classes, which likely differ in risk premium. The collective claim frequency and mean claim for a group are modeled as those of the class the group belongs to. For each group we find the Best Linear Predictor, also known as Credibility Estimator, in a generic model covering claim frequency and mean claim, as a weighted mean of the group’s individual estimate and the collective estimate. Assuming Poisson distributed claim numbers and some distributional properties of claim amounts, we find estimators of variance components, estimation errors of the collective claim frequency and mean claim, and covariances between observations, estimators, and stochastic parameters. Pseudo-estimators, i.e. estimators which are defined by expressions that contain them and which must be solved numerically, are given for between-groups variance components. Simulation results, where some of the assumptions are violated, indicate when they are preferable over non-pseudo-estimators. Journal: Scandinavian Actuarial Journal Pages: 770-791 Issue: 9 Volume: 2018 Year: 2018 Month: 10 X-DOI: 10.1080/03461238.2018.1455153 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1455153 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:9:p:770-791 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1461129_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: G. I. Papayiannis Author-X-Name-First: G. I. Author-X-Name-Last: Papayiannis Author-Name: A. N. Yannacopoulos Author-X-Name-First: A. N. Author-X-Name-Last: Yannacopoulos Title: Convex risk measures for the aggregation of multiple information sources and applications in insurance Abstract: We propose a novel class of convex risk measures, based on the concept of the Fréchet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty. Journal: Scandinavian Actuarial Journal Pages: 792-822 Issue: 9 Volume: 2018 Year: 2018 Month: 10 X-DOI: 10.1080/03461238.2018.1461129 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1461129 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:9:p:792-822 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1463556_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xiaobai Zhu Author-X-Name-First: Xiaobai Author-X-Name-Last: Zhu 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 an early exercise defined benefit underpin hybrid pension Abstract: In this paper, we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, which has been offered to public employees in the state of Florida since 2002. The state runs both defined contribution (DC) and defined benefit (DB) pension plans. Employees who initially join the DC plan have the option to convert to the (DB) plan at a time of their choosing. The cost of the switch is assessed in terms of the ABO (Accrued Benefit Obligation), which is the expected present value of the accrued DB pension at the time of the switch. If the ABO is greater than the DC account, the employee is required to fund the difference. The second is the DB Underpin option, also known as a ‘floor offset’ or a ‘Greater-of-benefit’ plan, under which the employee participates in a DC plan, but with a guaranteed minimum benefit based on a traditional DB formula. The third option can be considered a variation on each of the first two. We remove the requirement from the FSE option for employees to fund any shortfall at the switching date. The resulting plan is similar to the DB underpin, but with the possibility of early exercise. We adopt an arbitrage-free pricing methodology to value each option. We analyse and value the optimal switching strategy for the employee by constructing an exercise frontier, and we illustrate numerically the difference between the FSE, DB Underpin and Early Exercise DB Underpin options. Journal: Scandinavian Actuarial Journal Pages: 823-844 Issue: 9 Volume: 2018 Year: 2018 Month: 10 X-DOI: 10.1080/03461238.2018.1463556 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1463556 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:9:p:823-844 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1463557_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hiroshi Shiraishi Author-X-Name-First: Hiroshi Author-X-Name-Last: Shiraishi Author-Name: Zudi Lu Author-X-Name-First: Zudi Author-X-Name-Last: Lu Title: Semiparametric estimation in the optimal dividend barrier for the classical risk model Abstract: In the context of an insurance portfolio which provides dividend income for the insurance company’s shareholders, an important problem in risk theory is how the premium income will be paid to the shareholders as dividends according to a barrier strategy until the next claim occurs whenever the surplus attains the level of ‘barrier’. In this paper, we are concerned with the estimation of optimal dividend barrier, defined as the level of the barrier that maximizes the expected discounted dividends until ruin, under the widely used compound Poisson model as the aggregate claims process. We propose a semi-parametric statistical procedure for estimation of the optimal dividend barrier, which is critically needed in applications. We first construct a consistent estimator of the objective function that is complexly related to the expected discounted dividends and then the estimated optimal dividend barrier as the minimizer of the estimated objective function. In theory, we show that the constructed estimator of the optimal dividend barrier is statistically consistent. Numerical experiments by both simulated and real data analyses demonstrate that the proposed estimators work reasonably well with an appropriate size of samples. Journal: Scandinavian Actuarial Journal Pages: 845-862 Issue: 9 Volume: 2018 Year: 2018 Month: 10 X-DOI: 10.1080/03461238.2018.1463557 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1463557 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2018:y:2018:i:9:p:845-862 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1481454_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric C. K. Cheung Author-X-Name-First: Eric C. K. Author-X-Name-Last: Cheung Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Title: Periodic threshold-type dividend strategy in the compound Poisson risk model Abstract: In this paper, the compound Poisson risk model is considered. Inspired by Albrecher, Cheung, & Thonhauser. [(2011b). Randomized observation periods for the compound Poisson risk model: dividend. ASTIN Bulletin 41(2), 645–672], it is assumed that the insurer observes its surplus level periodically to decide on dividend payments at the arrival times of an Erlang(n) renewal process. If the observed surplus is larger than the maximum of a threshold b and the last observed (post-dividend) level, then a fraction of the excess is paid as a lump sum dividend. Ruin is declared when the observed surplus is negative. In this proposed periodic threshold-type dividend strategy, the insurer can have a ruin probability of less than one (as opposed to the periodic barrier strategy). The expected discounted dividends before ruin (denoted by V) will be analyzed. For arbitrary claim distribution, the general solution of V is derived. More explicit result for V is presented when claims have rational Laplace transform. Numerical examples are provided to illustrate the effect of randomized observations on V and the optimization of V with respect to b. When claims are exponential, convergence to the traditional threshold strategy is shown as the inter-observation times tend to zero. Journal: Scandinavian Actuarial Journal Pages: 1-31 Issue: 1 Volume: 2019 Year: 2019 Month: 1 X-DOI: 10.1080/03461238.2018.1481454 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1481454 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:1:p:1-31 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1483420_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mogens Bladt Author-X-Name-First: Mogens Author-X-Name-Last: Bladt Author-Name: Bo Friis Nielsen Author-X-Name-First: Bo Friis Author-X-Name-Last: Nielsen Author-Name: Oscar Peralta Author-X-Name-First: Oscar Author-X-Name-Last: Peralta Title: Parisian types of ruin probabilities for a class of dependent risk-reserve processes Abstract: For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities. Journal: Scandinavian Actuarial Journal Pages: 32-61 Issue: 1 Volume: 2019 Year: 2019 Month: 1 X-DOI: 10.1080/03461238.2018.1483420 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1483420 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:1:p:32-61 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1488272_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: A constraint-free approach to optimal reinsurance Abstract: Reinsurance is available for a reinsurance premium that is determined according to a convex premium principle H. The first insurer selects the reinsurance coverage that maximizes its expected utility. No conditions are imposed on the reinsurer's payment. The optimality condition involves the gradient of H. For several combinations of H and the first insurer's utility function, closed-form formulas for the optimal reinsurance are given. If H is a zero utility principle (for example, an exponential principle or an expectile principle), it is shown, by means of Borch's Theorem, that the optimal reinsurer's payment is a function of the total claim amount and that this function satisfies the so-called 1-Lipschitz condition. Frequently, authors impose these two conclusions as hypotheses at the outset. Journal: Scandinavian Actuarial Journal Pages: 62-79 Issue: 1 Volume: 2019 Year: 2019 Month: 1 X-DOI: 10.1080/03461238.2018.1488272 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1488272 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:1:p:62-79 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1498387_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Grandits Author-X-Name-First: Peter Author-X-Name-Last: Grandits Title: A two-dimensional dividend problem for collaborating companies and an optimal stopping problem Abstract: We consider two insurance companies with wealth processes described by two independent Brownian motions with drift. The goal of the companies is to maximize their expected aggregated discounted dividend payments until ruin. The companies are allowed to help each other by means of transfer payments. But in contrast to Gu et al. [(2018). Optimal dividend strategies of two collaborating businesses in the diffusion approximation model. Mathematics of Operations Research 43(2), 377–398], they are not obliged to do so, if one company faces ruin. We show that the problem is equivalent to a mixture of a one-dimensional singular control problem and an optimal stopping problem. The value function is explicitly constructed and a verification result is proved. Moreover, the optimal strategy is provided as well. Journal: Scandinavian Actuarial Journal Pages: 80-96 Issue: 1 Volume: 2019 Year: 2019 Month: 1 X-DOI: 10.1080/03461238.2018.1498387 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1498387 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:1:p:80-96 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1624274_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Author-Name: Mhamed Mesfioui Author-X-Name-First: Mhamed Author-X-Name-Last: Mesfioui Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Title: Concordance-based predictive measures in regression models for discrete responses Abstract: Dependence measures are often used in practice in order to assess the quality of a regression model. This is for instance the case with Kendall's tau and other association coefficients based on concordance probabilities. However, in case the response variable is discrete, correlation indices are often bounded and restricted to a sub-interval of $[-1,1] $[−1,1]. Hence, in this context, small positive values of Kendall's tau may actually support goodness of prediction when getting close to its highest attainable value. In this paper, we derive the best-possible upper bounds for Kendall's tau when the response variable is discrete. Two cases are considered, depending on whether the score is continuous or discrete. Also, we illustrate the obtained upper bounds on a motor third-party liability insurance portfolio. Journal: Scandinavian Actuarial Journal Pages: 824-836 Issue: 10 Volume: 2019 Year: 2019 Month: 11 X-DOI: 10.1080/03461238.2019.1624274 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1624274 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:10:p:824-836 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1626762_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Author-Name: Hok Kan Ling Author-X-Name-First: Hok Kan Author-X-Name-Last: Ling Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Author-Name: Sheung Chi Phillip Yam Author-X-Name-First: Sheung Chi Phillip Author-X-Name-Last: Yam Author-Name: Fei Lung Yuen Author-X-Name-First: Fei Lung Author-X-Name-Last: Yuen Title: On additivity of tail comonotonic risks Abstract: As perceived from daily experience together with numerous empirical studies, the multivariate risks demonstrate a strong coherence in the extremal dependence structure especially over the course of financial turmoil or industrial accidents and outbreaks. Under this motivating paradigm, we show the universal asymptotic additivity under upper tail comonotonicity, as the probability level approaching to 1, for Value-at-Risk and Conditional Tail Expectation for a portfolio of fixed number of risks, in which each marginal risk could be any one having a finite endpoint or belonging to one of the three max domains of attraction. Our obtained results do not require the tail equivalence assumption as needed in the existing literature. This resolves a lasting problem in quantitative risk management and covers most distributions commonly encountered in practice. Journal: Scandinavian Actuarial Journal Pages: 837-866 Issue: 10 Volume: 2019 Year: 2019 Month: 11 X-DOI: 10.1080/03461238.2019.1626762 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1626762 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:10:p:837-866 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1627574_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: K. Fergusson Author-X-Name-First: K. Author-X-Name-Last: Fergusson Title: Asymptotics of bond yields and volatilities for extended CIR models under the real-world measure Abstract: The Cox–Ingersoll–Ross CIR short rate model is a mean-reverting model of the short rate which, for suitably chosen parameters, permits closed-form valuation formulae of zero-coupon bonds and options on zero-coupon bonds. This article supplies proofs of the formulae for the expected present value of payoffs under the real-world probability measure, known as actuarial valuation. Importantly, we give formulae for asymptotic levels of bond yields and volatilities for extended CIR models when suitable conditions are imposed on the model parameters. Journal: Scandinavian Actuarial Journal Pages: 867-902 Issue: 10 Volume: 2019 Year: 2019 Month: 11 X-DOI: 10.1080/03461238.2019.1627574 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1627574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:10:p:867-902 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1628101_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: Ying Wang Author-X-Name-First: Ying Author-X-Name-Last: Wang Title: Reinsurance premium principles based on weighted loss functions Abstract: In this paper, we propose new reinsurance premium principles that minimize the expected weighted loss functions and balance the trade-off between the reinsurer's shortfall risk and the insurer's risk exposure in a reinsurance contract. Random weighting factors are introduced in the weighted loss functions so that weighting factors are based on the underlying insurance risks. The resulting reinsurance premiums depend on both the loss covered by the reinsurer and the loss retained by the insurer. The proposed premiums provide new ways for pricing reinsurance contracts and controlling the risks of both the reinsurer and the insurer. As applications of the proposed principles, the modified expectile reinsurance principle and the modified quantile reinsurance principle are introduced and discussed in details. The properties of the new reinsurance premium principles are investigated. Finally, the comparisons between the new reinsurance premium principles and the classical expectile principle, the classical quantile principle, and the risk-adjusted principle are provided. Journal: Scandinavian Actuarial Journal Pages: 903-923 Issue: 10 Volume: 2019 Year: 2019 Month: 11 X-DOI: 10.1080/03461238.2019.1628101 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1628101 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:10:p:903-923 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1511464_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Author-Name: Jia Liu Author-X-Name-First: Jia Author-X-Name-Last: Liu Title: A logistic two-population mortality projection model for modelling mortality at advanced ages for both sexes Abstract: In the current literature, numerous mortality projection models have been proposed and tested, but in general they have been designed for and applied to mainly ages below 90. As medical advances are being shifted to older ages over time and there is a rapid growth in the number of centenarians, there is a need to expand the modelling to older ages. We propose a logistic two-population mortality projection model for the death rates at ages 80 to 100+ for both sexes. We apply this model and its extensions to high quality old-age mortality data of Belgium, Sweden, Switzerland, and the UK and produce decent model performance in both mortality fitting and forecasting. The model structure also provides a reasonable way to close off the life table, which is supported by both theoretical arguments and empirical evidence. Journal: Scandinavian Actuarial Journal Pages: 97-112 Issue: 2 Volume: 2019 Year: 2019 Month: 2 X-DOI: 10.1080/03461238.2018.1511464 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1511464 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:2:p:97-112 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1513865_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: MingJie Hao Author-X-Name-First: MingJie Author-X-Name-Last: Hao Author-Name: Angus S. Macdonald Author-X-Name-First: Angus S. Author-X-Name-Last: Macdonald Author-Name: Pradip Tapadar Author-X-Name-First: Pradip Author-X-Name-Last: Tapadar Author-Name: R. Guy Thomas Author-X-Name-First: R. Guy Author-X-Name-Last: Thomas Title: Insurance loss coverage and social welfare Abstract: Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome, both for insurers and for society. However, a social benefit of modest adverse selection is that it can lead to an increase in ‘loss coverage’, defined as expected losses compensated by insurance for the whole population. We reconcile the concept of loss coverage to a utilitarian concept of social welfare commonly found in the economic literature on risk classification. For iso-elastic insurance demand, ranking risk classification schemes by (observable) loss coverage always give the same ordering as ranking by (unobservable) social welfare. Journal: Scandinavian Actuarial Journal Pages: 113-128 Issue: 2 Volume: 2019 Year: 2019 Month: 2 X-DOI: 10.1080/03461238.2018.1513865 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1513865 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:2:p:113-128 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1519847_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yinzhi Wang Author-X-Name-First: Yinzhi Author-X-Name-Last: Wang Author-Name: Ingrid Hobæk Haff Author-X-Name-First: Ingrid Author-X-Name-Last: Hobæk Haff Title: Focussed selection of the claim severity distribution Abstract: Risk assessment is a core theme within non-life insurance and estimation of quantiles far out in the upper tail is therefore one of the main applications of the total loss distribution of a non-life insurance portfolio. The choice of claim severity distribution should therefore reflect this. Therefore, we have explored how the focussed information criterion, FIC, aimed at finding the best model for estimating a given parameter of interest, the focus parameter, works as a tool for selecting the claim size distribution. As a quantile cannot be used directly as a focus parameter, we have tried different proxy focus parameters. To see how the FIC performs in this setting, compared to the other commonly used model selection methods AIC and BIC, we have performed a simulation study. In particular, we wanted to investigate the effect of the heaviness of the tail of the claim size distribution and the amount of available data. The performance of the different model selection methods was then evaluated based on the quality of the resulting estimates of the quantiles. Our study shows the best of the focussed criteria is the FIC $ _{\epsilon } $ ϵ, based on one single quantile from the claim severity distribution. Further, the performance of the FIC $ _{\epsilon } $ ϵ is mostly either comparable to or considerably better than that of the BIC, which is the best performing of the state of the art approaches. In particular, the FIC $ _{\epsilon } $ ϵ works well when the data are heavy-tailed, when the sample size is rather low and when the parameter of interest is the quantile far out in the tail of the total loss distribution. Journal: Scandinavian Actuarial Journal Pages: 129-142 Issue: 2 Volume: 2019 Year: 2019 Month: 2 X-DOI: 10.1080/03461238.2018.1519847 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1519847 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:2:p:129-142 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1523068_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Claims frequency modeling using telematics car driving data Abstract: We investigate the predictive power of covariates extracted from telematics car driving data using the speed-acceleration heatmaps of Gao, G. & Wüthrich, M. V. [(2017). Feature extraction from telematics car driving heatmaps. SSRN ID: 3070069]. These telematics covariates include K-means classification, principal components, and bottleneck activations from a bottleneck neural network. In the conducted case study it turns out that the first principal component and the bottleneck activations give a better out-of-sample prediction for claims frequencies than other traditional pricing factors such as driver's age. Based on these numerical examples we recommend the use of these telematics covariates for car insurance pricing. Journal: Scandinavian Actuarial Journal Pages: 143-162 Issue: 2 Volume: 2019 Year: 2019 Month: 2 X-DOI: 10.1080/03461238.2018.1523068 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1523068 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:2:p:143-162 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1528477_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Karim Barigou Author-X-Name-First: Karim Author-X-Name-Last: Barigou Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Title: Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting Abstract: A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. [Insurance: Mathematics & Economics, 76, 14–27 (2017)] in a single period framework. In particular, the authors considered mean-variance hedge-based (MVHB) valuations where fair valuations of insurance liabilities are expressed in terms of mean-variance hedges and actuarial valuations. In this paper, we generalize this MVHB approach to a multi-period dynamic investment setting. We show that the classes of fair valuations and MVHB valuations are equivalent in this generalized setting. We derive tractable formulas for the fair valuation of equity-linked contracts and show how the actuarial part of their MVHB valuation decomposes into a diversifiable and a non-diversifiable component. Journal: Scandinavian Actuarial Journal Pages: 163-187 Issue: 2 Volume: 2019 Year: 2019 Month: 2 X-DOI: 10.1080/03461238.2018.1528477 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1528477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:2:p:163-187 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1531781_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Miguel Ángel de la Llave Author-X-Name-First: Miguel Ángel Author-X-Name-Last: de la Llave Author-Name: Fernando A. López Author-X-Name-First: Fernando A. Author-X-Name-Last: López Author-Name: Ana Angulo Author-X-Name-First: Ana Author-X-Name-Last: Angulo Title: The impact of geographical factors on churn prediction: an application to an insurance company in Madrid's urban area Abstract: Geography has previously been noted as a decisive factor in business literature. This paper provides evidence of the significant role geography plays in customer lapse behaviour in an urban environment. This novel approach is based on the idea that the customers who cancel all policies and leave the company are not randomly distributed; rather, a mimetic performance of close individuals is noted. The physical proximity of the customer to the geographical focus (strategical centre, as insurance offices) and the interaction with nearby customer are spatial factors that increase (or decrease) the probability of churning. An empirical analysis using more than 7000 spatially georeferenced offline customers of a Spanish insurance company in the urban area of Madrid (Spain) demonstrated that the customer's proximity to offices of such insurance company under study decreases the probability of churning, whereas high lapse risk was detected in customers in the surroundings of the company's competitor branches. In addition, we identified spatial autocorrelation in churn probability, thus demonstrating that the probability of churn of a customer increases if nearby customers churn. Journal: Scandinavian Actuarial Journal Pages: 188-203 Issue: 3 Volume: 2019 Year: 2019 Month: 3 X-DOI: 10.1080/03461238.2018.1531781 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1531781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:3:p:188-203 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1541025_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ninna Reitzel Jensen Author-X-Name-First: Ninna Reitzel Author-X-Name-Last: Jensen Title: Life insurance decisions under recursive utility Abstract: In this paper, we generalize recursive utility to include lifetime uncertainty and utility from bequest. The generalization applies to discrete-time as well as continuous-time recursive utility, and it is an important step forward in the development of recursive utility. We formalize the problem of optimal consumption, investment, and life insurance choice under recursive utility, and we state a verification theorem with a generalized Hamilton-Jacobi-Bellman equation. Our generalization of recursive utility allows us to study optimal consumption, investment, and life insurance choice under separation of (market) risk aversion, elasticity of inter-temporal substitution, and elasticity of substitution between bequest and future utility. The separation gives rise to hump-shaped consumption patterns as observed in realized consumption. Journal: Scandinavian Actuarial Journal Pages: 204-227 Issue: 3 Volume: 2019 Year: 2019 Month: 3 X-DOI: 10.1080/03461238.2018.1541025 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1541025 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:3:p:204-227 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1543130_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghislain Léveillé Author-X-Name-First: Ghislain Author-X-Name-Last: Léveillé Author-Name: Emmanuel Hamel Author-X-Name-First: Emmanuel Author-X-Name-Last: Hamel Title: Compound trend renewal process with discounted claims: a unified approach Abstract: We derive recursive formulas for the moments of compound trend renewal sums with discounted claims. An integral expression for the moment generating function of this risk process is then obtained, from which particular distribution functions are found. We extend the compound (deterministic) trend renewal process by assuming a stochastic trend, a stochastic force of net interest and a stochastic dependence between the inter-occurrence times and the severities of the claims. Finally, stochastic dominance ordering is also observed between the compound trend renewal process and an associated non-homogeneous Poisson process. Journal: Scandinavian Actuarial Journal Pages: 228-246 Issue: 3 Volume: 2019 Year: 2019 Month: 3 X-DOI: 10.1080/03461238.2018.1543130 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1543130 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:3:p:228-246 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1546224_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Title: Modeling cause-of-death mortality using hierarchical Archimedean copula Abstract: Studying changes in cause-specific (or competing risks) mortality rates may provide significant insights for the insurance business as well as the pension systems, as they provide more information than the aggregate mortality data. However, the forecasting of cause-specific mortality rates requires new tools to capture the dependence among the competing causes. This paper introduces a class of hierarchical Archimedean copula (HAC) models for cause-specific mortality data. The approach extends the standard Archimedean copula models by allowing for asymmetric dependence among competing risks, while preserving closed-form expressions for mortality forecasts. Moreover, the HAC model allows for a convenient analysis of the impact of hypothetical reduction, or elimination, of mortality of one or more causes on the life expectancy. Using US cohort mortality data, we analyze the historical mortality patterns of different causes of death, provide an explanation for the ‘failure’ of the War on Cancer, and evaluate the impact on life expectancy of hypothetical scenarios where cancer mortality is reduced or eliminated. We find that accounting for longevity improvement across cohorts can alter the results found in existing studies that are focused on one single cohort. Journal: Scandinavian Actuarial Journal Pages: 247-272 Issue: 3 Volume: 2019 Year: 2019 Month: 3 X-DOI: 10.1080/03461238.2018.1546224 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1546224 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:3:p:247-272 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1557738_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yiying Zhang Author-X-Name-First: Yiying Author-X-Name-Last: Zhang Author-Name: Peng Zhao Author-X-Name-First: Peng Author-X-Name-Last: Zhao Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Title: Comparisons of aggregate claim numbers and amounts: a study of heterogeneity Abstract: In this paper, we investigate how the heterogeneity among occurrence probabilities and claim severities affects the aggregate claim numbers and aggregate claim amount for an insurance portfolio. We show that higher heterogeneity (and dependence) among occurrence probabilities results in both smaller aggregate claim numbers and aggregate claim amount in the sense of the mean residual lifetime order. We also prove that as the heterogeneity among the claims increases, the aggregate claim amount increases in the sense of the usual stochastic order when the vector of occurrence probabilities is left tail weakly stochastic arrangement increasing. These theoretical findings are applied to (i) study ordering properties of convolutions of binomial random variables, (ii) provide upper bounds for the mean residual lifetime functions of the aggregate claim numbers and amount, and (iii) compare stop-loss premiums and risk capital of different insurance portfolios. Journal: Scandinavian Actuarial Journal Pages: 273-290 Issue: 4 Volume: 2019 Year: 2019 Month: 4 X-DOI: 10.1080/03461238.2018.1557738 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1557738 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:4:p:273-290 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1557739_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Wenyuan Wang Author-X-Name-First: Wenyuan Author-X-Name-Last: Wang Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Title: Computing the Gerber–Shiu function by frame duality projection Abstract: Inspired by some works of Kirkby, J. L. [2015. Efficient option pricing by frame duality with the fast Fourier transform. SIAM Journal on Financial Mathematics 6(1), 713–747; 2016. An efficient transform method for Asian option pricing. SIAM Journal on Financial Mathematics 7(1), 845–892], we present a systematic study on effectively computing the Gerber–Shiu function in the Lévy risk model, where the frame duality projection is used for approximation. By introducing an auxiliary function, we provide a smooth extension of the Gerber–Shiu function, which has closed-form Fourier transform and is differentiable over the whole real line under some conditions. The objective function is approximated by its frame duality projection onto a Riesz basis, and the projection coefficients are readily computed by the fast Fourier transform algorithm. Error analysis is made and the effectiveness of our results will be further illustrated in the numerical experiments. Journal: Scandinavian Actuarial Journal Pages: 291-307 Issue: 4 Volume: 2019 Year: 2019 Month: 4 X-DOI: 10.1080/03461238.2018.1557739 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1557739 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:4:p:291-307 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1560357_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Kritzer Author-X-Name-First: Peter Author-X-Name-Last: Kritzer Author-Name: Gunther Leobacher Author-X-Name-First: Gunther Author-X-Name-Last: Leobacher Author-Name: Michaela Szölgyenyi Author-X-Name-First: Michaela Author-X-Name-Last: Szölgyenyi Author-Name: Stefan Thonhauser Author-X-Name-First: Stefan Author-X-Name-Last: Thonhauser Title: Approximation methods for piecewise deterministic Markov processes and their costs Abstract: In this paper, we analyse piecewise deterministic Markov processes (PDMPs), as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of PDMPs. There one is interested in computing certain quantities of interest such as the probability of ruin or the value of an insurance company. Instead of explicitly solving the related integro-(partial) differential equation (an approach which can only be used in few special cases), we adapt the problem in a manner that allows us to apply deterministic numerical integration algorithms such as quasi-Monte Carlo rules; this is in contrast to applying random integration algorithms such as Monte Carlo. To this end, we reformulate a general cost functional as a fixed point of a particular integral operator, which allows for iterative approximation of the functional. Furthermore, we introduce a smoothing technique which is applied to the integrands involved, in order to use error bounds for deterministic cubature rules. We prove a convergence result for our PDMPs approximation, which is of independent interest as it justifies phase-type approximations on the process level. We illustrate the smoothing technique for a risk-theoretic example, and compare deterministic and Monte Carlo integration. Journal: Scandinavian Actuarial Journal Pages: 308-335 Issue: 4 Volume: 2019 Year: 2019 Month: 4 X-DOI: 10.1080/03461238.2018.1560357 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1560357 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:4:p:308-335 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1560955_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: Kristina P. Sendova Author-X-Name-First: Kristina P. Author-X-Name-Last: Sendova Title: The expected discounted penalty function: from infinite time to finite time Abstract: In this paper we study the finite-time expected discounted penalty function (EDPF) and its decomposition in the classical risk model perturbed by diffusion. We first give the solution to a class of second-order partial integro-differential equations (PIDEs) with certain boundary conditions. We then show that the finite-time EDPFs as well as their decompositions satisfy this specific class of PIDEs so that their explicit expressions are obtained. Furthermore, we demonstrate that the finite-time EDPF may be expressed in terms of its ordinary counterpart (infinite-time) under the same risk model. Especially, the finite-time ruin probability due to oscillations and the finite-time ruin probability caused by a claim may also be expressed in terms of the corresponding quantities under the infinite-time horizon. Numerical examples are given when claims follow an exponential distribution. Journal: Scandinavian Actuarial Journal Pages: 336-354 Issue: 4 Volume: 2019 Year: 2019 Month: 4 X-DOI: 10.1080/03461238.2018.1560955 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1560955 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:4:p:336-354 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1525423_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric C.K. Cheung Author-X-Name-First: Eric C.K. Author-X-Name-Last: Cheung Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Title: Potential measures and expected present value of operating costs until ruin in renewal risk models with general interclaim times Abstract: In this paper, a Sparre Andersen risk process with arbitrary interclaim time distribution is considered. We analyze various ruin-related quantities in relation to the expected present value of total operating costs until ruin, which was first proposed by Cai et al. [(2009a). On the expectation of total discounted operating costs up to default and its applications. Advances in Applied Probability 41(2), 495–522] in the piecewise-deterministic compound Poisson risk model. The analysis in this paper is applicable to a wide range of quantities including (i) the insurer's expected total discounted utility until ruin; and (ii) the expected discounted aggregate claim amounts until ruin. On one hand, when claims belong to the class of combinations of exponentials, explicit results are obtained using the ruin theoretic approach of conditioning on the first drop via discounted densities (e.g. Willmot [(2007). On the discounted penalty function in the renewal risk model with general interclaim times. Insurance: Mathematics and Economics 41(1), 17–31]). On the other hand, without any distributional assumption on the claims, we also show that the expected present value of total operating costs until ruin can be expressed in terms of some potential measures, which are common tools in the literature of Lévy processes (e.g. Kyprianou [(2014). Fluctuations of L'evy processes with applications: introductory lectures, 2nd ed. Berlin Heidelberg: Springer-Verlag]). These potential measures are identified in terms of the discounted distributions of ascending and descending ladder heights. We shall demonstrate how the formulas resulting from the two seemingly different methods can be reconciled. The cases of (i) stationary renewal risk model and (ii) surplus-dependent premium are briefly discussed as well. Some interesting invariance properties in the former model are shown to hold true, extending a well-known ruin probability result in the literature. Numerical illustrations concerning the expected total discounted utility until ruin are also provided. Journal: Scandinavian Actuarial Journal Pages: 355-386 Issue: 5 Volume: 2019 Year: 2019 Month: 5 X-DOI: 10.1080/03461238.2018.1525423 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1525423 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:5:p:355-386 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1556727_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Daniel H. Alai Author-X-Name-First: Daniel H. Author-X-Name-Last: Alai Title: Multivariate lifetime distributions for the exponential dispersion family Abstract: We consider a general form of a multivariate lifetime model in which dependence is induced via a common shock component. The univariate marginal distributions come from the well-known and widely applied exponential dispersion family that includes the normal, compound-Poisson, gamma and negative binomial distributions. Any combination of truncation or censoring, either left or right, is considered, for which all moments are derived. This allows for the model to be calibrated to any affine transformation of lifetime data. Journal: Scandinavian Actuarial Journal Pages: 387-405 Issue: 5 Volume: 2019 Year: 2019 Month: 5 X-DOI: 10.1080/03461238.2018.1556727 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1556727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:5:p:387-405 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1563911_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Cary Chi-Liang Tsai Author-X-Name-First: Cary Chi-Liang Author-X-Name-Last: Tsai Author-Name: Ying Zhang Author-X-Name-First: Ying Author-X-Name-Last: Zhang Title: A multi-dimensional Bühlmann credibility approach to modeling multi-population mortality rates Abstract: In this paper, we first propose a multi-dimensional Bühlmann credibility approach to forecasting mortality rates for multiple populations, and then compare forecasting performances among the proposed approach, the CBD model, the Lee-Carter model (LC), the joint-k (JoK-LC), the co-integrated (CoI-LC), and the augmented common factor (ACF-LC) Lee-Carter models for multiple populations. Mortality data from the Human Mortality Database are fitted to the underlying mortality models for both genders of three well-developed countries (the US, the UK, and Japan) and both genders of a developed country (France) and a developing country (Poland) with an age span 25–84 and a wide range of fitting year spans. Empirical illustrations show that the proposed multi-dimensional Bühlmann credibility approach contributes to more accurate forecast results, measured by AMAPE (average of mean absolute percentage errors over all fitting year spans), than the CBD, LC, JoK-LC, CoI-LC and ACF-LC models for three forecasting year spans 2004–2013 (10-year wide), 1994–2013 (20-year wide) and 1984–2013 (30-year wide). Journal: Scandinavian Actuarial Journal Pages: 406-431 Issue: 5 Volume: 2019 Year: 2019 Month: 5 X-DOI: 10.1080/03461238.2018.1563911 File-URL: http://hdl.handle.net/10.1080/03461238.2018.1563911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:5:p:406-431 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1573753_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Qihe Tang Author-X-Name-First: Qihe Author-X-Name-Last: Tang Author-Name: Yang Yang Author-X-Name-First: Yang Author-X-Name-Last: Yang Title: Interplay of insurance and financial risks in a stochastic environment Abstract: Consider an insurer who makes risky investments and hence faces both insurance and financial risks. The insurance business is described by a discrete-time risk model modulated by a stochastic environment that poses systemic and systematic impacts on both the insurance and financial markets. This paper endeavors to quantitatively understand the interplay of the two risks in causing ruin of the insurer. Under the bivariate regular variation framework, we obtain an asymptotic formula to describe the impacts on the insurer's solvency of the two risks and of the stochastic environment. Journal: Scandinavian Actuarial Journal Pages: 432-451 Issue: 5 Volume: 2019 Year: 2019 Month: 5 X-DOI: 10.1080/03461238.2019.1573753 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1573753 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:5:p:432-451 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1574237_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: María Concepción López-Díaz Author-X-Name-First: María Concepción Author-X-Name-Last: López-Díaz Author-Name: Miguel López-Díaz Author-X-Name-First: Miguel Author-X-Name-Last: López-Díaz Author-Name: Sergio Martínez-Fernández Author-X-Name-First: Sergio Author-X-Name-Last: Martínez-Fernández Title: A criterion for the comparison of binary classifiers based on a stochastic dominance with an application to the sale of home insurances Abstract: Binary classification is an essential matter in multiple real-life problems, and so, the comparison of the performance of classifiers is a key issue. A criterion for that purpose is introduced in this manuscript. That criterion is based on a stochastic dominance, and permits to compare classifiers in subgroups of the population with the same size. By means of the new criterion, the alteration of the size of the subgroups where classifiers are compared, does not entail the modification of the suitable classifier. Characterization results of the criterion are proved. For that purpose, connections of the criterion with the theory of copulas, and with a tool introduced in the manuscript, the so-called continuity modelling vector, are essential. An application to the comparison of some classifiers for the detection of purchasers of home insurances is developed. Journal: Scandinavian Actuarial Journal Pages: 453-477 Issue: 6 Volume: 2019 Year: 2019 Month: 7 X-DOI: 10.1080/03461238.2019.1574237 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1574237 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:6:p:453-477 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1574889_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Hieber Author-X-Name-First: Peter Author-X-Name-Last: Hieber Author-Name: Jan Natolski Author-X-Name-First: Jan Author-X-Name-Last: Natolski Author-Name: Ralf Werner Author-X-Name-First: Ralf Author-X-Name-Last: Werner Title: Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios Abstract: Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis. Journal: Scandinavian Actuarial Journal Pages: 478-507 Issue: 6 Volume: 2019 Year: 2019 Month: 7 X-DOI: 10.1080/03461238.2019.1574889 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1574889 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:6:p:478-507 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1576146_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Oskar Tufvesson Author-X-Name-First: Oskar Author-X-Name-Last: Tufvesson Author-Name: Johan Lindström Author-X-Name-First: Johan Author-X-Name-Last: Lindström Author-Name: Erik Lindström Author-X-Name-First: Erik Author-X-Name-Last: Lindström Title: Spatial statistical modelling of insurance risk: a spatial epidemiological approach to car insurance Abstract: Spatial models, such as the Besag, York and Mollie (BYM) model, have long been used in epidemiology and disease mapping. A common research question in these subjects is modelling the number of disease events per region; here the BYM models provides a holistic framework for both covariates and dependencies between regions. We use these tools to assess the relative insurance risk associated with the policyholders geographical location. A Bayesian modelling approach is presented and an elastic net is used to reduce the large number of possible geographic covariates. The final inference is performed using Integrated Nested Laplace Approximation. The model is applied to car insurance data from If P&C Insurance together with spatially referenced covariate data of high resolution, provided by Insightone. The entire analysis is performed using freely available R-packages. Including spatial dependence when modelling the number of claims significantly improves on the result obtained using ordinary generalised linear models. However, the support for adding a spatial component to the model for claims cost is weaker. Journal: Scandinavian Actuarial Journal Pages: 508-522 Issue: 6 Volume: 2019 Year: 2019 Month: 7 X-DOI: 10.1080/03461238.2019.1576146 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1576146 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:6:p:508-522 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1580610_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Francesco Ungolo Author-X-Name-First: Francesco Author-X-Name-Last: Ungolo Author-Name: Marcus C. Christiansen Author-X-Name-First: Marcus C. Author-X-Name-Last: Christiansen Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Author-Name: Angus S. MacDonald Author-X-Name-First: Angus S. Author-X-Name-Last: MacDonald Title: Survival analysis of pension scheme mortality when data are missing Abstract: Missing data is a problem that may be faced by actuaries when analysing mortality data. In this paper we deal with pension scheme data, where the future lifetime of each member is modelled by means of parametric survival models incorporating covariates, which may be missing for some individuals. Parameters are estimated by likelihood-based techniques. We analyse statistical issues, such as parameter identifiability, and propose an algorithm to handle the estimation task. Finally, we analyse the financial impact of including covariates maximally, compared with excluding parts of the mortality experience where data are missing; in particular we consider annuity factors and mis-estimation risk capital requirements. Journal: Scandinavian Actuarial Journal Pages: 523-547 Issue: 6 Volume: 2019 Year: 2019 Month: 7 X-DOI: 10.1080/03461238.2019.1580610 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1580610 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:6:p:523-547 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1573754_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nicholas Syring Author-X-Name-First: Nicholas Author-X-Name-Last: Syring 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: Gibbs posterior inference on value-at-risk Abstract: Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a function of that parameter. This indirect approach exposes the insurer to model misspecification bias or estimation inefficiency, depending on whether the parameter is finite- or infinite-dimensional. In this paper, we link data and VaR directly via what we call a discrepancy function, and this leads naturally to a Gibbs posterior distribution for VaR that does not suffer from the aforementioned biases and inefficiencies. Asymptotic consistency and root-n concentration rate of the Gibbs posterior are established, and simulations highlight its superior finite-sample performance compared to other approaches. Journal: Scandinavian Actuarial Journal Pages: 548-557 Issue: 7 Volume: 2019 Year: 2019 Month: 8 X-DOI: 10.1080/03461238.2019.1573754 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1573754 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:7:p:548-557 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1581837_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Frédéric Godin Author-X-Name-First: Frédéric Author-X-Name-Last: Godin Author-Name: Van Son Lai Author-X-Name-First: Van Son Author-X-Name-Last: Lai Author-Name: Denis-Alexandre Trottier Author-X-Name-First: Denis-Alexandre Author-X-Name-Last: Trottier Title: A general class of distortion operators for pricing contingent claims with applications to CAT bonds Abstract: The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation. Journal: Scandinavian Actuarial Journal Pages: 558-584 Issue: 7 Volume: 2019 Year: 2019 Month: 8 X-DOI: 10.1080/03461238.2019.1581837 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1581837 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:7:p:558-584 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1584912_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Limor Langbord Author-X-Name-First: Limor Author-X-Name-Last: Langbord Author-Name: Zinoviy Landsman Author-X-Name-First: Zinoviy Author-X-Name-Last: Landsman Author-Name: Udi E. Makov Author-X-Name-First: Udi E. Author-X-Name-Last: Makov Title: Intrinsic objective Bayesian estimation of the mean of the Tweedie family Abstract: The Tweedie family, which is classified by the choice of power unit variance function, includes heavy tailed distributions, and as such could be of significant relevance to actuarial science. The class includes the Normal, Poisson, Gamma, Inverse Gaussian, Stable and Compound Poisson distributions. In this study, we explore the intrinsic objective Bayesian point estimator for the mean value of the Tweedie family based on the intrinsic discrepancy loss function – which is an inherent loss function arising only from the underlying distribution or model, without any subjective considerations – and the Jeffreys prior distribution, which is designed to express absence of information about the quantity of interest. We compare the proposed point estimator with the Bayes estimator, which is the posterior mean based on quadratic loss function and the Jeffreys prior distribution. We carry a numerical study to illustrate the methodology in the context of the Inverse Gaussian model, which is fully unexplored in this novel context, and which is useful to insurance contracts. Journal: Scandinavian Actuarial Journal Pages: 585-603 Issue: 7 Volume: 2019 Year: 2019 Month: 8 X-DOI: 10.1080/03461238.2019.1584912 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1584912 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:7:p:585-603 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1586756_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anthony Medford Author-X-Name-First: Anthony Author-X-Name-Last: Medford Author-Name: James W. Vaupel Author-X-Name-First: James W. Author-X-Name-Last: Vaupel Title: An introduction to gevistic regression mortality models Abstract: Many common stochastic mortality models can be formulated as a generalized linear model (GLM). When these GLMs are used to model one year-death probabilities, $ q_x $ qx, deaths are assumed to be binomially distributed, and the canonical logit link function has been used by default. In this work we present the quantile function of the Generalized Extreme Value distribution as an alternative link function to the standard canonical logit link and show that its theoretical advantages enable a better fit for mortality models in cases when data are highly imbalanced or sparse. We provide an example that shows that this link function also enables superior fits to mortality data at the very highest ages in the case of the Cairns Blake Dowd family of mortality models. Journal: Scandinavian Actuarial Journal Pages: 604-620 Issue: 7 Volume: 2019 Year: 2019 Month: 8 X-DOI: 10.1080/03461238.2019.1586756 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1586756 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:7:p:604-620 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1586757_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Walther Neuhaus Author-X-Name-First: Walther Author-X-Name-Last: Neuhaus Title: One-year estimation uncertainty in some claim development models Abstract: The paper studies the one-year estimation uncertainty associated with using credibility-based loss reserving methods, when claim development can be described by the models of Bühlmann-Straub or Hesselager-Witting. Having found a formula, it seems natural to minimise the one-year estimation uncertainty in the same way as one can minimise the ultimate uncertainty, i.e. to minimise the MSEP. It turns out that minimisation of the one-year estimation uncertainty leads to unreasonable and unsightly results. This puts into question the sanity of the concept of one-year estimation uncertainty. Journal: Scandinavian Actuarial Journal Pages: 621-635 Issue: 7 Volume: 2019 Year: 2019 Month: 8 X-DOI: 10.1080/03461238.2019.1586757 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1586757 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:7:p:621-635 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1589565_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mogens Steffensen Author-X-Name-First: Mogens Author-X-Name-Last: Steffensen Title: Ragnar Norberg (1945–2017): an actuary of a unique kind Journal: Scandinavian Actuarial Journal Pages: 637-641 Issue: 8 Volume: 2019 Year: 2019 Month: 9 X-DOI: 10.1080/03461238.2019.1589565 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1589565 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:8:p:637-641 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1596151_J.xml processed with: repec_from_tfjats.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: Extending composite loss models using a general framework of advanced computational tools Abstract: Composite models have a long history in actuarial science because they provide a flexible method of curve-fitting for heavy-tailed insurance losses. The ongoing research in this area continuously suggests methodological improvements for existing composite models and considers new composite models. A number of different composite models have been previously proposed in the literature to fit the popular data set related to Danish fire losses. This paper provides the most comprehensive analysis of composite loss models on the Danish fire losses data set to date by evaluating 256 composite models derived from 16 parametric distributions that are commonly used in actuarial science. If not suitably addressed, inevitable computational challenges are encountered when estimating these composite models that may lead to sub-optimal solutions. General implementation strategies are developed for parameter estimation in order to arrive at an automatic way to reach a viable solution, regardless of the specific head and/or tail distributions specified. The results lead to an identification of new well-fitting composite models and provide valuable insights into the selection of certain composite models for which the tail-evaluation measures can be useful in making risk management decisions. Journal: Scandinavian Actuarial Journal Pages: 642-660 Issue: 8 Volume: 2019 Year: 2019 Month: 9 X-DOI: 10.1080/03461238.2019.1596151 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1596151 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:8:p:642-660 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1596974_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marius D. Pascariu Author-X-Name-First: Marius D. Author-X-Name-Last: Pascariu Author-Name: Adam Lenart Author-X-Name-First: Adam Author-X-Name-Last: Lenart Author-Name: Vladimir Canudas-Romo Author-X-Name-First: Vladimir Author-X-Name-Last: Canudas-Romo Title: The maximum entropy mortality model: forecasting mortality using statistical moments Abstract: The age-at-death distribution is a representation of the mortality experience in a population. Although it proves to be highly informative, it is often neglected when it comes to the practice of past or future mortality assessment. We propose an innovative method to mortality modeling and forecasting by making use of the location and shape measures of a density function, i.e. statistical moments. Time series methods for extrapolating a limited number of moments are used and then the reconstruction of the future age-at-death distribution is performed. The predictive power of the method seems to be net superior when compared to the results obtained using classical approaches to extrapolating age-specific-death rates, and the accuracy of the point forecast (MASE) is improved on average by 33% respective to the state-of-the-art, the Lee–Carter model. The method is tested using data from the Human Mortality Database and implemented in a publicly available R package. Journal: Scandinavian Actuarial Journal Pages: 661-685 Issue: 8 Volume: 2019 Year: 2019 Month: 9 X-DOI: 10.1080/03461238.2019.1596974 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1596974 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:8:p:661-685 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1598482_J.xml processed with: repec_from_tfjats.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: 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: Multivariate Cox Hidden Markov models with an application to operational risk Abstract: Modeling multivariate time-series aggregate losses is an important actuarial topic that is very challenging due to the fact that losses can be serially dependent with heterogeneous dependence structures across loss types and business lines. In this paper, we investigate a flexible class of multivariate Cox Hidden Markov Models for the joint arrival process of loss events. Some of the nice properties possessed by this class of models, such as closed-form expressions, thinning properties and model versatility are discussed in details. We provide the expectation-maximization (EM) algorithm for efficient model calibration. Applying the proposed model to an operational risk dataset, we demonstrate that the model offers sufficient flexibility to capture most characteristics of the observed loss frequencies. By modeling the log-transformed loss severities through mixture of Erlang distributions, we can model the aggregate losses. Finally, out-of-sample testing shows that the proposed model is adequate to predict short-term future operational risk losses. Journal: Scandinavian Actuarial Journal Pages: 686-710 Issue: 8 Volume: 2019 Year: 2019 Month: 9 X-DOI: 10.1080/03461238.2019.1598482 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1598482 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:8:p:686-710 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1598890_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mohamed Amine Lkabous Author-X-Name-First: Mohamed Amine Author-X-Name-Last: Lkabous Author-Name: Jean-François Renaud Author-X-Name-First: Jean-François Author-X-Name-Last: Renaud Title: A unified approach to ruin probabilities with delays for spectrally negative Lévy processes Abstract: In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays: ruin is declared the first time an excursion in the red zone lasts longer than an implementation delay with a deterministic and a stochastic component. For this Parisian ruin with mixed delays, we identify the joint distribution of the time of ruin and the deficit at ruin, therefore providing generalizations of many results previously obtained, such as in Baurdoux et al. (2016) and Loeffen et al. (in press) for the case of an exponential delay and that of a deterministic delay, respectively. Journal: Scandinavian Actuarial Journal Pages: 711-728 Issue: 8 Volume: 2019 Year: 2019 Month: 9 X-DOI: 10.1080/03461238.2019.1598890 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1598890 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:8:p:711-728 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1598891_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Author-Name: Wing Fung Chong Author-X-Name-First: Wing Fung Author-X-Name-Last: Chong Author-Name: Ambrose Lo Author-X-Name-First: Ambrose Author-X-Name-Last: Lo Title: Budget-constrained optimal reinsurance design under coherent risk measures Abstract: Reinsurance is a versatile risk management strategy commonly employed by insurers to optimize their risk profile. In this paper, we study an optimal reinsurance design problem minimizing a general law-invariant coherent risk measure of the net risk exposure of a generic insurer, in conjunction with a general law-invariant comonotonic additive convex reinsurance premium principle and a premium budget constraint. Due to its intrinsic generality, this contract design problem encompasses a wide body of optimal reinsurance models commonly encountered in practice. A three-step solution scheme is presented. Firstly, the objective and constraint functions are exhibited in the so-called Kusuoka's integral representations. Secondly, the mini-max theorem for infinite dimensional spaces is applied to interchange the infimum on the space of indemnities and the supremum on the space of probability measures. Thirdly, the recently developed Neyman–Pearson methodology due to Lo (2017a) is adopted to solve the resulting infimum problem. Analytic and transparent expressions for the optimal reinsurance policy are provided, followed by illustrative examples. Journal: Scandinavian Actuarial Journal Pages: 729-751 Issue: 9 Volume: 2019 Year: 2019 Month: 10 X-DOI: 10.1080/03461238.2019.1598891 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1598891 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:9:p:729-751 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1604426_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Duni Hu Author-X-Name-First: Duni Author-X-Name-Last: Hu Author-Name: Hailong Wang Author-X-Name-First: Hailong Author-X-Name-Last: Wang Title: Optimal proportional reinsurance with a loss-dependent premium principle Abstract: Empirical studies suggest that many insurance companies recontract with their clients on premiums by extrapolating past losses: a client is offered a decrease in premium if the monetary amounts of his claims do not exceed some prespecified quantities, otherwise, an increase in premium. In this paper, we formulate the empirical studies and investigate optimal reinsurance problems of a risk-averse insurer by introducing a loss-dependent premium principle, which uses a weighted average of history losses and the expectation of future losses to replace the expectation in the expected premium principle. This premium principle satisfies the bonus-malus and smoothes the insurer's wealth. Explicit expressions for the optimal reinsurance strategies and value functions are derived. If the reinsurer applies the loss-dependent premium principle to continuously adjust his premium, we show that the insurer always needs less reinsurance when he also adopts this premium principle than when he adopts the expected premium principle. Journal: Scandinavian Actuarial Journal Pages: 752-767 Issue: 9 Volume: 2019 Year: 2019 Month: 10 X-DOI: 10.1080/03461238.2019.1604426 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1604426 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:9:p:752-767 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1615543_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Gero Junike Author-X-Name-First: Gero Author-X-Name-Last: Junike Title: Representation of concave distortions and applications Abstract: A family of concave distortion functions is a set of concave and increasing functions, mapping the unity interval onto itself. Distortion functions play an important role defining coherent risk measures. We prove that any family of distortion functions which fulfils a certain translation equation, can be represented by a distribution function. An application can be found in actuarial science: moment-based premium principles are easy to understand but in general are not monotone and cannot be used to compare the riskiness of different insurance contracts with each other. Our representation theorem makes it possible to compare two insurance risks with each other consistent with a moment-based premium principle by defining an appropriate coherent risk measure. Journal: Scandinavian Actuarial Journal Pages: 768-783 Issue: 9 Volume: 2019 Year: 2019 Month: 10 X-DOI: 10.1080/03461238.2019.1615543 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1615543 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:9:p:768-783 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1616323_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: K. C. Cheung Author-X-Name-First: K. C. Author-X-Name-Last: Cheung Author-Name: S. C. P. Yam Author-X-Name-First: S. C. P. Author-X-Name-Last: Yam Author-Name: F. L. Yuen Author-X-Name-First: F. L. Author-X-Name-Last: Yuen Title: Reinsurance contract design with adverse selection Abstract: In light of the richness of their structures in connection with practical implementation, we follow the seminal works in economics to use the principal–agent (multidimensional screening) models to study a monopolistic reinsurance market with adverse selection; instead of adopting the classical expected utility paradigm, the novelty of our present work is to model the risk assessment of each insurer (agent) by his value-at-risk at his own chosen risk tolerance level consistent with Solvency II. Under information asymmetry, the reinsurer (principal) aims to maximize his average profit by designing an optimal policy provision (menu) of ‘shirt-fit’ reinsurance contracts for every insurer from one of the two groups with hidden characteristics. Our results show that a quota-share component, on the top of simple stop-loss, is very crucial for mitigating asymmetric information from the insurers to the reinsurer. Journal: Scandinavian Actuarial Journal Pages: 784-798 Issue: 9 Volume: 2019 Year: 2019 Month: 10 X-DOI: 10.1080/03461238.2019.1616323 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1616323 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:9:p:784-798 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1622592_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Florin Avram Author-X-Name-First: Florin Author-X-Name-Last: Avram Author-Name: Dan Goreac Author-X-Name-First: Dan Author-X-Name-Last: Goreac Title: A pontryaghin maximum principle approach for the optimization of dividends/consumption of spectrally negative markov processes, until a generalized draw-down time Abstract: The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process $X_t $Xt and on its supremum $\overline X_t:=\sup _{0\leq s\leq t} X_s $X¯t:=sup0≤s≤tXs. Strongly connected to Azema-Yor/generalized draw-down/trailing stop time this framework provides a natural unification of draw-down  and classic first passage  times. We illustrate here the potential of this unified framework by solving a variation of the De Finetti problem of maximizing expected discounted cumulative dividends/consumption gained under a barrier policy, until an optimally chosen Azema-Yor time, with a general spectrally negative Markov model. While previously studied cases of this problem assumed either Lévy or diffusion models, and the draw-down function to be fixed, we describe, for a general spectrally negative Markov model, not only the optimal barrier but also the optimal draw-down function. This is achieved by solving a variational problem tackled by Pontryaghin's maximum principle. As a by-product we show that in the Lévy case the classic first passage solution is indeed optimal; in the diffusion case, we obtain the optimality equations, but the behavior of associated solutions for further explicit models and the question of whether they do better than the classic solution is left for future work. Instead, we illustrate the novelty by a toy example, with a conveniently chosen scale-like function. Journal: Scandinavian Actuarial Journal Pages: 799-823 Issue: 9 Volume: 2019 Year: 2019 Month: 10 X-DOI: 10.1080/03461238.2019.1622592 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1622592 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2019:y:2019:i:9:p:799-823 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1633394_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrea Gabrielli Author-X-Name-First: Andrea Author-X-Name-Last: Gabrielli Author-Name: Ronald Richman Author-X-Name-First: Ronald Author-X-Name-Last: Richman Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Neural network embedding of the over-dispersed Poisson reserving model Abstract: The main idea of this paper is to embed a classical actuarial regression model into a neural network architecture. This nesting allows us to learn model structure beyond the classical actuarial regression model if we use as starting point of the neural network calibration exactly the classical actuarial model. Such models can be fitted efficiently which allows us to explore bootstrap methods for prediction uncertainty. As an explicit example, we consider the cross-classified over-dispersed Poisson model for general insurance claims reserving. We demonstrate how this model can be improved by neural network features. Journal: Scandinavian Actuarial Journal Pages: 1-29 Issue: 1 Volume: 2020 Year: 2020 Month: 1 X-DOI: 10.1080/03461238.2019.1633394 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1633394 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:1:p:1-29 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1633395_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: An Chen Author-X-Name-First: An Author-X-Name-Last: Chen Author-Name: Peter Hieber Author-X-Name-First: Peter Author-X-Name-Last: Hieber Author-Name: Lars Lämmlein Author-X-Name-First: Lars Author-X-Name-Last: Lämmlein Title: Regulatory measures for distressed insurance undertakings: a comparative study Abstract: In Europe, the introduction of the regulatory scheme Solvency II wants to improve the risk management practice in insurance undertakings. One aspect of the new regulatory rules is an improved supervision of distressed insurance undertakings. In case the insurance undertaking is in financial distress, the regulator may force it to take appropriate precautionary measures to avoid bankruptcy. In this article, we compare the two most common regulatory measures in case of distress: A decrease of the asset investment risk and contingent equity capital. In a Black-Scholes-Merton economy, we model the insurance undertaking's assets and liabilities by a structural default model. We consider a regulator acting in the interests of the policyholder and analyze the effect of the regulatory measures on the policyholder's benefits. We find that the contingent equity capital seems more efficient in terms of increasing the benefits of the policyholders. Journal: Scandinavian Actuarial Journal Pages: 30-43 Issue: 1 Volume: 2020 Year: 2020 Month: 1 X-DOI: 10.1080/03461238.2019.1633395 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1633395 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:1:p:30-43 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1636858_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Baños Author-X-Name-First: David Author-X-Name-Last: Baños Author-Name: Erik Bølviken Author-X-Name-First: Erik Author-X-Name-Last: Bølviken Author-Name: Sindre Duedahl Author-X-Name-First: Sindre Author-X-Name-Last: Duedahl Author-Name: Frank Proske Author-X-Name-First: Frank Author-X-Name-Last: Proske Title: Modeling and estimation of stochastic transition rates in life insurance with regime switching based on generalized Cox processes Abstract: In this paper we aim at modeling stochastic transition rates of state processes in life insurance by using generalized Cox processes. A feature of a our non-Gaussian model is that it can be used to capture ‘regime switching’ effects of data which may be due to regulatory changes in insurance markets or external ‘shocks’ caused e.g. by an economical crisis, natural disasters or epidemics. We propose a method how to estimate the unknown parameters of our model for stochastic transition rates from insurance data by using non-linear filtering techniques for Lévy processes. As a result we also obtain an explicit formula for the unnormalized density of a filtering problem with singular coefficients. Journal: Scandinavian Actuarial Journal Pages: 44-83 Issue: 1 Volume: 2020 Year: 2020 Month: 1 X-DOI: 10.1080/03461238.2019.1636858 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1636858 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:1:p:44-83 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1777194_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stephen J. Richards Author-X-Name-First: Stephen J. Author-X-Name-Last: Richards Author-Name: Stefan J. Ramonat Author-X-Name-First: Stefan J. Author-X-Name-Last: Ramonat Author-Name: Gregory T. Vesper Author-X-Name-First: Gregory T. Author-X-Name-Last: Vesper Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Title: Modelling seasonal mortality with individual data Abstract: Most studies of seasonal variation in mortality rely on aggregated death counts at population level. In this paper, we use individual data to present a series of models for different aspects of seasonal variation. The models are fitted to a variety of international pensioner data sets and suggest a high degree of commonality across countries with different climates and different health systems. The power of individual life-history survival modelling allows the detection of seasonal patterns in even modest-sized portfolios. We measure the tendency for seasonal fluctuations to increase with age, and we again find strong similarities between geographically distinct populations. We further find that seasonal effects are generally uncorrelated with gender, but that low-income pensioners can suffer greater seasonal swings than high-income ones. Finally, we propose a single-parameter measure for the extent to which winter mortality is a spike and summer mortality is a shallower trough, and show results for a variety of data sets. Journal: Scandinavian Actuarial Journal Pages: 864-878 Issue: 10 Volume: 2020 Year: 2020 Month: 11 X-DOI: 10.1080/03461238.2020.1777194 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1777194 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:10:p:864-878 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1788136_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xia Han Author-X-Name-First: Xia Author-X-Name-Last: Han Author-Name: Zhibin Liang Author-X-Name-First: Zhibin Author-X-Name-Last: Liang Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Optimal reinsurance to minimize the probability of drawdown under the mean-variance premium principle Abstract: In this paper, we determine the optimal reinsurance strategy to minimize the probability of drawdown, namely, the probability that the insurer's surplus process reaches some fixed fraction of its maximum value to date. We assume that the reinsurance premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We derive closed-form expressions of the optimal reinsurance strategy and the corresponding minimum probability of drawdown. Then, under the variance premium principle, we show that the safe level can never be reached before drawdown under the optimally controlled surplus process. Finally, we present some numerical examples to show the impact of model parameters on the optimal results. Journal: Scandinavian Actuarial Journal Pages: 879-903 Issue: 10 Volume: 2020 Year: 2020 Month: 11 X-DOI: 10.1080/03461238.2020.1788136 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1788136 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:10:p:879-903 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1790030_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claudia Ceci Author-X-Name-First: Claudia Author-X-Name-Last: Ceci Author-Name: Katia Colaneri Author-X-Name-First: Katia Author-X-Name-Last: Colaneri Author-Name: Alessandra Cretarola Author-X-Name-First: Alessandra Author-X-Name-Last: Cretarola Title: Indifference pricing of pure endowments via BSDEs under partial information Abstract: In this paper, we investigate the pricing problem of a pure endowment contract when the insurance company has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset and the mortality index dynamics. Since the market is incomplete due to the presence of basis risk, in alternative to arbitrage pricing we use expected utility maximization under exponential preferences as evaluation approach, which leads to the so-called indifference price. Under partial information this methodology requires filtering techniques that can reduce the original control problem to an equivalent problem in complete information. Using stochastic dynamics techniques, we characterize the indifference price of the insurance derivative in terms of the solutions of two backward stochastic differential equations. Finally, we discuss two special cases where we get a more explicit representation of the indifference price process. Journal: Scandinavian Actuarial Journal Pages: 904-933 Issue: 10 Volume: 2020 Year: 2020 Month: 11 X-DOI: 10.1080/03461238.2020.1790030 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1790030 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:10:p:904-933 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1790413_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kristian Buchardt Author-X-Name-First: Kristian Author-X-Name-Last: Buchardt Author-Name: Christian Furrer Author-X-Name-First: Christian Author-X-Name-Last: Furrer Author-Name: Thomas Møller Author-X-Name-First: Thomas Author-X-Name-Last: Møller Title: Tax- and expense-modified risk-minimization for insurance payment processes Abstract: We study the problem of determining risk-minimizing investment strategies for insurance payment processes in the presence of taxes and expenses. We consider the situation where taxes and expenses are paid continuously and symmetrically and introduce the concept of tax- and expense-modified risk-minimization. Risk-minimizing strategies in the presence of taxes and expenses are derived and linked to Galtchouk-Kunita-Watanabe decompositions associated with modified versions of the original payment processes. Furthermore, we show equivalence to an alternative approach involving an artificial market consisting of after-tax and after-expense assets, and we establish – in a certain sense – consistency with classic risk-minimization. Finally, a case study involving classic multi-state life insurance payments in combination with a bond market exemplifies the results. Journal: Scandinavian Actuarial Journal Pages: 934-961 Issue: 10 Volume: 2020 Year: 2020 Month: 11 X-DOI: 10.1080/03461238.2020.1790413 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1790413 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:10:p:934-961 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1636859_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yinghui Dong Author-X-Name-First: Yinghui Author-X-Name-Last: Dong Author-Name: Sang Wu Author-X-Name-First: Sang Author-X-Name-Last: Wu Author-Name: Wenxin Lv Author-X-Name-First: Wenxin Author-X-Name-Last: Lv Author-Name: Guojing Wang Author-X-Name-First: Guojing Author-X-Name-Last: Wang Title: Optimal asset allocation for participating contracts under the VaR and PI constraint Abstract: Participating contracts provide a maturity guarantee for the policyholder. However, the terminal payoff to the policyholder should be related to financial risks of participating insurance contracts. We investigate an optimal investment problem under a joint value-at-risk and portfolio insurance constraint faced by the insurer who offers participating contracts. The insurer aims to maximize the expected utility of the terminal payoff to the insurer. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the joint value-at-risk and the portfolio insurance constraint impacts the optimal terminal wealth. Journal: Scandinavian Actuarial Journal Pages: 84-109 Issue: 2 Volume: 2020 Year: 2020 Month: 2 X-DOI: 10.1080/03461238.2019.1636859 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1636859 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:2:p:84-109 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1642239_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stephen J. Richards Author-X-Name-First: Stephen J. Author-X-Name-Last: Richards Title: A Hermite-spline model of post-retirement mortality Abstract: We present a model for post-retirement mortality where differentials automatically reduce with increasing age, but without the fitted mortality rates for subgroups crossing over. Selection effects are catered for, as are age-modulated time trends and seasonal variation in mortality. Central to the model are Hermite splines, which permit parsimonious modelling of complex risk factors in even modest-sized portfolios. The model is therefore suitable for the stand-alone analysis of experience data for reinsurance, bulk annuities and longevity swaps. We also illustrate the contrast between the statistical significance of a risk factor and its financial significance and discuss reasons why one might include risk factors like season that are not directly financially significant. Journal: Scandinavian Actuarial Journal Pages: 110-127 Issue: 2 Volume: 2020 Year: 2020 Month: 2 X-DOI: 10.1080/03461238.2019.1642239 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1642239 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:2:p:110-127 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1655475_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yuying Liu Author-X-Name-First: Yuying Author-X-Name-Last: Liu Author-Name: Zhaoyang Liu Author-X-Name-First: Zhaoyang Author-X-Name-Last: Liu Author-Name: Guoxin Liu Author-X-Name-First: Guoxin Author-X-Name-Last: Liu Title: Optimal dividend problems for Sparre Andersen risk model with bounded dividend rates Abstract: This paper concerns the optimal dividend problem with bounded dividend rate for Sparre Andersen risk model. The analytic characterizations of admissible strategies and Markov strategies are given. We use the measure-valued generator theory to derive a measure-valued dynamic programming equation. The value function is proved to be of locally finite variation along the path, which belongs to the domain of the measure-valued generator. The verification theorem is proved without additional assumptions on the regularity of the value function. Actually, the value function may have jumps. Under certain conditions, the optimal strategy is presented as a Markov strategy with space-time band structure. We present an iterative algorithm to approximate the optimal value function and the optimal dividend strategy. As applications, some numerical examples are given. Journal: Scandinavian Actuarial Journal Pages: 128-151 Issue: 2 Volume: 2020 Year: 2020 Month: 2 X-DOI: 10.1080/03461238.2019.1655475 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1655475 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:2:p:128-151 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1655476_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: David Engler Author-X-Name-First: David Author-X-Name-Last: Engler Title: Bayesian multivariate regime-switching models and the impact of correlation structure misspecification in variable annuity pricing Abstract: We develop Bayesian multivariate regime-switching models for correlated assets, comparing three different ways to flexibly structure the correlation matrix. After developing the models, we examine their relative characteristics and performance, first in a straightforward asset simulation example, and later applied to a variable annuity product with guarantees. We find that the freedom allowed by the more flexible structures enables these models to more accurately reflect the actual asset dependence structure. We also show that the correlation structures inferred by the most commonly used (and simplest) model will result in significantly larger estimates of the cost of the annuity guarantees. Journal: Scandinavian Actuarial Journal Pages: 152-171 Issue: 2 Volume: 2020 Year: 2020 Month: 2 X-DOI: 10.1080/03461238.2019.1655476 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1655476 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:2:p:152-171 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1655477_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Rosy Oh Author-X-Name-First: Rosy Author-X-Name-Last: Oh Author-Name: Peng Shi Author-X-Name-First: Peng Author-X-Name-Last: Shi Author-Name: Jae Youn Ahn Author-X-Name-First: Jae Youn Author-X-Name-Last: Ahn Title: Bonus-Malus premiums under the dependent frequency-severity modeling Abstract: A Bonus-Malus System (BMS) in insurance is a premium adjustment mechanism widely used in a posteriori ratemaking process to set the premium for the next contract period based on a policyholder's claim history. The current practice in BMS implementation relies on the assumption of independence between claim frequency and severity, despite the fact that a series of recent studies report evidence of a significant frequency-severity relationship, particularly in automobile insurance. To address this discrepancy, we propose a copula-based correlated random effects model to accommodate the dependence between claim frequency and severity, and further illustrate how to incorporate such dependence into the current BMS. We derive analytical solutions to the optimal relativities under the proposed framework and provide numerical experiments based on real data analysis to assess the effect of frequency-severity dependence in BMS ratemaking. Journal: Scandinavian Actuarial Journal Pages: 172-195 Issue: 3 Volume: 2020 Year: 2020 Month: 3 X-DOI: 10.1080/03461238.2019.1655477 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1655477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:3:p:172-195 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1657936_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kim Aguirre Nolsøe Author-X-Name-First: Kim Author-X-Name-Last: Aguirre Nolsøe Author-Name: Dieter Degrijse Author-X-Name-First: Dieter Author-X-Name-Last: Degrijse Author-Name: Sofie Ahm Author-X-Name-First: Sofie Author-X-Name-Last: Ahm Author-Name: Kristoffer Brix Author-X-Name-First: Kristoffer Author-X-Name-Last: Brix Author-Name: Mads Storgaard Author-X-Name-First: Mads Author-X-Name-Last: Storgaard Author-Name: Jesper Strodl Author-X-Name-First: Jesper Author-X-Name-Last: Strodl Title: Cash flow techniques for asset liability management Abstract: Motivated by Solvency II, requiring the incorporation of policyholder behavior and portfolio performance into the liability modeling of a life insurance company, we propose some new techniques to efficiently compute future values of the first-order reserve and the third order cash flow under varying economic scenarios. Journal: Scandinavian Actuarial Journal Pages: 196-217 Issue: 3 Volume: 2020 Year: 2020 Month: 3 X-DOI: 10.1080/03461238.2019.1657936 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1657936 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:3:p:196-217 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1658619_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhongyang Sun Author-X-Name-First: Zhongyang Author-X-Name-Last: Sun Author-Name: Xin Zhang Author-X-Name-First: Xin Author-X-Name-Last: Zhang Author-Name: Kam Chuen Yuen Author-X-Name-First: Kam Chuen Author-X-Name-Last: Yuen Title: Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option Abstract: This paper considers an optimal asset-liability management (ALM) problem for an insurer under the mean-variance criterion. It is assumed that the value of liabilities is described by a geometric Brownian motion (GBM). The insurer's surplus process is modeled by a general jump process generated by a marked point process. The financial market consists of one risk-free asset and n risky assets with the risk premium relying on an affine diffusion factor process. By transferring a proportion of insurance risk to a reinsurer and investing the surplus into the financial market, the insurer aims to maximize the expected terminal net wealth and, at the same time, minimize the corresponding variance of the terminal net wealth. By using a backward stochastic differential equation (BSDE) approach, closed-form expressions for both the efficient strategy and efficient frontier are derived. To illustrate the main results, we study an example with the Heston stochastic volatility (SV) model and numerically analyze the economic behavior of the efficient frontier. Finally, a generalization of the Mutual Fund Theorem is obtained. Journal: Scandinavian Actuarial Journal Pages: 218-244 Issue: 3 Volume: 2020 Year: 2020 Month: 3 X-DOI: 10.1080/03461238.2019.1658619 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1658619 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:3:p:218-244 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1659177_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario Ghossoub Author-X-Name-First: Mario Author-X-Name-Last: Ghossoub Title: Budget-constrained optimal retention with an upper limit on the retained loss Abstract: Unlike sophisticated institutional insurance buyers, individual insurance seekers often use simple heuristic tools for risk management purposes, such as requiring that an insurance arrangement will not result in a retained loss that exceeds a certain predetermined and fixed level. In this paper, we re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss; but we further impose an additional upper-limit constraint on the retained loss and assume that the insurer distorts his subjective probability measure. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. We characterize the optimal retention function and show that it has a simple two-part structure: zero retention (full insurance) on an event to which the insurer assigns zero probability, and a retention that could be described as a limited variable deductible on the complement of this event. As an illustration, we examine the case of a distorted Esscher premium principle. Journal: Scandinavian Actuarial Journal Pages: 245-271 Issue: 3 Volume: 2020 Year: 2020 Month: 3 X-DOI: 10.1080/03461238.2019.1659177 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1659177 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:3:p:245-271 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1661280_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Guglielmo D'Amico Author-X-Name-First: Guglielmo Author-X-Name-Last: D'Amico Author-Name: Riccardo De Blasis Author-X-Name-First: Riccardo Author-X-Name-Last: De Blasis Title: A multivariate Markov chain stock model Abstract: We propose a dividend stock valuation model where multiple dividend growth series and their dependencies are modelled using a multivariate Markov chain. Our model advances existing Markov chain stock models. First, we determine assumptions that guarantee the finiteness of the price and risk as well as the fulfilment of transversality conditions. Then, we compute the first- and second-order price-dividend ratios by solving corresponding linear systems of equations and show that a different price-dividend ratio is attached to each combination of states of the dividend growth process of each stock. Subsequently, we provide a formula for the computation of the variances and covariances between stocks in a portfolio. Finally, we apply the theoretical model to the dividend series of three US stocks and perform comparisons with existing models. The results could also be applied for actuarial purposes as a general stochastic investment model and for calculating the initial endowment to fund a portfolio of dependent perpetuities. Journal: Scandinavian Actuarial Journal Pages: 272-291 Issue: 4 Volume: 2020 Year: 2020 Month: 4 X-DOI: 10.1080/03461238.2019.1661280 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1661280 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:4:p:272-291 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1663444_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Title: On series expansions for scale functions and other ruin-related quantities Abstract: In this note, we consider a nonstandard analytic approach to the examination of scale functions in some special cases of spectrally negative Lévy processes. In particular, we consider the compound Poisson risk process with or without perturbation from an independent Brownian motion. New explicit expressions for the first and second scale functions are derived which complement existing results in the literature. We specifically consider cases where the claim size distribution is gamma, uniform or inverse Gaussian. Some ruin-related quantities will also be re-examined in light of the aforementioned results. Journal: Scandinavian Actuarial Journal Pages: 292-306 Issue: 4 Volume: 2020 Year: 2020 Month: 4 X-DOI: 10.1080/03461238.2019.1663444 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1663444 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:4:p:292-306 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1663553_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Han Lin Shang Author-X-Name-First: Han Lin Author-X-Name-Last: Shang Title: Dynamic principal component regression for forecasting functional time series in a group structure Abstract: When generating social policies and pricing annuity at national and subnational levels, it is essential both to forecast mortality accurately and ensure that forecasts at the subnational level add up to the forecasts at the national level. This has motivated recent developments in forecasting functional time series in a group structure, where static principal component analysis is used. In the presence of moderate to strong temporal dependence, static principal component analysis designed for independent and identically distributed functional data may be inadequate. Thus, through using the dynamic functional principal component analysis, we consider a functional time series forecasting method with static and dynamic principal component regression to forecast each series in a group structure. Through using the regional age-specific mortality rates in Japan obtained from the Japanese Mortality Database [(2019). National Institute of Population and Social Security Research. Available at http://www.ipss.go.jp/p-toukei/JMD/index-en.asp (data downloaded on 14 August 2018)], we investigate the point and interval forecast accuracies of our proposed extension, and subsequently make recommendations. Journal: Scandinavian Actuarial Journal Pages: 307-322 Issue: 4 Volume: 2020 Year: 2020 Month: 4 X-DOI: 10.1080/03461238.2019.1663553 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1663553 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:4:p:307-322 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1667424_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: C. Constantinescu Author-X-Name-First: C. Author-X-Name-Last: Constantinescu Author-Name: G. Delsing Author-X-Name-First: G. Author-X-Name-Last: Delsing Author-Name: M. Mandjes Author-X-Name-First: M. Author-X-Name-Last: Mandjes Author-Name: L. Rojas Nandayapa Author-X-Name-First: L. Author-X-Name-Last: Rojas Nandayapa Title: A ruin model with a resampled environment Abstract: This paper considers a Cramér–Lundberg risk setting, where the components of the underlying model change over time. We allow the more general setting of the cumulative claim process being modeled as a spectrally positive Lévy process. We provide an intuitively appealing mechanism to create such parameter uncertainty: at Poisson epochs, we resample the model components from a finite number of d settings. It results in a setup that is particularly suited to describe situations in which the risk reserve dynamics are affected by external processes. We extend the classical Cramér–Lundberg approximation (asymptotically characterizing the all-time ruin probability in a light-tailed setting) to this more general setup. In addition, for the situation that the driving Lévy processes are sums of Brownian motions and compound Poisson processes, we find an explicit uniform bound on the ruin probability. In passing we propose an importance-sampling algorithm facilitating efficient estimation, and prove it has bounded relative error. In a series of numerical experiments we assess the accuracy of the asymptotics and bounds, and illustrate that neglecting the resampling can lead to substantial underestimation of the risk. Journal: Scandinavian Actuarial Journal Pages: 323-341 Issue: 4 Volume: 2020 Year: 2020 Month: 4 X-DOI: 10.1080/03461238.2019.1667424 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1667424 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:4:p:323-341 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1669218_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ailing Gu Author-X-Name-First: Ailing Author-X-Name-Last: Gu Author-Name: Frederi G. Viens Author-X-Name-First: Frederi G. Author-X-Name-Last: Viens Author-Name: Yang Shen Author-X-Name-First: Yang Author-X-Name-Last: Shen Title: Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model Abstract: We discuss an optimal excess-of-loss reinsurance contract in a continuous-time principal-agent framework where the surplus of the insurer (agent/he) is described by a classical Cramér-Lundberg (C-L) model. In addition to reinsurance, the insurer and the reinsurer (principal/she) are both allowed to invest their surpluses into a financial market containing one risk-free asset (e.g. a short-rate account) and one risky asset (e.g. a market index). In this paper, the insurer and the reinsurer are ambiguity averse and have specific modeling risk aversion preferences for the insurance claims (this relates to the jump term in the stochastic models) and the financial market's risk (this encompasses the models' diffusion term). The reinsurer designs a reinsurance contract that maximizes the exponential utility of her terminal wealth under a worst-case scenario which depends on the retention level of the insurer. By employing the dynamic programming approach, we derive the optimal robust reinsurance contract, and the value functions for the reinsurer and the insurer under this contract. In order to provide a more explicit reinsurance contract and to facilitate our quantitative analysis, we discuss the case when the claims follow an exponential distribution; it is then possible to show explicitly the impact of ambiguity aversion on the optimal reinsurance. Journal: Scandinavian Actuarial Journal Pages: 342-375 Issue: 4 Volume: 2020 Year: 2020 Month: 4 X-DOI: 10.1080/03461238.2019.1669218 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1669218 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:4:p:342-375 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1670249_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mario Brandtner Author-X-Name-First: Mario Author-X-Name-Last: Brandtner Author-Name: Wolfgang Kürsten Author-X-Name-First: Wolfgang Author-X-Name-Last: Kürsten Author-Name: Robert Rischau Author-X-Name-First: Robert Author-X-Name-Last: Rischau Title: Nonlinearly transformed risk measures: properties and application to optimal reinsurance Abstract: We propose the novel class of nonlinearly transformed risk measures (NTRMs) and apply them to the standard reinsurance problem in which an insurant seeks the risk-minimizing reinsurance contract. NTRMs transform both the outcomes and the probabilities of the insurant's uncertain final wealth by means of nonlinear functions. We prove relevant properties of NTRMs and show that they include popular Conditional Value-at-Risk (CVaR), Weighted Expected Shortfall (WES), Tail Nonlinearly Transformed Risk Measure (TNT), and Disutility Based Risk Measure (DBRM) as special cases. Regarding the reinsurance problem, we show that, under NTRMs, the optimal contract is of stop-loss type. We determine the optimal deductibles and provide comparative statics with respect to the insurant's risk aversion and initial wealth. Regarding comparative risk aversion, we show that the recently proposed WES, TNT, and DBRM help to overcome the restrictive all-or-nothing reinsurance decisions that prevail under CVaR. We further address the comparative statics with respect to initial wealth and show that under CVaR as well as WES and TNT, initial wealth is irrelevant: increasing initial wealth does not alter the optimal deductible. We show that NTRMs are able to overcome this shortcoming when the nonlinear transformation function of the outcomes is appropriately chosen. Journal: Scandinavian Actuarial Journal Pages: 376-395 Issue: 5 Volume: 2020 Year: 2020 Month: 5 X-DOI: 10.1080/03461238.2019.1670249 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1670249 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:5:p:376-395 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1676301_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Haluk Yener Author-X-Name-First: Haluk Author-X-Name-Last: Yener Title: Proportional reinsurance and investment in multiple risky assets under borrowing constraint Abstract: In this paper, we consider the ruin probability minimization of an insurance company that buys proportional reinsurance and invests in markets where borrowing is constrained. We use a diffusion approximation model for the surplus process of this company and assume that the company invests its surplus into a riskless and multiple risk assets that are modeled as geometric Brownian motions. To find the results, we introduce an auxiliary market parametrized with fictitious processes to relax the borrowing constraint and apply the techniques of stochastic optimal control. In this way, we find the optimal proportional reinsurance and investment strategy of an insurance company investing into multiple risky assets to minimize its ruin probability under the borrowing constraint. Furthermore, from our solutions, we show how our results connect to economic survival analysis and how investment and reinsurance strategies are related. Journal: Scandinavian Actuarial Journal Pages: 396-418 Issue: 5 Volume: 2020 Year: 2020 Month: 5 X-DOI: 10.1080/03461238.2019.1676301 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1676301 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:5:p:396-418 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1683761_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ning Wang Author-X-Name-First: Ning Author-X-Name-Last: Wang Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Title: Robust reinsurance contracts with risk constraint Abstract: This paper aims to investigate optimal reinsurance contracts in a continuous-time modelling framework from the perspective of a principal-agent problem. The reinsurer plays the role of the principal and aims to determine an optimal reinsurance premium to maximize the expected utility on terminal wealth. It is supposed that the reinsurer faces ambiguity about the insurance claim process. The insurer acts as the agent whose objective is to determine an optimal retention level in a proportional reinsurance to maximize the expected utility on terminal wealth. It is postulated that the insurer is subject to a dynamic Value-at-Risk constraint, which may be attributed to capital requirements specified by Solvency II. The Hamilton-Jacobi-Bellman (HJB) dynamic programming is adopted to discuss the optimization problems of the reinsurer and insurer. Explicit expressions for the optimal solutions of the problems are obtained in the case of exponential utility functions. Numerical examples are provided to illustrate economic intuition and insights. Journal: Scandinavian Actuarial Journal Pages: 419-453 Issue: 5 Volume: 2020 Year: 2020 Month: 5 X-DOI: 10.1080/03461238.2019.1683761 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1683761 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:5:p:419-453 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1685589_J.xml processed with: repec_from_tfjats.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Johannes M. Schumacher Author-X-Name-First: Johannes M. Author-X-Name-Last: Schumacher Title: Efficiency of institutional spending and investment rules Abstract: Endowment funds and similar institutions aim to generate a benefit stream of unlimited duration on the basis of an initially donated capital. Towards this purpose, responsible trustees need to design a spending policy as well as an investment policy. A combined spending and investment policy is said to be efficient if the total net present value of benefits that are paid according to the policy is equal to the initial capital, and inefficient if the total net present value is less than that. For several strategies, analytical expressions are given for the total net present value of benefits under the Black-Scholes assumptions. One of the strategies considered is the combination of a fixed-mix investment policy with a benefit policy that pays inflation-indexed benefits as long as ruin does not occur. This strategy is shown to be inefficient in many cases; the effective loss of capital can range from 5% to 15% under realistic parameter values. The inefficiency can be removed by adapting the investment policy and raising the benefits, without increasing the probability of ruin. Journal: Scandinavian Actuarial Journal Pages: 454-476 Issue: 5 Volume: 2020 Year: 2020 Month: 5 X-DOI: 10.1080/03461238.2019.1685589 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1685589 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:5:p:454-476 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1694973_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stephan M. Bischofberger Author-X-Name-First: Stephan M. Author-X-Name-Last: Bischofberger Author-Name: Munir Hiabu Author-X-Name-First: Munir Author-X-Name-Last: Hiabu Author-Name: Alex Isakson Author-X-Name-First: Alex Author-X-Name-Last: Isakson Title: Continuous chain-ladder with paid data Abstract: We introduce a continuous-time framework for the prediction of outstanding liabilities, in which chain-ladder development factors arise as a histogram estimator of a cost-weighted hazard function running in reversed development time. We use this formulation to show that under our assumptions on the individual data chain-ladder is consistent. Consistency is understood in the sense that both the number of observed claims grows to infinity and the level of aggregation tends to zero. We propose alternatives to chain-ladder development factors by replacing the histogram estimator with kernel smoothers and by estimating a cost-weighted density instead of a cost-weighted hazard. Finally, we provide a real-data example and a simulation study confirming the strengths of the proposed alternatives. Journal: Scandinavian Actuarial Journal Pages: 477-502 Issue: 6 Volume: 2020 Year: 2020 Month: 7 X-DOI: 10.1080/03461238.2019.1694973 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1694973 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:6:p:477-502 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1694974_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 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Jan Beirlant Author-X-Name-First: Jan Author-X-Name-Last: Beirlant Title: Combined tail estimation using censored data and expert information Abstract: We study tail estimation in Pareto-like settings for datasets with a high percentage of randomly right-censored data, and where some expert information on the tail index is available for the censored observations. This setting arises for instance naturally for liability insurance claims, where actuarial experts build reserves based on the specificity of each open claim, which can be used to improve the estimation based on the already available data points from closed claims. Through an entropy-perturbed likelihood, we derive an explicit estimator and establish a close analogy with Bayesian methods. Embedded in an extreme value approach, asymptotic normality of the estimator is shown, and when the expert is clair-voyant, a simple combination formula can be deduced, bridging the classical statistical approach with the expert information. Following the aforementioned combination formula, a combination of quantile estimators can be naturally defined. In a simulation study, the estimator is shown to often outperform the Hill estimator for censored observations and recent Bayesian solutions, some of which require more information than usually available. Finally we perform a case study on a motor third-party liability insurance claim dataset, where Hill-type and quantile plots incorporate ultimate values into the estimation procedure in an intuitive manner. Journal: Scandinavian Actuarial Journal Pages: 503-525 Issue: 6 Volume: 2020 Year: 2020 Month: 7 X-DOI: 10.1080/03461238.2019.1694974 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1694974 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:6:p:503-525 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1696223_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yajing Xu Author-X-Name-First: Yajing Author-X-Name-Last: Xu Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: Jonathan Ziveyi Author-X-Name-First: Jonathan Author-X-Name-Last: Ziveyi Title: Continuous-time multi-cohort mortality modelling with affine processes Abstract: Continuous-time mortality models, based on affine processes, provide many advantages over discrete-time models, especially for financial applications, where such processes are commonly used for interest rate and credit risks. This paper presents a multi-cohort mortality model for age-cohort mortality rates with common factors across cohorts as well as cohort-specific factors. The mortality model is based on well-developed and used techniques from interest rate theory and has many applications including the valuation of longevity-linked products. The model has many appealing features. It is a multi-cohort model that describes the whole mortality surface, it captures cohort effects, it allows for observed imperfect correlation between different cohorts, it is shown to fit historical data at pension-related ages very well, it has closed-form expressions for survival curves and we show that it outperforms a number of other commonly used discrete-time mortality models in forecasting future survival curves. Journal: Scandinavian Actuarial Journal Pages: 526-552 Issue: 6 Volume: 2020 Year: 2020 Month: 7 X-DOI: 10.1080/03461238.2019.1696223 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1696223 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:6:p:526-552 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1696885_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: D. Kuang Author-X-Name-First: D. Author-X-Name-Last: Kuang Author-Name: B. Nielsen Author-X-Name-First: B. Author-X-Name-Last: Nielsen Title: Generalized log-normal chain-ladder Abstract: We propose an asymptotic theory for distribution forecasting from the log-normal chain-ladder model. The theory overcomes the difficulty of convoluting log-normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder-based bootstrap. We embed the log-normal chain-ladder model in a class of infinitely divisible distributions called the generalized log-normal chain-ladder model. The asymptotic theory uses small σ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application. Journal: Scandinavian Actuarial Journal Pages: 553-576 Issue: 6 Volume: 2020 Year: 2020 Month: 7 X-DOI: 10.1080/03461238.2019.1696885 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1696885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:6:p:553-576 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1698452_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Weighted utility optimization of the participating endowment contract Abstract: In a participating endowment contract, the special loss compensation and profit sharing mechanism leads to heterogeneous benchmarks to distinguish the gain and loss for the policyholder's and the insurance company's S-shaped utilities. Because of the intense competition among the insurance companies and the requirement of the regulators, the benefits of the policyholders should be considered. As such, choosing the weighted utility of the two counterparts as the optimization objective is a rational setting. This setting induces a non-HARA (hyperbolic absolute risk aversion) and non-concave objective utility whose exact concavity and convexity are unknown. The difficulties not only come from this highly non-concave optimization problem, but also exist in the implicit integration of the optimum when solving the expected utilities of the two counterparts. We originally design an identification method to establish two categories of concave envelopes to solve the optimization problem, and propose an innovative numerical integration by substitution technique to deal with the implicit integration problem. The numerical simulation results recognize the existence of Pareto improvement of the two counterparts, which shows that the utilities of the policyholder and the insurance company can be simultaneously improved by switching into the weighted objective and appropriately amending the contract. Journal: Scandinavian Actuarial Journal Pages: 577-613 Issue: 7 Volume: 2020 Year: 2020 Month: 8 X-DOI: 10.1080/03461238.2019.1698452 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1698452 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:7:p:577-613 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1707109_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Miguel Santolino Author-X-Name-First: Miguel Author-X-Name-Last: Santolino Title: The Lee-Carter quantile mortality model Abstract: The Lee-Carter (LC) stochastic mortality model has been widely used for making future projections of mortality rates. In the framework of the LC model, the response function is non-linear in parameters. Here, we adapt this LC framework to compute conditional quantiles. The LC quantile model can be defined as quantile non-linear regression conditioned to age and the calendar year. Two strategies for estimating coefficients based on interior-point methods are described. We show that the LC quantile model provides additional information to that furnished by the traditional LC conditional mean. An application to Spanish mortality data is reported. Journal: Scandinavian Actuarial Journal Pages: 614-633 Issue: 7 Volume: 2020 Year: 2020 Month: 8 X-DOI: 10.1080/03461238.2019.1707109 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1707109 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:7:p:614-633 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1711154_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 Author-Name: Ryan Martin Author-X-Name-First: Ryan Author-X-Name-Last: Martin Title: Model misspecification, Bayesian versus credibility estimation, and Gibbs posteriors Abstract: In the context of predicting future claims, a fully Bayesian analysis – one that specifies a statistical model, prior distribution, and updates using Bayes's formula – is often viewed as the gold-standard, while Bühlmann's credibility estimator serves as a simple approximation. But those desirable properties that give the Bayesian solution its elevated status depend critically on the posited model being correctly specified. Here we investigate the asymptotic behavior of Bayesian posterior distributions under a misspecified model, and our conclusion is that misspecification bias generally has damaging effects that can lead to inaccurate inference and prediction. The credibility estimator, on the other hand, is not sensitive at all to model misspecification, giving it an advantage over the Bayesian solution in those practically relevant cases where the model is uncertain. This begs the question: does robustness to model misspecification require that we abandon uncertainty quantification based on a posterior distribution? Our answer to this question is No, and we offer an alternative Gibbs posterior construction. Furthermore, we argue that this Gibbs perspective provides a new characterization of Bühlmann's credibility estimator. Journal: Scandinavian Actuarial Journal Pages: 634-649 Issue: 7 Volume: 2020 Year: 2020 Month: 8 X-DOI: 10.1080/03461238.2019.1711154 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1711154 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:7:p:634-649 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1711450_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: Yajing Xu Author-X-Name-First: Yajing Author-X-Name-Last: Xu Author-Name: Jonathan Ziveyi Author-X-Name-First: Jonathan Author-X-Name-Last: Ziveyi Title: Cohort and value-based multi-country longevity risk management Abstract: Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson–Siegel model for the dynamics of interest rates. Index-based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer's portfolio and hedging strategies. We illustrate the effectiveness of using a value-based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and the UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks. Journal: Scandinavian Actuarial Journal Pages: 650-676 Issue: 7 Volume: 2020 Year: 2020 Month: 8 X-DOI: 10.1080/03461238.2019.1711450 File-URL: http://hdl.handle.net/10.1080/03461238.2019.1711450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:7:p:650-676 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1719880_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Guohui Guan Author-X-Name-First: Guohui Author-X-Name-Last: Guan Author-Name: Xiaojun Wang Author-X-Name-First: Xiaojun Author-X-Name-Last: Wang Title: Time-consistent reinsurance and investment strategies for an AAI under smooth ambiguity utility Abstract: This paper investigates time-consistent reinsurance(excess-of-loss, proportional) and investment strategies for an ambiguity averse insurer(abbr. AAI). The AAI is ambiguous towards the insurance and financial markets. In the AAI's attitude, the intensity of the insurance claims' number and the market price of risk of a stock can not be estimated accurately. This formulation of ambiguity is similar to the uncertainty of different equivalent probability measures. The AAI can purchase excess-of-loss or proportional reinsurance to hedge the insurance risk and invest in a financial market with cash and an ambiguous stock. We investigate the optimization goal under smooth ambiguity given in Klibanoff, P., Marinacci, M., & Mukerji, S. [(2005). A smooth model of decision making under ambiguity. Econometrica 73, 1849–1892], which aims to search the optimal strategies under average case. The utility function does not satisfy the Bellman's principle and we employ the extended HJB equation proposed in Björk, T. & Murgoci, A. [(2014). A theory of Markovian time-inconsistent stochastic control in discrete time. Finance and Stochastics 18(3), 545–592] to solve this problem. In the end of this paper, we derive the equilibrium reinsurance and investment strategies under smooth ambiguity and present the sensitivity analysis to show the AAI's economic behaviors. Journal: Scandinavian Actuarial Journal Pages: 677-699 Issue: 8 Volume: 2020 Year: 2020 Month: 9 X-DOI: 10.1080/03461238.2020.1719880 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1719880 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:8:p:677-699 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1724192_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Poontavika Naka Author-X-Name-First: Poontavika Author-X-Name-Last: Naka Author-Name: María del Carmen Boado-Penas Author-X-Name-First: María del Carmen Author-X-Name-Last: Boado-Penas Author-Name: Gauthier Lanot Author-X-Name-First: Gauthier Author-X-Name-Last: Lanot Title: A multiple state model for the working-age disabled population using cross-sectional data Abstract: A multiple state model describes the transitions of the disability risk among the states of active, inactive and dead. Ideally, estimations of transition probabilities and transition intensities rely on longitudinal data; however, most of the national surveys of disability are based on cross-sectional data measuring the disabled status of an individual at one point in time. This paper aims to propose a generic method of the estimation of the expected transition probabilities when the model allows recovery from disability using the UK cross-sectional data. The disability prevalence rates are modelled by taking into consideration the effect of age and time. Under some plausible assumptions concerning the death rates among inactive and active people, the estimated prevalence rates of disability are used to decompose survival probabilities in each state. Journal: Scandinavian Actuarial Journal Pages: 700-717 Issue: 8 Volume: 2020 Year: 2020 Month: 9 X-DOI: 10.1080/03461238.2020.1724192 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1724192 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:8:p:700-717 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1725911_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Grigori Jasnovidov Author-X-Name-First: Grigori Author-X-Name-Last: Jasnovidov Title: Approximation of ruin probability and ruin time in discrete Brownian risk models Abstract: We analyze the classical Brownian risk models discussing the approximation of ruin probabilities (classical, γ-reflected, Parisian and cumulative Parisian) for the case that ruin can occur only on specific discrete grids. A practical and natural grid of points is for instance $G(1)= \{0, 1, 2, \ldots \} $G(1)={0,1,2,…}, which allows us to study the probability of the ruin on the first day, second day, and so one. For such a discrete setting, there are no explicit formulas for the ruin probabilities mentioned above. In this contribution we derive accurate approximations of ruin probabilities for uniform grids by letting the initial capital to grow to infinity. Journal: Scandinavian Actuarial Journal Pages: 718-735 Issue: 8 Volume: 2020 Year: 2020 Month: 9 X-DOI: 10.1080/03461238.2020.1725911 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1725911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:8:p:718-735 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1726808_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lianzeng Zhang Author-X-Name-First: Lianzeng Author-X-Name-Last: Zhang Author-Name: He Liu Author-X-Name-First: He Author-X-Name-Last: Liu Title: On a discrete-time risk model with time-dependent claims and impulsive dividend payments Abstract: A discrete-time risk model with a mathematically tractable dependence structure between interclaim times and claim sizes is considered in the presence of an impulsive dividend strategy. Under such a strategy, once the insurer's reserve upcrosses the level b, the excess of the reserve over $a~(a\leq b) $a (a≤b) is paid off as dividends. We derive difference equations for both the expected discounted penalty function and the expected present value of dividend payments. Solution procedures for these difference equations are provided. When the joint distribution of the interclaim time and claim size is a finite mixture of bivariate geometric distributions, closed-form expressions are given. Numerical results for several sets of parameters are also provided to illustrate the applicability of the results obtained. Journal: Scandinavian Actuarial Journal Pages: 736-753 Issue: 8 Volume: 2020 Year: 2020 Month: 9 X-DOI: 10.1080/03461238.2020.1726808 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1726808 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:8:p:736-753 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1740314_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yumo Dong Author-X-Name-First: Yumo Author-X-Name-Last: Dong Author-Name: Fei Huang Author-X-Name-First: Fei Author-X-Name-Last: Huang Author-Name: Honglin Yu Author-X-Name-First: Honglin Author-X-Name-Last: Yu Author-Name: Steven Haberman Author-X-Name-First: Steven Author-X-Name-Last: Haberman Title: Multi-population mortality forecasting using tensor decomposition Abstract: In this paper, we formulate the multi-population mortality forecasting problem based on 3-way (age, year, and country/gender) decompositions. By applying the canonical polyadic decomposition (CPD) and the different forms of the Tucker decomposition to multi-population mortality data (10 European countries and 2 genders), we find that the out-of-sample forecasting performance is significantly improved both for individual populations and the aggregate population compared with using the single-population mortality model based on rank-1 singular value decomposition (SVD), or the Lee–Carter model. The results also shed lights on the similarity and difference of mortality among different countries. Additionally, we compare the variance-explained method and the out-of-sample validation method for rank (hyper-parameter) selection. Results show that the out-of-sample validation method is preferred for forecasting purposes. Journal: Scandinavian Actuarial Journal Pages: 754-775 Issue: 8 Volume: 2020 Year: 2020 Month: 9 X-DOI: 10.1080/03461238.2020.1740314 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1740314 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:8:p:754-775 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1742478_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Correction Journal: Scandinavian Actuarial Journal Pages: i-ii Issue: 8 Volume: 2020 Year: 2020 Month: 9 X-DOI: 10.1080/03461238.2020.1742478 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1742478 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:8:p:i-ii Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1748102_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 Author-Name: Kenneth Wong Author-X-Name-First: Kenneth Author-X-Name-Last: Wong Title: Incorporating structural changes in mortality improvements for mortality forecasting Abstract: In recent decades, there have been decreasing mortality improvements at younger ages but increasing mortality improvements at older ages in many countries. We propose a modified Lee-Carter method to allow for these structural changes, in which the entire data period is divided into more homogeneous subperiods and a unique set of age-specific parameters is incorporated for each subperiod. We consider a number of methods to project these age patterns into the future. Our results show that the new method can reasonably capture the underlying movements in the age patterns over time and can potentially improve the forecast accuracy of death rates and life expectancies. It is interesting to observe that the highest age sensitivity has been moving gradually to older ages and it is important to take this trend into account in mortality forecasting. Journal: Scandinavian Actuarial Journal Pages: 776-791 Issue: 9 Volume: 2020 Year: 2020 Month: 10 X-DOI: 10.1080/03461238.2020.1748102 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1748102 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:9:p:776-791 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1750469_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ze Chen Author-X-Name-First: Ze Author-X-Name-Last: Chen Author-Name: Bingzheng Chen Author-X-Name-First: Bingzheng Author-X-Name-Last: Chen Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Title: Fair dynamic valuation of insurance liabilities: a loss averse convex hedging approach Abstract: Hedging techniques have been widely adopted in market-consistent or fair valuation approach required by recent solvency regulations, to take into account the market prices of the hedgeable parts of insurance liabilities. In this study, we investigate the fair dynamic valuation of insurance liabilities, which are model-consistent (mark-to-model), market-consistent (mark-to-market), and time-consistent, as proposed by Barigou et al. (2019) in a multi-period setting. We introduce the loss averse convex hedging technique, which ‘punishes’ loss outcomes more than gain outcomes. We prove that fair dynamic valuations are equivalent to the class of loss averse convex hedge-based valuation. Moreover, we propose and provide a complete characterization of loss averse mean–variance hedging and show how to implement loss averse mean–variance hedge-based dynamic valuations using numerical examples. Journal: Scandinavian Actuarial Journal Pages: 792-818 Issue: 9 Volume: 2020 Year: 2020 Month: 10 X-DOI: 10.1080/03461238.2020.1750469 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1750469 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:9:p:792-818 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1758762_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lanpeng Ji Author-X-Name-First: Lanpeng Author-X-Name-Last: Ji Title: On the cumulative Parisian ruin of multi-dimensional Brownian motion risk models Abstract: Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial capital tends to infinity. An asymptotic distribution for the conditional cumulative Parisian ruin time is also derived. The obtained results on the cumulative Parisian ruin can be seen as generalisations of some of the results derived in D $\c{e} $ȩbicki et al. [(2018). Extremal behavior of hitting a cone by correlated Brownian motion with drift. Stochastic Processes and Their Applications 128, 4171–4206]. As a particular interesting case, the two-dimensional Brownian motion risk model is discussed in detail. Journal: Scandinavian Actuarial Journal Pages: 819-842 Issue: 9 Volume: 2020 Year: 2020 Month: 10 X-DOI: 10.1080/03461238.2020.1758762 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1758762 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:9:p:819-842 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1773523_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Dynamic modelling and coherent forecasting of mortality rates: a time-varying coefficient spatial-temporal autoregressive approach Abstract: Existing literature argues that the mortality rate of a specific age is affected not only by its own lags but by the lags of neighbouring ages, known as cohort effects. Although these effects are assumed constant in most studies, they can be dynamic over a long timespan. Consequently, popular mortality models with time-invariant age-dependent coefficients, including the Lee-Carter (LC) and vector autoregression (VAR) models, are incapable of modelling these dynamic cohort effects. To capture such dynamic patterns, we propose a time-varying coefficient spatial-temporal autoregressive (TVSTAR) model that allows for flexible time-dependent parameters. The proposed TVSTAR model is compatible with multi-population modelling and enjoys sound statistical properties. Using empirical results of mortality data from the United Kingdom (UK) and France over the period 1950–2016, we show that the TVSTAR model consistently outperforms the LC (Li-Lee, or LL) and the original STAR model under the single-population (multi-population) modelling framework. Finally, our empirical results suggest that cohort effects strengthen over time for very old ages in both the UK and France. Using simulation evidence, we argue that this observed upward trend can be caused by the overall advancement in the mortality evolution of the same cohort. Journal: Scandinavian Actuarial Journal Pages: 843-863 Issue: 9 Volume: 2020 Year: 2020 Month: 10 X-DOI: 10.1080/03461238.2020.1773523 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1773523 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2020:y:2020:i:9:p:843-863 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1768889_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Rosy Oh Author-X-Name-First: Rosy Author-X-Name-Last: Oh Author-Name: Jae Youn Ahn Author-X-Name-First: Jae Youn Author-X-Name-Last: Ahn Author-Name: Woojoo Lee Author-X-Name-First: Woojoo Author-X-Name-Last: Lee Title: On copula-based collective risk models: from elliptical copulas to vine copulas Abstract: Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model, and two-part frequency-severity model. This study focuses on the copula approach to develop collective risk models that allow a flexible dependence structure for frequency and severity. We first revisit the bivariate copula method for frequency and average severity. After examining the inherent difficulties of the bivariate copula model, we alternatively propose modeling the dependence of frequency and individual severities using multivariate Gaussian and t-copula functions. We also explain how to generalize those copulas in the format of a vine copula. The proposed copula models have computational advantages and provide intuitive interpretations for the dependence structure. Our analytical findings are illustrated by analyzing automobile insurance data. Journal: Scandinavian Actuarial Journal Pages: 1-33 Issue: 1 Volume: 2021 Year: 2021 Month: 01 X-DOI: 10.1080/03461238.2020.1768889 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1768889 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:1:p:1-33 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1793218_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Olivier Lopez Author-X-Name-First: Olivier Author-X-Name-Last: Lopez Author-Name: Xavier Milhaud Author-X-Name-First: Xavier Author-X-Name-Last: Milhaud Title: Individual reserving and nonparametric estimation of claim amounts subject to large reporting delays Abstract: Thanks to nonparametric estimators coming from machine learning, microlevel reserving has become more and more popular for actuaries. Recent research focused on how to integrate the whole information one can have on claims to predict individual reserves, with varying success due to incomplete observations. Using the CART algorithm, we develop new results that allow us to deal with large reporting delays and partially observed explanatory variables. Statistically speaking, we extend CART to take into account truncation of the data and introduce plug-in estimators. Our applications are based on real-life insurance portfolios embedding Income Protection and Third-Party Liability guarantees. The full knowledge of the claim lifetime is shown to be crucial to predict the individual reserves efficiently. Journal: Scandinavian Actuarial Journal Pages: 34-53 Issue: 1 Volume: 2021 Year: 2021 Month: 01 X-DOI: 10.1080/03461238.2020.1793218 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1793218 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:1:p:34-53 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1795714_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Oytun Haçarız Author-X-Name-First: Oytun Author-X-Name-Last: Haçarız Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Author-Name: Angus S. Macdonald Author-X-Name-First: Angus S. Author-X-Name-Last: Macdonald Title: Genetics, insurance and hypertrophic cardiomyopathy Abstract: We specify a mathematical model of Hypertrophic Cardiomyopathy (HCM) and consider the potential costs arising from adverse selection in a life insurance market. HCM is a dominantly inherited heart disorder which is relatively common and has high mortality; a population prevalence of 0.2% and annual mortality hazard (force of mortality) of 1% have been widely cited. Adverse selection may arise if insurers may not take account of adverse DNA-based genetic tests for a causative mutation. A novel feature of our model is that it includes cascade genetic testing (CGT) in nuclear families. CGT is the form of testing used in HCM. Among other things, it implies that genetic testing occurs only if a family history exists. We find in most scenarios the premium increases necessitated by adverse selection to be very small – fractions of 1% – but we ask under what circumstances these might increase to appreciable levels. Insurers' inability to use family history in underwriting would have a large impact. We note that the epidemiology of HCM is still evolving and that 0.2% is likely to be a considerable underestimate of mutation prevalence, while recent estimates of annual mortality hazards are much less than 1%. The first of these in particular is likely to limit any adverse selection costs. Journal: Scandinavian Actuarial Journal Pages: 54-81 Issue: 1 Volume: 2021 Year: 2021 Month: 01 X-DOI: 10.1080/03461238.2020.1795714 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1795714 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:1:p:54-81 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1902853_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Krzysztof Dȩbicki Author-X-Name-First: Krzysztof Author-X-Name-Last: Dȩbicki Author-Name: Enkelejd Hashorva Author-X-Name-First: Enkelejd Author-X-Name-Last: Hashorva Author-Name: Konrad Krystecki Author-X-Name-First: Konrad Author-X-Name-Last: Krystecki Title: Finite-time ruin probability for correlated Brownian motions Abstract: Let $(W_1(s), W_2(t)), s,t\ge 0 $(W1(s),W2(t)),s,t≥0 be a two-dimensional Gaussian process with standard Brownian motion marginals and constant correlation $\rho \in (-1,1) $ρ∈(−1,1). Define the joint survival probability of both supremum functionals by \[ \pi_\rho(c_1,c_2; u, v)=\pk{\sup_{s \in [0,1]} \left(W_1(s)-c_1s\right) \gt u,\sup_{t \in [0,1]} \left(W_2(t)-c_2t\right) \gt v}, \]πρ(c1,c2;u,v)=Psups∈[0,1]W1(s)−c1s>u,supt∈[0,1]W2(t)−c2t>v, where $c_1,c_2 \in \mathbb {R} $c1,c2∈R and u, v are given positive constants. Approximation of $\pi _\rho (c_1,c_2; u, v) $πρ(c1,c2;u,v) is of interest for the analysis of ruin probability in bivariate Brownian risk model, as well as in the study of the power of bivariate test statistics. In this contribution, we derive tight bounds for $\pi _\rho (c_1,c_2; u, v) $πρ(c1,c2;u,v) in the case $\rho \in (0,1) $ρ∈(0,1) and obtain precise approximations for all $\rho \in (-1,1) $ρ∈(−1,1) by letting $u\to \infty $u→∞ and taking v = au for some fixed positive constant a. Journal: Scandinavian Actuarial Journal Pages: 890-915 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1902853 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1902853 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:890-915 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1918578_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Guangyuan Gao Author-X-Name-First: Guangyuan Author-X-Name-Last: Gao Author-Name: Yanlin Shi Author-X-Name-First: Yanlin Author-X-Name-Last: Shi Title: Age-coherent extensions of the Lee–Carter model Abstract: Age coherence describes the property that forecast mortality rates across ages will not diverge in the long run. Although intuitively and biologically reasonable, this property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. In this paper, we propose two effective extensions of the LC model, allowing for the geometric (LC-G) and hyperbolic (LC-H) decayed relative speed of mortality decline at each age, over the out-of-sample forecasting steps. Those approaches are based on the original in-sample estimates of LC, which are easy to obtain. An inversed Epanechnikov kernel is employed to model the geometric and hyperbolic parameters across ages, and unknown parameters are selected via a data-driven method. With little added computational cost to LC, our approaches incorporate the dynamic and rotating relative speeds of mortality decline over ages, recognize the growing difficulty of such declines at older ages, provide age-coherent forecasts of mortality rates in the long run, and is easily extensible to multi-population cases. Using a large sample of 15 countries, we demonstrate that LC-G and LC-H, as well as their multi-population counterparties, consistently improve the forecasting accuracy of the competing LC model and its single- and multi-population extensions.Feng, L., Shi, Y., & Chang, L. (2021). Forecasting mortality with a hyperbolic spatial temporal VAR model. International Journal of Forecasting, 37(1), 255–273. Journal: Scandinavian Actuarial Journal Pages: 998-1016 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1918578 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1918578 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:998-1016 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1895298_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Søren Asmussen Author-X-Name-First: Søren Author-X-Name-Last: Asmussen Author-Name: Corina Constantinescu Author-X-Name-First: Corina Author-X-Name-Last: Constantinescu Author-Name: Julie Thøgersen Author-X-Name-First: Julie Author-X-Name-Last: Thøgersen Title: On the risk of credibility premium rules Abstract: A discrete-time risk process is considered where the full distribution of the claim size X is not completely known to the insurance company. Rather, it assumes that the distribution of X given $Z=\zeta $Z=ζ is $F_\zeta $Fζ where Z is some structural random variable for which a prior is available. The main emphasis of the paper is the unconditional ruin probability $\psi (u) $ψ(u) in this setting where the premium is either updated according to incoming information about the claim distribution or computed by the expected value principle. This is in turn studied via the conditional ruin probability $\psi _\zeta (u) $ψζ(u), for which large deviations estimates are available. Rigorous proofs are given only for the case of the $F_\zeta $Fζ forming a scale parameter family, including the classical case of gamma claims with a gamma prior. However, the analysis readily suggests what should be the behaviour of $\psi (u) $ψ(u) in different models for the claims. Journal: Scandinavian Actuarial Journal Pages: 866-889 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1895298 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1895298 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:866-889 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1886981_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ning Wang Author-X-Name-First: Ning Author-X-Name-Last: Wang Author-Name: Zhuo Jin Author-X-Name-First: Zhuo Author-X-Name-Last: Jin Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Ming Qiu Author-X-Name-First: Ming Author-X-Name-Last: Qiu Title: Household consumption-investment-insurance decisions with uncertain income and market ambiguity Abstract: In this paper, we aim to study optimal decisions on consumption, investment and purchasing life insurance of a household with two consecutive generations, say parents and children. A continuous-time model featuring the impacts of labor income uncertainty and model uncertainty on those decisions is considered. Specifically, as in the economic literature about the labor income process, we consider the situation where the income growth rate is unobservable. The model takes account of the decision makings of both the parents and the children who are supposed to be ambiguity-averse expected utility maximizers. An attention is given to exploring the impacts of life insurance purchasing on the decision makings. The robustness approach to economic decision makings, which is implemented in the continuous-time model through a Girsanov's measure change for a Brownian motion, is applied to capture ambiguity aversion. Employing the known mathematical techniques in stochastic optimal control, say the Hamilton-Jacobi-Bellman dynamic programing principle, closed-form solutions are obtained. Numerical studies are provided to illustrate the economic implications of the solutions. Journal: Scandinavian Actuarial Journal Pages: 832-865 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1886981 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1886981 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:832-865 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1911840_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fatah Cheurfa Author-X-Name-First: Fatah Author-X-Name-Last: Cheurfa Author-Name: Baya Takhedmit Author-X-Name-First: Baya Author-X-Name-Last: Takhedmit Author-Name: Sofiane Ouazine Author-X-Name-First: Sofiane Author-X-Name-Last: Ouazine Author-Name: Karim Abbas Author-X-Name-First: Karim Author-X-Name-Last: Abbas Title: Functional sensitivity analysis of ruin probability in the classical risk models Abstract: Sensitivity analysis investigates how the change in the output of a computational model can be attributed to changes of its input parameters. Identifying the input parameters that propagate more uncertainty on the ruin probability associated with insurance risk models is a challenging problem. In this paper, we consider the classical risk model, where an epistemic-uncertainty veils the true values of the claim size distribution rate and the Poisson arrival rate. Based on the available data for calibrating the probability distributions that model gaps of knowledge on these rates, and using the Taylor-series expansion methodology, we obtain the ruin probability under polynomial form in uncertain rates as a computational model. Specifically, we get a new sensitivity estimate of the ruin probability with respect to uncertain parameters. We provide a coherent framework within which we can accurately characterize statistically the uncertain ruin probability. In addition, we use the Markov's inequality to estimate the risk incurred by working with uncertain ruin probability rather than that evaluated at fixed parameters. A series of numerical experiments are presented to illustrate the potential of the proposed approach. Journal: Scandinavian Actuarial Journal Pages: 936-968 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1911840 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1911840 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:936-968 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1921017_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Aritra Halder Author-X-Name-First: Aritra Author-X-Name-Last: Halder Author-Name: Shariq Mohammed Author-X-Name-First: Shariq Author-X-Name-Last: Mohammed Author-Name: Kun Chen Author-X-Name-First: Kun Author-X-Name-Last: Chen Author-Name: Dipak K. Dey Author-X-Name-First: Dipak K. Author-X-Name-Last: Dey Title: Spatial Tweedie exponential dispersion models: an application to insurance rate-making Abstract: In this paper we propose a statistical modeling framework that contributes to advancing methods for modeling insurance policy premium in the actuarial literature. Specification of separate frequency and severity models, accounting for territorial risk and performing accurate inference, are some of the challenges an actuary faces while modeling policy premium. Policy premiums are characterized to follow a semi-continuous probability distribution, featuring a non-zero probability at zero along with a positive continuous support. Interpretability is a concern when quantifying unobserved risks premiums face from spatial variation. Commonly used strategies in the literature are known to successfully quantify this risk, but do not necessarily produce interpretable estimates. Resorting to frequency-severity models leaves the actuary indecisive about the specification of covariates and spatial effects. The novelty of our proposed approach lies in the development of a parsimonious and interpretable zero-adjusted modeling framework that allows for joint estimation of the effect of policy and individual characteristics on the mean premium and dispersion, while quantifying spatial variability in the mean model. The developed methods are applied to a database featuring premiums arising from the collision coverage in insurance policies for motor vehicles within the state of Connecticut, USA, for the year 2008. Journal: Scandinavian Actuarial Journal Pages: 1017-1036 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1921017 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1921017 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:1017-1036 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1907783_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mohamed Amine Lkabous Author-X-Name-First: Mohamed Amine Author-X-Name-Last: Lkabous Title: Poissonian occupation times of spectrally negative Lévy processes with applications Abstract: In this paper, we introduce the concept of Poissonian occupation times below level 0 of a spectrally negative Lévy process. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known continuously observed quantities involving occupation times of spectrally negative Lévy processes. As an application, we establish a link between Poissonian occupation times and insurance risk models with Parisian implementation delays. Journal: Scandinavian Actuarial Journal Pages: 916-935 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1907783 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1907783 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:916-935 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1918577_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peng Yang Author-X-Name-First: Peng Author-X-Name-Last: Yang Author-Name: Zhiping Chen Author-X-Name-First: Zhiping Author-X-Name-Last: Chen Author-Name: Xiangyu Cui Author-X-Name-First: Xiangyu Author-X-Name-Last: Cui Title: Equilibrium reinsurance strategies for n insurers under a unified competition and cooperation framework Abstract: We propose a unified competition and cooperation framework for n insurers and investigate the resulting reinsurance game problem. Each insurer's surplus is assumed to be a diffusion process. Each insurer can purchase the proportional reinsurance to reduce his claim risk, and the reinsurance premium is determined via the variance value principle. The objective of each insurer is to find a reinsurance strategy so as to maximize the expected utility of his terminal payoff. We establish a Hamilton–Jacobi–Bellman (HJB) equation and the corresponding verification theorem. Furthermore, we derive the explicit solutions for both the equilibrium reinsurance strategy and the value function by solving the HJB equation. Finally, numerical experiments are carried out to illustrate the influences of model parameters such as the size of a group, the number of groups on the equilibrium reinsurance strategy. The numerical results reveal some similarities and differences between the competition case and the cooperation case, and the detailed effects of different competition and cooperation patterns, which provide useful insights for reinsurance in reality. Journal: Scandinavian Actuarial Journal Pages: 969-997 Issue: 10 Volume: 2021 Year: 2021 Month: 11 X-DOI: 10.1080/03461238.2021.1918577 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1918577 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:10:p:969-997 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1806917_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nicole Bäuerle Author-X-Name-First: Nicole Author-X-Name-Last: Bäuerle Author-Name: Gregor Leimcke Author-X-Name-First: Gregor Author-X-Name-Last: Leimcke Title: Robust optimal investment and reinsurance problems with learning Abstract: In this paper, we consider an optimal investment and reinsurance problem with partially unknown model parameters which are allowed to be learned. The model includes multiple business lines and dependency between them. The aim is to maximize the expected exponential utility of terminal wealth which is shown to imply a robust approach. We can solve this problem using a generalized HJB equation where derivatives are replaced by Clarke's generalized gradient. The optimal investment strategy can be determined explicitly and the optimal reinsurance strategy is given in terms of the solution of an equation. Since this equation is hard to solve, we derive bounds for the optimal reinsurance strategy via comparison arguments. Journal: Scandinavian Actuarial Journal Pages: 82-109 Issue: 2 Volume: 2021 Year: 2021 Month: 02 X-DOI: 10.1080/03461238.2020.1806917 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1806917 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:2:p:82-109 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1814855_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Andrea Nigri Author-X-Name-First: Andrea Author-X-Name-Last: Nigri Author-Name: Susanna Levantesi Author-X-Name-First: Susanna Author-X-Name-Last: Levantesi Author-Name: Mario Marino Author-X-Name-First: Mario Author-X-Name-Last: Marino Title: Life expectancy and lifespan disparity forecasting: a long short-term memory approach Abstract: After the World War II, developed countries experienced a constant decline in mortality. As a result, life expectancy has never stopped increasing, despite an evident deceleration in developed countries, e.g. England, USA and Denmark. In this paper, we propose a new approach for forecasting life expectancy and lifespan disparity based on the recurrent neural networks with a long short-term memory. This type of neural network leads to predicting future values of longevity indexes while maintaining the significant influence of the past trend, but at the same time adequately reproducing the recent trend into forecasting. The model was applied to five countries for two fitting periods focusing on the forecasting life expectancy and lifespan disparity, both independently and simultaneously at birth and age 65. The results were compared to the projections obtained by four different models, namely, the Double Gap, ARIMA, CoDa and Lee-Carter in the independent case and the first-order Vector Autoregression model in the simultaneous case. Our predictions seem to be coherent with historical trends and biologically reasonable, providing a more accurate portrait of the future life expectancy and lifespan disparity. Journal: Scandinavian Actuarial Journal Pages: 110-133 Issue: 2 Volume: 2021 Year: 2021 Month: 02 X-DOI: 10.1080/03461238.2020.1814855 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1814855 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:2:p:110-133 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1815238_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Erengul Dodd Author-X-Name-First: Erengul Author-X-Name-Last: Dodd Author-Name: Jonathan J. Forster Author-X-Name-First: Jonathan J. Author-X-Name-Last: Forster Author-Name: Jakub Bijak Author-X-Name-First: Jakub Author-X-Name-Last: Bijak Author-Name: Peter W. F. Smith Author-X-Name-First: Peter W. F. Author-X-Name-Last: Smith Title: Stochastic modelling and projection of mortality improvements using a hybrid parametric/semi-parametric age–period–cohort model Abstract: We propose a comprehensive and coherent approach for mortality projection using a maximum-likelihood method which benefits from full use of the substantial data available on mortality rates, their improvement rates, and the associated variability. Under this approach, we fit a negative binomial distribution to overcome one of the several limitations of existing approaches such as insufficiently robust mortality projections as a result of employing a model (e.g. Poisson) which provides a poor fit to the data. We also impose smoothness in parameter series which vary over age, cohort, and time in an integrated way. Generalised Additive Models (GAMs), being a flexible class of semi-parametric statistical models, allow us to differentially smooth components, such as cohorts, more heavily in areas of sparse data for the component concerned. While GAMs can provide a reasonable fit for the ages where there is adequate data, estimation and extrapolation of mortality rates using a GAM at higher ages is problematic due to high variation in crude rates. At these ages, parametric models can give a more robust fit, enabling a borrowing of strength across age groups. Our projection methodology assumes a smooth transition between a GAM at lower ages and a fully parametric model at higher ages. Journal: Scandinavian Actuarial Journal Pages: 134-155 Issue: 2 Volume: 2021 Year: 2021 Month: 02 X-DOI: 10.1080/03461238.2020.1815238 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1815238 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:2:p:134-155 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1820372_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 Title: An application of parametric quantile regression to extend the two-stage quantile regression for ratemaking Abstract: This paper deals with the use of parametric quantile regression for the calculation of a loaded premium, based on a quantile measure, corresponding to individual insurance risk. Heras et al. have recently introduced a ratemaking process based on a two-stage quantile regression model. In the first stage, a probability to have at least one claim is estimated by a GLM logit, whereas in the second stage several quantile regressions are necessary for the estimate of the severity component. The number of quantile regressions to be performed is equal to the number of risk classes selected for ratemaking. In the actuarial context, when a large number of risk classes are considered (e.g. in Motor Third Party Liability), such approach can imply an over-parameterization and time-consuming. To this aim, in the second stage, we suggest to apply a more parsimonious approach based on Parametric Quantile Regression as introduced by Frumento and Bottai and never used in the actuarial context. This more conservative approach allows you not to lose efficiency in the estimation of premiums compared to the traditional Quantile Regression. Journal: Scandinavian Actuarial Journal Pages: 156-170 Issue: 2 Volume: 2021 Year: 2021 Month: 02 X-DOI: 10.1080/03461238.2020.1820372 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1820372 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:2:p:156-170 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1823464_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Lina Palmborg Author-X-Name-First: Lina Author-X-Name-Last: Palmborg Author-Name: Mathias Lindholm Author-X-Name-First: Mathias Author-X-Name-Last: Lindholm Author-Name: Filip Lindskog Author-X-Name-First: Filip Author-X-Name-Last: Lindskog Title: Financial position and performance in IFRS 17 Abstract: The general principles for determining the financial performance of a company is that revenue is earned as goods are delivered or services provided, and that expenses in the period are made up of the costs associated with this earned revenue. In the insurance industry, premium payments are typically made upfront, and can provide coverage for several years, or be paid many years before the coverage period starts. The associated costs are often not fully known until many years later. Hence, complexity arises both in determining how a premium paid should be earned over time, and in valuing the costs associated with this earned premium. IFRS 17 attempts to align the insurance industry with these general accounting principles. We bring this new accounting standard into the realm of actuarial science, through a mathematical interpretation of the regulatory texts, and by defining the algorithm for profit or loss in accordance with the new standard. Furthermore, we suggest a computationally efficient risk-based method of valuing a portfolio of insurance contracts and an allocation of this value to subportfolios. Finally, we demonstrate the practicability of these methods and the algorithm for profit or loss in a large-scale numerical example. Journal: Scandinavian Actuarial Journal Pages: 171-197 Issue: 3 Volume: 2021 Year: 2021 Month: 03 X-DOI: 10.1080/03461238.2020.1823464 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1823464 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:3:p:171-197 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1824158_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mi Chen Author-X-Name-First: Mi Author-X-Name-Last: Chen Author-Name: Kam Chuen Yuen Author-X-Name-First: Kam Chuen Author-X-Name-Last: Yuen Author-Name: Wenyuan Wang Author-X-Name-First: Wenyuan Author-X-Name-Last: Wang Title: Optimal reinsurance and dividends with transaction costs and taxes under thinning structure Abstract: In this paper, we investigate the problem of optimal reinsurance and dividends under the Cramér–Lundberg risk model with the thinning-dependence structure which was first introduced by Wang and Yuen [Wang, G. & Yuen, K. C. (2005). On a correlated aggregate claims model with thinning-dependence structure. Insurance: Mathematics and Economics 36(3), 456–468]. The optimization criterion is to maximize the expected accumulated discounted dividends paid until ruin. To enhance the practical relevance of the optimal dividend and reinsurance problem, non-cheap reinsurance is considered and transaction costs and taxes are imposed on dividends. These realistic features convert our optimization problem into a mixed classical-impulse control problem. For the sake of mathematical tractability, we replace the Cramér–Lundberg risk model by its diffusion approximation. Using the method of quasi-variational inequalities, we show that the optimal reinsurance follows a two-dimensional excess-of-loss reinsurance strategy, and the optimal dividend strategy turns out to be an impulse dividend strategy with an upper and a lower barrier, i.e. everything above the lower barrier is paid as dividends whenever the surplus goes beyond the upper barrier, and no dividends are paid otherwise. Under the diffusion risk model, closed-form expressions for the value function associated with the optimal dividend and reinsurance strategy are derived. In addition, some numerical examples are presented to illustrate the optimality results. Journal: Scandinavian Actuarial Journal Pages: 198-217 Issue: 3 Volume: 2021 Year: 2021 Month: 03 X-DOI: 10.1080/03461238.2020.1824158 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1824158 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:3:p:198-217 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1830845_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nuria Torrado Author-X-Name-First: Nuria Author-X-Name-Last: Torrado Author-Name: Jorge Navarro Author-X-Name-First: Jorge Author-X-Name-Last: Navarro Title: Ranking the extreme claim amounts in dependent individual risk models Abstract: In risk theory, the distribution of extreme claim amounts of dependent risks is an essential element, since it provides valuable information to companies for developing risk reduction strategies. In this article, we obtain a representation of the distributions of the smallest and the largest claim amounts based on a new concept of semi-distorted distribution. This concept extends the well known concept of distorted distributions introduced previously in risk theory. Based on this representation, we obtain distribution-free comparisons between extreme claim amounts in the sense of different stochastic dominances when the risks have a fixed dependence structure. Several examples illustrate the application of the theoretical results. Journal: Scandinavian Actuarial Journal Pages: 218-247 Issue: 3 Volume: 2021 Year: 2021 Month: 03 X-DOI: 10.1080/03461238.2020.1830845 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1830845 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:3:p:218-247 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1830846_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Anna Glazyrina Author-X-Name-First: Anna Author-X-Name-Last: Glazyrina Author-Name: Alexander Melnikov Author-X-Name-First: Alexander Author-X-Name-Last: Melnikov Title: Quantile hedging in a defaultable market with life insurance applications Abstract: The paper is devoted to quantile hedging in a market with defaultable securities. Both perfect and quantile hedging strategies are given for a European call option on a vulnerable equity. Application of quantile methodology to pricing the equity-linked life insurance contracts is demonstrated. A numerical example is provided to illustrate the effect of a default on the option price, on the probability of successful hedging, and on the insurance-related variables. Journal: Scandinavian Actuarial Journal Pages: 248-265 Issue: 3 Volume: 2021 Year: 2021 Month: 03 X-DOI: 10.1080/03461238.2020.1830846 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1830846 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:3:p:248-265 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1833697_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Correction Journal: Scandinavian Actuarial Journal Pages: i-i Issue: 3 Volume: 2021 Year: 2021 Month: 03 X-DOI: 10.1080/03461238.2020.1833697 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1833697 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:3:p:i-i Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1844791_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Romain Gauchon Author-X-Name-First: Romain Author-X-Name-Last: Gauchon Author-Name: Stéphane Loisel Author-X-Name-First: Stéphane Author-X-Name-Last: Loisel Author-Name: Jean-Louis Rulliere Author-X-Name-First: Jean-Louis Author-X-Name-Last: Rulliere Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Title: Optimal prevention of large risks with two types of claims Abstract: In this paper, we propose and study a risk model with two types of claims in which the insurer may invest into a prevention plan which decreases the intensity of large claims without impacting the small claims. We identify a necessary and sufficient condition for insurers to use prevention if there is no surplus. If, in addition, the severity of large claims dominates that of small claims by the harmonic mean residual life (HMRL) order, insurers invest more in prevention in the presence of a surplus. Finally, we characterize the asymptotic optimal prevention strategy when the initial surplus tends to infinity in the two main cases where both claim types are light-tailed and where one of them is light-tailed and the other one is heavy-tailed. Journal: Scandinavian Actuarial Journal Pages: 323-334 Issue: 4 Volume: 2021 Year: 2021 Month: 04 X-DOI: 10.1080/03461238.2020.1844791 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1844791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:4:p:323-334 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1845231_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhuo Jin Author-X-Name-First: Zhuo Author-X-Name-Last: Jin Author-Name: Huafu Liao Author-X-Name-First: Huafu Author-X-Name-Last: Liao Author-Name: Yue Yang Author-X-Name-First: Yue Author-X-Name-Last: Yang Author-Name: Xiang Yu Author-X-Name-First: Xiang Author-X-Name-Last: Yu Title: Optimal dividend strategy for an insurance group with contagious default risk Abstract: This paper studies the optimal dividend for a multi-line insurance group, in which each subsidiary runs a product line and is exposed to some external credit risk. The default contagion is considered such that one default event may increase the default probabilities of all surviving subsidiaries. The total dividend problem for the insurance group is investigated and we find that the optimal dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier of each subsidiary is modulated by the default state. That is, how many and which subsidiaries have defaulted will determine the dividend threshold of each surviving subsidiary. These conclusions are based on the analysis of the associated recursive system of Hamilton–Jacobi–Bellman variational inequalities (HJBVIs). The existence of the classical solution is established and the verification theorem is proved. In the case of two subsidiaries, the value function and optimal barriers are given in analytical forms, allowing us to conclude that the optimal barrier of one subsidiary decreases if the other subsidiary defaults. Journal: Scandinavian Actuarial Journal Pages: 335-361 Issue: 4 Volume: 2021 Year: 2021 Month: 04 X-DOI: 10.1080/03461238.2020.1845231 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1845231 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:4:p:335-361 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1836676_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mark Kiermayer Author-X-Name-First: Mark Author-X-Name-Last: Kiermayer Author-Name: Christian Weiß Author-X-Name-First: Christian Author-X-Name-Last: Weiß Title: Grouping of contracts in insurance using neural networks Abstract: Despite the high importance of grouping in practice, there exists little research on the respective topic. The present work presents a framework for grouping and a novel method to optimize model points in life insurance. We introduce a supervised clustering algorithm using neural networks to form a less complex portfolio, alias grouping. In a two-step approach, we first approximate selected characteristics of a portfolio. Next, we nest this estimator in a neural network, such that cluster representatives, alias model points, are calibrated in accordance with their effect on the characteristics of the portfolio. This approach is similar to the work by Horvath, B., Muguruza, A. & Tomas, M. [(2019). Deep learning volatility. Available on arXiv 1901.09647.], who focus on the calibration of implied volatility models. Our numerical experiments for term life insurance and defined contribution pension plans show significant improvements, in terms of capturing the characteristics of a portfolio, of the neural network approach over K-means clustering, a common baseline algorithm for grouping. These results are further confirmed by a sensitivity analysis of the investment surplus, where we additionally show the flexibility of the model to include common industry practice. Journal: Scandinavian Actuarial Journal Pages: 295-322 Issue: 4 Volume: 2021 Year: 2021 Month: 04 X-DOI: 10.1080/03461238.2020.1836676 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1836676 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:4:p:295-322 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1832911_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ahmad Salahnejhad Ghalehjooghi Author-X-Name-First: Ahmad Author-X-Name-Last: Salahnejhad Ghalehjooghi Author-Name: Antoon Pelsser Author-X-Name-First: Antoon Author-X-Name-Last: Pelsser Title: Time-consistent and market-consistent actuarial valuation of the participating pension contract Abstract: The regulator in Europe calls for the market-consistent valuation of the insurance liabilities that usually are not (fully) tradable. An example of such liabilities is the participating pension contract that is generally long-dated and vulnerable to the medium-time dynamics of the underlying risk drivers. Dealing with these characteristics requires time-consistent pricing. However, the well-known non-linear premium principles, often used as pricing operators, are not time-consistent. Based on this motivation, we study the time-consistent and market- consistent (TCMC) actuarial valuation of the participating pension contracts with hybrid payoff. We use a standard profit-sharing mechanism with guaranteed interest rate, and generalize it to a hybrid profit-sharing mechanism with the actuarial and hedgeable financial risks, over the course of the contract. Market-consistency is maintained by “two-step actuarial valuation” in a one-period setting. Time-consistency is obtained by a “backward iteration” of these one-period two-step valuations over the predetermined sub-intervals of the valuation period. We use the Least-Square Monte-Carlo method to implement the conditional operators in the backward iteration. We compare the results of TCMC price to the expected value of the discounted payoff and measure the relative risk loading and time-consistency risk premium. Besides, we investigate the effect of the stochastic interest rate as compared to the deterministic one. Journal: Scandinavian Actuarial Journal Pages: 266-294 Issue: 4 Volume: 2021 Year: 2021 Month: 04 X-DOI: 10.1080/03461238.2020.1832911 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1832911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:4:p:266-294 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1848912_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Carole Bettonville Author-X-Name-First: Carole Author-X-Name-Last: Bettonville Author-Name: Louise d'Oultremont Author-X-Name-First: Louise Author-X-Name-Last: d'Oultremont 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 Author-Name: Robin Van Oirbeek Author-X-Name-First: Robin Author-X-Name-Last: Van Oirbeek Title: Matrix calculation for ultimate and 1-year risk in the Semi-Markov individual loss reserving model Abstract: This paper proposes a multistate model with a Semi-Markov dependence structure describing the different stages in the settlement process of individual claims in general insurance. Every trajectory, from reporting to closure is combined with a modeling of individual link ratios to obtain the ultimate cost of each claim. Analytical expressions are derived for the moments of ultimate amounts whereas quantile risk measures can be obtained by simulation. In the 1-year view, the proposed matrix calculations avoid the simulation-within-simulation issue and offer a tractable evaluation method. A case study illustrates the relevance of the proposed approach. Journal: Scandinavian Actuarial Journal Pages: 380-407 Issue: 5 Volume: 2021 Year: 2021 Month: 05 X-DOI: 10.1080/03461238.2020.1848912 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1848912 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:5:p:380-407 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1845788_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter Grandits Author-X-Name-First: Peter Author-X-Name-Last: Grandits Author-Name: Maike Klein Author-X-Name-First: Maike Author-X-Name-Last: Klein Title: Ruin probability in a two-dimensional model with correlated Brownian motions Abstract: We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing maximally the company with less endowment is the optimal strategy for the collaboration if the Brownian motions are correlated and the transfer rate can exceed the drift rates. Moreover, we obtain an explicit formula for the minimal ruin probability in case of perfectly positively correlated Brownian motions where we also allow for different diffusion coefficients. Journal: Scandinavian Actuarial Journal Pages: 362-379 Issue: 5 Volume: 2021 Year: 2021 Month: 05 X-DOI: 10.1080/03461238.2020.1845788 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1845788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:5:p:362-379 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1852595_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: An Chen Author-X-Name-First: An Author-X-Name-Last: Chen Author-Name: Linyi Qian Author-X-Name-First: Linyi Author-X-Name-Last: Qian Author-Name: Zhixin Yang Author-X-Name-First: Zhixin Author-X-Name-Last: Yang Title: Tontines with mixed cohorts Abstract: With the advancements of medical technology and the improvements in quality of life, the demand for innovative retirement products designed to address increasing longevity risks has been growing in recent decades. Tontines and tontine-like products, where the insurers and policyholder share longevity risks, are being explored as an alternative to annuities. As of now, homogeneous policyholders are often assumed in the design process of this mortality-pooling product type. Inspired by the work of Milevsky M. A. & Salisbury T. S. [(2016). Equitable retirement income tontines: mixing cohorts without discriminating. ASTIN Bulletin 46(3), 571–604] in which heterogeneous cohorts are considered, we also extend the tontine products to heterogeneous policyholders. Different from the method employed in Milevsky M. A. & Salisbury T. S. [(2016). Equitable retirement income tontines: mixing cohorts without discriminating. ASTIN Bulletin 46(3), 571–604], we establish the explicit expression of optimal withdrawal rates under the actuarial fairness budget constraint held for one single cohort. In addition, we propose a numerical procedure to achieve approximate fairness among the cohorts by choosing participation rates (or the share prices) properly. Journal: Scandinavian Actuarial Journal Pages: 437-455 Issue: 5 Volume: 2021 Year: 2021 Month: 05 X-DOI: 10.1080/03461238.2020.1852595 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1852595 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:5:p:437-455 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1852105_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sixian Tang Author-X-Name-First: Sixian Author-X-Name-Last: Tang Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Title: Market pricing of longevity-linked securities Abstract: One way of mitigating longevity risk is constructing a hedge using longevity- or mortality-linked securities. A fundamental question is how to price these securities in an incomplete life market where liabilities are not liquidly traded. Although various premium principles have been developed in the literature, no consensus has been reached on the best choice to price longevity risk. This study explores the impact of mortality model uncertainty and pricing rule uncertainty on the valuation of longevity-linked securities. Twelve premium principles based on risk-neutral and real-world measures are investigated under the Lee-Carter model and the generalised CBD model. Calibration constraints are set using the quotations of UK pension annuities to incorporate the market view of longevity risk. Different premium principles and model assumptions are tested and compared based on the estimated prices of S-forwards and longevity swaps with different maturities. Journal: Scandinavian Actuarial Journal Pages: 408-436 Issue: 5 Volume: 2021 Year: 2021 Month: 05 X-DOI: 10.1080/03461238.2020.1852105 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1852105 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:5:p:408-436 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1858153_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: Yilun Song Author-X-Name-First: Yilun Author-X-Name-Last: Song Author-Name: Qi Ye Author-X-Name-First: Qi Author-X-Name-Last: Ye Title: Optimal contribution rate of PAYGO pension Abstract: In this paper, we study the optimal contribution rate of pay-as-you-go (PAYGO) pension under a Nash equilibrium between the participants and the government. Given the fixed contribution rate, the participants of different cohorts choose optimal consumption and asset allocation policies to achieve their objectives. Using the variational method, we derive the closed-form solution. The value function of the participants is monotonous with respect to the PAYGO contribution rate under constant population growth rate. As such, we modify the ‘Samuelson-Aaron’ criterion that the preference between PAYGO and fully funded pensions depends not only on the demography, investment and salary parameters but also on the age of the cohort. Moreover, we establish the critical age to separate the preference and the ex-post admissible scope for the contribution rate adjustment. As a central planner, the government is fully aware of the participants' optimal feedback functions. The objective of the government is to maximize the overall utility of the participants weighted by each cohort's population. For a shrinking population, the fully funded scheme is more preferable and only the elderly cohorts prefer PAYGO scheme. However, taking into account the larger political power of the elderly cohorts in the objective function, the optimal contribution rate raises slightly. Journal: Scandinavian Actuarial Journal Pages: 505-531 Issue: 6 Volume: 2021 Year: 2021 Month: 07 X-DOI: 10.1080/03461238.2020.1858153 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1858153 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:6:p:505-531 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1809509_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kenneth Bruhn Author-X-Name-First: Kenneth Author-X-Name-Last: Bruhn Author-Name: Alexander Sevel Lollike Author-X-Name-First: Alexander Sevel Author-X-Name-Last: Lollike Title: Retrospective reserves and bonus Abstract: Modern legislation has increased the amount of quantities that insurance companies should report in order to prove solvent as well as prudent. More of these quantities require not just simple bookkeeping but a mere projection of the future. In this paper, we provide a solid base for this crystal ball exercise as we derive differential equations for the retrospective reserves of a pension company, in a setting where the surplus and the dividends are modelled. The differential equations rely on dynamics of the stochastic reserve that are affine functions of the stochastic reserve themselves. The retrospective reserves are defined as conditional expected values, given limited information, leading to computational tractable differential equations for the reserves. We wrap up the theoretical part by suggestions for practical use in terms of considering validation of guarantees and discretionary benefits at future time points. Journal: Scandinavian Actuarial Journal Pages: 457-475 Issue: 6 Volume: 2021 Year: 2021 Month: 07 X-DOI: 10.1080/03461238.2020.1809509 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1809509 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:6:p:457-475 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1852596_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Claude Lefèvre Author-X-Name-First: Claude Author-X-Name-Last: Lefèvre Author-Name: Stéphane Loisel Author-X-Name-First: Stéphane Author-X-Name-Last: Loisel Author-Name: Pierre Montesinos Author-X-Name-First: Pierre Author-X-Name-Last: Montesinos Title: On s-convex bounds for Beta-unimodal distributions with applications to basis risk assessment Abstract: This paper is concerned with properties of Beta-unimodal distributions and their use to assess the basis risk inherent to index-based insurance or reinsurance contracts. To this extent, we first characterize s-convex stochastic orders for Beta-unimodal distributions in terms of the Weyl fractional integral. We then determine s-convex extrema for such distributions, focusing in particular on the cases s = 2, 3, 4. Next, we define an Enterprise Risk Management framework that relies on Beta-unimodality to assess these hedge imperfections, introducing several penalty functions and worst case scenarios. Some of the results obtained are illustrated numerically via a representative catastrophe model. Journal: Scandinavian Actuarial Journal Pages: 476-504 Issue: 6 Volume: 2021 Year: 2021 Month: 07 X-DOI: 10.1080/03461238.2020.1852596 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1852596 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:6:p:476-504 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1863856_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Seul Ki Kang Author-X-Name-First: Seul Author-X-Name-Last: Ki Kang Author-Name: Liang Peng Author-X-Name-First: Liang Author-X-Name-Last: Peng Author-Name: Andrew Golub Author-X-Name-First: Andrew Author-X-Name-Last: Golub Title: Two-step risk analysis in insurance ratemaking Abstract: Recently, Heras et al. (2018. An application of two-stage quantile regression to insurance ratemaking. Scandinavian Actuarial Journal 9, 753–769) propose a two-step inference to forecast the Value-at-Risk of aggregated losses in insurance ratemaking by combining logistic regression and quantile regression without discussing the critical issue of uncertainty quantification. This paper proposes a random weighted bootstrap method to quantify the estimation uncertainty and an alternative two-step inference via weighted quantile regression. Journal: Scandinavian Actuarial Journal Pages: 532-542 Issue: 6 Volume: 2021 Year: 2021 Month: 07 X-DOI: 10.1080/03461238.2020.1863856 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1863856 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:6:p:532-542 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1867232_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Francesca Perla Author-X-Name-First: Francesca Author-X-Name-Last: Perla Author-Name: Ronald Richman Author-X-Name-First: Ronald Author-X-Name-Last: Richman Author-Name: Salvatore Scognamiglio Author-X-Name-First: Salvatore Author-X-Name-Last: Scognamiglio Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Time-series forecasting of mortality rates using deep learning Abstract: The time-series nature of mortality rates lends itself to processing through neural networks that are specialized to deal with sequential data, such as recurrent and convolutional networks. The aim of this work is to show how the structure of the Lee–Carter model can be generalized using a relatively simple shallow convolutional network model, allowing for its components to be evaluated in familiar terms. Although deep networks have been applied successfully in many areas, we find that deep networks do not lead to an enhanced predictive performance in our approach for mortality forecasting, compared to the proposed shallow one. Our model produces highly accurate forecasts on the Human Mortality Database, and, without further modification, generalizes well to the United States Mortality Database. Journal: Scandinavian Actuarial Journal Pages: 572-598 Issue: 7 Volume: 2021 Year: 2021 Month: 08 X-DOI: 10.1080/03461238.2020.1867232 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1867232 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:7:p:572-598 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1867631_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tim J. Boonen Author-X-Name-First: Tim J. Author-X-Name-Last: Boonen Author-Name: Ka Chun Cheung Author-X-Name-First: Ka Chun Author-X-Name-Last: Cheung Author-Name: Yiying Zhang Author-X-Name-First: Yiying Author-X-Name-Last: Zhang Title: Bowley reinsurance with asymmetric information on the insurer's risk preferences Abstract: The Bowley solution refers to the optimal pricing density for the reinsurer and optimal ceded loss for the insurer when there is a monopolistic reinsurer. In a sequential game, the reinsurer first sets the pricing kernel, and thereafter the insurer selects the reinsurance contract given the pricing kernel. In this article, we study Bowley solutions under asymmetric information on the insurer's risk preferences where the identity of the insurer is unknown to the reinsurer. By assuming that the insurer adopts a Value-at-Risk measure or a convex distortion risk measure, the optimal pricing kernel for the insurer and the optimal ceded loss function for the reinsurer are determined. Numerical examples are presented to illustrate the results. Journal: Scandinavian Actuarial Journal Pages: 623-644 Issue: 7 Volume: 2021 Year: 2021 Month: 08 X-DOI: 10.1080/03461238.2020.1867631 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1867631 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:7:p:623-644 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1862291_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xiaobai Zhu Author-X-Name-First: Xiaobai Author-X-Name-Last: Zhu 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: Structure of intergenerational risk-sharing plans: optimality and fairness Abstract: In this paper, we derive optimal designs for a stylized Intergenerational Risk Sharing (IRS) pension plan. We study a Defined Ambition plan under which both contributions and pension benefits are adjusted based on the funding level. Our objective function focuses on the stability of members' lifetime consumption, both in the contribution and benefit phases, formulating the optimization as an ergodic control problem. We illustrate the drawbacks of unconstrained optimization and demonstrate the importance of including regulatory requirements for the sake of fairness across generations. Our results show that a linear risk sharing protocol is transparent, and with reasonable constraints on the funding level, can deliver a risk sharing plan that is fair with respect to intergenerational risk transfers, and is sustainable. Journal: Scandinavian Actuarial Journal Pages: 543-571 Issue: 7 Volume: 2021 Year: 2021 Month: 08 X-DOI: 10.1080/03461238.2020.1862291 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1862291 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:7:p:543-571 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1867233_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yanchun Zhao Author-X-Name-First: Yanchun Author-X-Name-Last: Zhao Author-Name: Tiantian Mao Author-X-Name-First: Tiantian Author-X-Name-Last: Mao Author-Name: Fan Yang Author-X-Name-First: Fan Author-X-Name-Last: Yang Title: Estimation of the Haezendonck-Goovaerts risk measure for extreme risks Abstract: The Haezendonck-Goovaerts (H-G) risk measure, proposed by Haezendonck & Goovaerts [(1982). A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1(1), 41–53], has attracted much attention in the fields of finance, insurance and quantitative risk management in recent years. In this paper, we focus on the study of efficient estimators for the H-G risk measure. We first propose a new estimator for the H-G risk measure with a power Young function based on its first-order expansion at intermediate levels, and then we extend it to extreme levels under the second-order regular variation condition by using extreme value theory. Asymptotic normality is established for both the intermediate- and extreme-level estimators. We also propose an estimator for the H-G risk measure with a general Young function and establish its consistency. Numerical simulations are conducted to show that the performances of the proposed estimators are quite good and their computation processes are easy, thereby making the H-G risk measure highly efficient for practical applications. An analysis of real data is also provided. Journal: Scandinavian Actuarial Journal Pages: 599-622 Issue: 7 Volume: 2021 Year: 2021 Month: 08 X-DOI: 10.1080/03461238.2020.1867233 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1867233 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:7:p:599-622 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1869069_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Benjamin Avanzi Author-X-Name-First: Benjamin Author-X-Name-Last: Avanzi Author-Name: Hayden Lau Author-X-Name-First: Hayden Author-X-Name-Last: Lau Author-Name: Bernard Wong Author-X-Name-First: Bernard Author-X-Name-Last: Wong Title: Optimal periodic dividend strategies for spectrally negative Lévy processes with fixed transaction costs Abstract: Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, periodic dividend strategies were recently introduced (Albrecher et al. 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal periodic dividend strategy with fixed transaction costs for spectrally negative Lévy processes. The value function of a periodic $(b_u,b_l) $(bu,bl) strategy is calculated by means of exiting identities and Itô's excusion when the surplus process is of unbounded variation. We show that a sufficient condition for optimality is that the Lévy measure admits a density which is completely monotonic. Under such assumptions, a periodic $(b_u,b_l) $(bu,bl) strategy is confirmed to be optimal. Results are illustrated. Journal: Scandinavian Actuarial Journal Pages: 645-670 Issue: 8 Volume: 2021 Year: 2021 Month: 09 X-DOI: 10.1080/03461238.2020.1869069 File-URL: http://hdl.handle.net/10.1080/03461238.2020.1869069 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:8:p:645-670 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1873176_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sergio Alvares Maffra Author-X-Name-First: Sergio Author-X-Name-Last: Alvares Maffra Author-Name: John Armstrong Author-X-Name-First: John Author-X-Name-Last: Armstrong Author-Name: Teemu Pennanen Author-X-Name-First: Teemu Author-X-Name-Last: Pennanen Title: Stochastic modeling of assets and liabilities with mortality risk Abstract: This paper describes a general approach for the stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income instruments including short- and long-maturity fixed-rate bonds as well as index-linked and corporate bonds. On the liability side, the risks are driven by future mortality developments as well as price and wage inflation. All the risk factors are modeled as a multivariate stochastic process that captures the dynamics and the dependencies across different risk factors. The model is easy to interpret and to calibrate to both historical data and to forecasts or expert views concerning the future. This feature is particularly useful in unprecedented circumstances like pandemics when historical data alone does not give a reasonable description of the future. The simple structure of the model allows for efficient computations. The construction of a million scenarios takes only a few minutes on a personal computer. The approach is illustrated with an asset-liability analysis of a defined benefit pension fund, pre- and post-COVID-19. Journal: Scandinavian Actuarial Journal Pages: 695-725 Issue: 8 Volume: 2021 Year: 2021 Month: 09 X-DOI: 10.1080/03461238.2021.1873176 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1873176 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:8:p:695-725 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1895299_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Christian Genest Author-X-Name-First: Christian Author-X-Name-Last: Genest Author-Name: Nikolai Kolev Author-X-Name-First: Nikolai Author-X-Name-Last: Kolev Title: A law of uniform seniority for dependent lives Abstract: The law of uniform seniority is an actuarial principle which justifies the replacement of an annuity on joint lives of unequal ages by an annuity on a single life, often computed at a different rate. Gompertz's law of mortality is a prime example of distribution which meets this condition. This paper proposes an extension of this principle to the case of two dependent lives and relates it to aging concepts. In the important special case of a bilinear averaging function, it is shown that the lifetimes have a dependence structure which is Archimedean and marginal distributions from the same scale family. This leads to both functional and stochastic representations for these models, which enjoy closure properties with respect to some common operations. The dependence and aging properties of the models are then discussed. The challenges involved in a multivariate extension are also mentioned. Journal: Scandinavian Actuarial Journal Pages: 726-743 Issue: 8 Volume: 2021 Year: 2021 Month: 09 X-DOI: 10.1080/03461238.2021.1895299 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1895299 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:8:p:726-743 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1872694_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Caroline Hillairet Author-X-Name-First: Caroline Author-X-Name-Last: Hillairet Author-Name: Olivier Lopez Author-X-Name-First: Olivier Author-X-Name-Last: Lopez Title: Propagation of cyber incidents in an insurance portfolio: counting processes combined with compartmental epidemiological models Abstract: In this paper, we propose a general framework to design accumulation scenarios that can be used to anticipate the impact of a massive cyber attack on an insurance portfolio. The aim is also to emphasize the role of countermeasures in stopping the spread of the attack over the portfolio and to quantify the benefits of implementing such strategies of response. Our approach consists of separating the global dynamic of the cyber event (that can be described through compartmental epidemiological models), the effect on the portfolio, and the response strategy. This general framework allows us to obtain Gaussian approximations for the corresponding processes, and sharp confidence bounds for the losses. A detailed simulation study, which mimics the effects of a Wannacry scenario, illustrates the practical implementation of the method. Journal: Scandinavian Actuarial Journal Pages: 671-694 Issue: 8 Volume: 2021 Year: 2021 Month: 09 X-DOI: 10.1080/03461238.2021.1872694 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1872694 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:8:p:671-694 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1881809_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peng Li Author-X-Name-First: Peng Author-X-Name-Last: Li Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Title: Nested Monte Carlo simulation in financial reporting: a review and a new hybrid approach Abstract: Risk assessment on a stochastic basis has become prevalent in financial reporting due to increasingly sophisticated regulatory requirements. Many applications require nested stochastic projections, for which crude Monte Carlo can be too costly and time-consuming to perform to reach a reasonable degree of accuracy. While there has been ample literature on nested simulation methods in the area of portfolio management, less is known in the literature regarding nested simulation for financial reporting and internal risk management. There has been little research dealing with unique challenges arising from the structure of insurance liabilities. This paper intends to fill the gap in the literature by providing an overview of the use of nested stochastic modeling for different regulatory purposes and investigating the multi-period nested stochastic model, common in insurance products. The paper reviews a variety of so-called ‘stochastic-on-stochastic’ methods to speed up nested simulations. In addition, the paper presents a new hybrid ‘deterministic-on-stochastic’ method based on partial differential equation (PDE). To the best knowledge of the authors, this is the first time that a PDE method has been introduced for the purpose of nested stochastic projection. A numerical example is provided to show the high efficiency of the hybrid PDE method in a multi-period nested model for financial reporting. Journal: Scandinavian Actuarial Journal Pages: 744-778 Issue: 9 Volume: 2021 Year: 2021 Month: 10 X-DOI: 10.1080/03461238.2021.1881809 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1881809 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:9:p:744-778 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1882550_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Himchan Jeong Author-X-Name-First: Himchan Author-X-Name-Last: Jeong Author-Name: Hyunwoong Chang Author-X-Name-First: Hyunwoong Author-X-Name-Last: Chang Author-Name: Emiliano A. Valdez Author-X-Name-First: Emiliano A. Author-X-Name-Last: Valdez Title: A non-convex regularization approach for stable estimation of loss development factors Abstract: In this article, we apply non-convex regularization methods in order to obtain stable estimation of loss development factors in insurance claims reserving. Among the non-convex regularization methods, we focus on the use of the log-adjusted absolute deviation (LAAD) penalty and provide discussion on optimization of LAAD penalized regression model, which we prove to converge with a coordinate descent algorithm under mild conditions. This has the advantage of obtaining a consistent estimator for the regression coefficients while allowing for the variable selection, which is linked to the stable estimation of loss development factors. We calibrate our proposed model using a multi-line insurance dataset from a property and casualty insurer where we observed reported aggregate loss along accident years and development periods. When compared to other regression models, our LAAD penalized regression model provides very promising results. Journal: Scandinavian Actuarial Journal Pages: 779-803 Issue: 9 Volume: 2021 Year: 2021 Month: 10 X-DOI: 10.1080/03461238.2021.1882550 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1882550 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:9:p:779-803 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1885483_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric C. K. Cheung Author-X-Name-First: Eric C. K. Author-X-Name-Last: Cheung Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Title: Simple approximation for the ruin probability in renewal risk model under interest force via Laguerre series expansion Abstract: Although the ruin probability in a renewal insurance risk model with credit interest may be viewed as a classical research problem, exact solutions are only available in the literature in very special cases when both the claim amounts and the interclaim times follow distributions such as the exponential. This is a long standing problem especially from a computational point of view, and the difficulty lies in the fact that the ruin probability usually satisfies a higher order integro-differential equation and/or an ordinary differential equation with non-constant coefficients. In this paper, for a large class of interclaim time distributions (including a combination of exponentials), we shall develop an approximation for the ruin probability using Laguerre series expansion as a function of the initial surplus level. It is shown that the (approximated) Laguerre coefficients can be solved from a system of linear equations, a procedure that is very easy to implement. A main advantage of our approach is that no specific distributional assumption on the claim amounts is required, apart from some mild differentiability and integrability conditions that can be verified. Numerical examples are provided to illustrate the very good performance of our approximation including both light-tailed and heavy-tailed claims. Journal: Scandinavian Actuarial Journal Pages: 804-831 Issue: 9 Volume: 2021 Year: 2021 Month: 10 X-DOI: 10.1080/03461238.2021.1885483 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1885483 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2021:y:2021:i:9:p:804-831 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1925735_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Joshua Gavagan Author-X-Name-First: Joshua Author-X-Name-Last: Gavagan Author-Name: Liang Hu Author-X-Name-First: Liang Author-X-Name-Last: Hu Author-Name: Gee Y. Lee Author-X-Name-First: Gee Y. Author-X-Name-Last: Lee Author-Name: Haiyan Liu Author-X-Name-First: Haiyan Author-X-Name-Last: Liu Author-Name: Anna Weixel Author-X-Name-First: Anna Author-X-Name-Last: Weixel Title: Optimal reinsurance with model uncertainty and Stackelberg game Abstract: In this paper, we obtain an optimal reinsurance contract explicitly in the form of excess-of-loss with a limit when the risk measure is Range-Value-at-Risk. Then we study optimal reinsurance with model uncertainty, where the uncertainty set contains a greatest element in the sense of stochastic order. Furthermore, we study the Stackelberg game in reinsurance with model uncertainty. In order to illustrate how our findings can be applied in practice to determine the optimal reinsurance contract, we perform an empirical study using the Wisconsin Local Government Property Insurance Fund dataset. Tweedie distributions are fit to the building and contents loss amounts from the property fund, and used to determine the optimal loading factor, and reinsurance contract corresponding to the loading factor. From the analysis, we discover that some policies have more recoveries from the optimal reinsurance contract than the premium paid, while others have smaller recoveries than the premium. Journal: Scandinavian Actuarial Journal Pages: 29-48 Issue: 1 Volume: 2022 Year: 2022 Month: 01 X-DOI: 10.1080/03461238.2021.1925735 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1925735 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:1:p:29-48 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1921836_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Łukasz Delong Author-X-Name-First: Łukasz Author-X-Name-Last: Delong Author-Name: Mathias Lindholm Author-X-Name-First: Mathias Author-X-Name-Last: Lindholm Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: Collective reserving using individual claims data Abstract: The aim of this paper is to operationalize claims reserving based on individual claims data. We design a modeling architecture that is based on six different neural networks. Each network is a separate module that serves a certain modeling purpose. We apply our architecture to individual claims data and predict their settlement processes on a monthly time grid. A proof of concept is provided by benchmarking the resulting claims reserves with the ones received from the classical chain-ladder method which uses much coarser (aggregated) data. Journal: Scandinavian Actuarial Journal Pages: 1-28 Issue: 1 Volume: 2022 Year: 2022 Month: 01 X-DOI: 10.1080/03461238.2021.1921836 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1921836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:1:p:1-28 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1928542_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marie-Pier Bergeron-Boucher Author-X-Name-First: Marie-Pier Author-X-Name-Last: Bergeron-Boucher Author-Name: Søren Kjærgaard Author-X-Name-First: Søren Author-X-Name-Last: Kjærgaard Title: Mortality forecasting at age 65 and above: an age-specific evaluation of the Lee-Carter model Abstract: The Lee-Carter (LC) model has been recurrently used to forecast mortality, including by national statistical offices. This model has many advantages, but tends to underpredict life expectancy due to its assumption of constant age-specific response to the time index. Does this bias emerge from all ages or from specific ages only? In this paper, we aim to provide a more detailed evaluation of the model, by evaluating its accuracy, bias and robustness by age. Our analysis is based on 806 out-of-sample forecasts using various different fitting periods and forecast horizons. We focus on age 65 and above, as most deaths occur at older ages nowadays. We showed that the LC model is not fundamentally biased, but its main assumption of constant age-specific response to the time index, often leading to constant rates of mortality improvement, is not appropriate in all populations and at all ages. Journal: Scandinavian Actuarial Journal Pages: 64-79 Issue: 1 Volume: 2022 Year: 2022 Month: 01 X-DOI: 10.1080/03461238.2021.1928542 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1928542 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:1:p:64-79 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1934104_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Delia Coculescu Author-X-Name-First: Delia Author-X-Name-Last: Coculescu Author-Name: Freddy Delbaen Author-X-Name-First: Freddy Author-X-Name-Last: Delbaen Title: Group cohesion under individual regulatory constraints Abstract: We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit; more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures. In the commonotonic case, we show that they are tail expectations but calculated under a different probability. Journal: Scandinavian Actuarial Journal Pages: 80-93 Issue: 1 Volume: 2022 Year: 2022 Month: 01 X-DOI: 10.1080/03461238.2021.1934104 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1934104 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:1:p:80-93 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1926315_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hanspeter Schmidli Author-X-Name-First: Hanspeter Author-X-Name-Last: Schmidli Title: Dividends and capital injections in a renewal model with Erlang distributed inter-arrival times Abstract: We consider a renewal risk model with general Erlang distributed inter-arrival times. We treat this as a Markov modulated risk model and assume, for simplicity, that the states are observable. The insurer can pay dividends and has to inject capital in order to keep the surplus positive. We determine the optimal dividend/capital injection strategy. Journal: Scandinavian Actuarial Journal Pages: 49-63 Issue: 1 Volume: 2022 Year: 2022 Month: 01 X-DOI: 10.1080/03461238.2021.1926315 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1926315 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:1:p:49-63 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2037016_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Donatien Hainaut Author-X-Name-First: Donatien Author-X-Name-Last: Hainaut Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link Abstract: Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. To speed up calculations, boosting is often applied to gradients of the loss function, not to responses (hence the name gradient boosting). When the model is trained by minimizing Poisson deviance, this amounts to apply the least-squares principle to raw residuals. This exposes gradient boosting to the same problems that lead to replace least-squares with Poisson Generalized Linear Models (GLM) to analyze low counts (typically, the number of reported claims at policy level in personal lines). This paper shows that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each step. Numerical illustrations demonstrate similar or better performances compared to gradient boosting when trees are used as weak learners, with a higher level of transparency since responses are used instead of gradients. Journal: Scandinavian Actuarial Journal Pages: 841-866 Issue: 10 Volume: 2022 Year: 2022 Month: 11 X-DOI: 10.1080/03461238.2022.2037016 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2037016 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:10:p:841-866 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2049635_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Runhuan Feng Author-X-Name-First: Runhuan Author-X-Name-Last: Feng Author-Name: Guojun Gan Author-X-Name-First: Guojun Author-X-Name-Last: Gan Author-Name: Ning Zhang Author-X-Name-First: Ning Author-X-Name-Last: Zhang Title: Variable annuity pricing, valuation, and risk management: a survey Abstract: Variable annuity is arguably the most complex individual retirement planning product in the financial market. Its intricacy stems from a variety of product features including investment options, guaranteed benefits, withdrawal options, etc. In many ways, variable annuities can be viewed as traditional life and annuity products at the next level of sophistication with added financial options. Despite a significant amount of publications by practitioners and academics on the subject matter, there have been few research papers that systematically exploit the basic principles underlying the operation of variable annuities. This survey paper aims to fill in the gap in the literature for an overview of state-of-the-art technology and recent trends in the development of variable annuities. Journal: Scandinavian Actuarial Journal Pages: 867-900 Issue: 10 Volume: 2022 Year: 2022 Month: 11 X-DOI: 10.1080/03461238.2022.2049635 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2049635 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:10:p:867-900 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2049636_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Julian Jetses Author-X-Name-First: Julian Author-X-Name-Last: Jetses Author-Name: Marcus C. Christiansen Author-X-Name-First: Marcus C. Author-X-Name-Last: Christiansen Title: A general surplus decomposition principle in life insurance Abstract: In with-profit life insurance, the prudent valuation of future insurance liabilities leads to systematic surplus that mainly belongs to the policyholders and is redistributed as bonus. For a fair and lawful redistribution of surplus, the insurer needs to decompose the total portfolio surplus with respect to the contributions of individual policies and with respect to different risk sources. For this task, actuaries have a number of heuristic decomposition formulas, but an overarching decomposition principle is still missing. This paper fills that gap by introducing a so-called ISU decomposition principle that bases on infinitesimal sequential updates of the insurer's valuation basis. It is shown that the existing heuristic decomposition formulas can be replicated as ISU decompositions. Furthermore, alternative decomposition principles and their relation to the ISU decomposition principle are discussed. The generality of the ISU concept makes it a useful tool also beyond classical surplus decompositions in life insurance. Journal: Scandinavian Actuarial Journal Pages: 901-925 Issue: 10 Volume: 2022 Year: 2022 Month: 11 X-DOI: 10.1080/03461238.2022.2049636 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2049636 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:10:p:901-925 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1930136_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Oytun Haçarız Author-X-Name-First: Oytun Author-X-Name-Last: Haçarız Author-Name: Torsten Kleinow Author-X-Name-First: Torsten Author-X-Name-Last: Kleinow Author-Name: Angus S. Macdonald Author-X-Name-First: Angus S. Author-X-Name-Last: Macdonald Title: An actuarial model of arrhythmogenic right ventricular cardiomyopathy and life insurance Abstract: Many countries ban insurers from using genetic test results in underwriting. One study [Howard, R. C. W. (2014). Report to CIA research committee: Genetic testing model: If the underwriters had no access to known results. Canadian Institute of Actuaries (CIA).] stated that such a ban in Canada would expose life insurers to adverse selection, causing premiums to increase by 12%. More than a quarter of this cost was attributable to a single disorder, Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC). We model ARVC in a life insurance market, following the methodology of [Haçarız, O., Kleinow, T. & Macdonald, A. S. (2021). Genetics, insurance and hypertrophic cardiomyopathy. Scandinavian Actuarial Journal 2021, 54–81.], including ‘cascade’ genetic testing (CGT), so the rôle of family history in underwriting is modelled explicitly. We review (in the Appendix) the published epidemiology of ARVC, in particular the existence of an effective treatment, which we also include in our model. Our results are consistent with those of [Macdonald, A. S. & Yu, F. (2011). The impact of genetic information on the insurance industry: Conclusions from the ‘bottom-up’ modelling programme. Astin Bulletin 41(02), 343–376.] and [Haçarız, O., Kleinow, T. & Macdonald, A. S. (2021). Genetics, insurance and hypertrophic cardiomyopathy. Scandinavian Actuarial Journal 2021, 54–81.], namely, that in realistic scenarios premium increases would be negligible. We also consider the possibility of life settlement companies ‘gaming’ insurers by learning of adverse genetic test results, and conclude that to profit from purchasing policies from affected individuals, they would have to predict the future trajectory of the epidemiology of ARVC better than the epidemiologists themselves. Journal: Scandinavian Actuarial Journal Pages: 94-114 Issue: 2 Volume: 2022 Year: 2022 Month: 02 X-DOI: 10.1080/03461238.2021.1930136 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1930136 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:2:p:94-114 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1938198_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: An Chen Author-X-Name-First: An Author-X-Name-Last: Chen Author-Name: Hong Li Author-X-Name-First: Hong Author-X-Name-Last: Li Author-Name: Mark B. Schultze Author-X-Name-First: Mark B. Author-X-Name-Last: Schultze Title: Tail index-linked annuity: A longevity risk sharing retirement plan Abstract: This paper proposes an innovative retirement product focusing on longevity risk sharing, a contract we refer to as tail index-linked annuity (TILA). Specifically, the proposed TILA pays out variable annual payments, which will be equal to a regular nominal amount when a reference survival index is lower than a predetermined threshold (i.e. normal evolution of longevity risk), and a reduced, index-dependent payment when the threshold is passed (i.e. highly unfavorable evolution of longevity risk). The proposed TILA aims at not only improving the benefits of the policyholders, which has been the focus in recent literature on innovative retirement products, but also reducing the longevity risk exposure of the insurer, particularly for advanced retirement ages. Using real-world mortality data and a stochastic multi-population mortality model, we find that the proposed TILA leads to higher expected lifetime utility than regular annuities for policyholders with different degrees of risk aversions. Meanwhile, numerical analysis shows that the proposed TILA could greatly mitigate the solvency risk of the insurer, leading to a substantially lower loss probability and expected (tail-) loss than regular annuities in the presence of a longevity shock, and therefore could reduce the insurer's required solvency capital under the latest solvency regulations. Journal: Scandinavian Actuarial Journal Pages: 139-164 Issue: 2 Volume: 2022 Year: 2022 Month: 02 X-DOI: 10.1080/03461238.2021.1938198 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1938198 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:2:p:139-164 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1937305_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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: On the analysis of a discrete-time risk model with INAR(1) processes Abstract: This paper considers an extension of the classical discrete-time risk model for which an INAR(1) process is utilized to model a temporal dependence between the number of claims. We apply a recursive method for deriving the Laplace transform of the aggregate claims with or without discounting in this framework. This methodology is implemented for the class of INAR(1) processes with an arbitrary innovations' distribution. Three risk models via specific INAR(1) processes are studied when the distribution of the individual claim sizes belongs to the class of mixed Erlang distributions. These different models allow us to discuss the frequent manifestations of equidispersion, overdispersion and zero inflation, and to evaluate the distribution of the (discounted) aggregate claims. Numerical examples are performed in order to illustrate the results obtained in this paper. Journal: Scandinavian Actuarial Journal Pages: 115-138 Issue: 2 Volume: 2022 Year: 2022 Month: 02 X-DOI: 10.1080/03461238.2021.1937305 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1937305 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:2:p:115-138 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1938199_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhuo Jin Author-X-Name-First: Zhuo Author-X-Name-Last: Jin Author-Name: Zuo Quan Xu Author-X-Name-First: Zuo Author-X-Name-Last: Quan Xu Author-Name: Bin Zou Author-X-Name-First: Bin Author-X-Name-Last: Zou Title: A perturbation approach to optimal investment, liability ratio, and dividend strategies Abstract: We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expected utility of dividend payments over an infinite horizon. By applying a perturbation approach, we obtain the optimal strategy and the value function in closed form for log and power utility. We conduct an economic analysis to investigate the impact of various model parameters and risk aversion on the insurer's optimal strategy. Journal: Scandinavian Actuarial Journal Pages: 165-188 Issue: 2 Volume: 2022 Year: 2022 Month: 02 X-DOI: 10.1080/03461238.2021.1938199 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1938199 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:2:p:165-188 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1944905_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jun Cai Author-X-Name-First: Jun Author-X-Name-Last: Cai Author-Name: Huameng Jia Author-X-Name-First: Huameng Author-X-Name-Last: Jia Author-Name: Tiantian Mao Author-X-Name-First: Tiantian Author-X-Name-Last: Mao Title: A multivariate CVaR risk measure from the perspective of portfolio risk management Abstract: In this paper, we define a new multivariate conditional Value-at-Risk (MCVaR) risk measure. This MCVaR considers both individual risks and the aggregate risk of a portfolio, but prioritizes the aggregate risk. The new MCVaR risk measure is based on the minimization of the expectation of a multivariate loss function, which balances the shortfall and surplus risks of the aggregate risk and the individual risks in an overall risk of a portfolio. It is shown that the MCVaR risk measure holds the properties of positive homogeneity, translation invariance, subadditivity, and monotonicity under certain conditions. Numerical examples of the MCVaR risk measure are presented to illustrate the effect of dependence among individual risks on the MCVaR. Journal: Scandinavian Actuarial Journal Pages: 189-215 Issue: 3 Volume: 2022 Year: 2022 Month: 03 X-DOI: 10.1080/03461238.2021.1944905 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1944905 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:3:p:189-215 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1951346_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jens Christian Wahl Author-X-Name-First: Jens Christian Author-X-Name-Last: Wahl Author-Name: Fredrik Lohne Aanes Author-X-Name-First: Fredrik Lohne Author-X-Name-Last: Aanes Author-Name: Kjersti Aas Author-X-Name-First: Kjersti Author-X-Name-Last: Aas Author-Name: Sindre Froyn Author-X-Name-First: Sindre Author-X-Name-Last: Froyn Author-Name: Daniel Piacek Author-X-Name-First: Daniel Author-X-Name-Last: Piacek Title: Spatial modelling of risk premiums for water damage insurance Abstract: In this paper, we compare different spatial models for modelling the risk premium for water damage insurance on the level of the policyholder. We evaluate four models that take the spatial variability into account: (1) the Intrinsic Conditional Auto-Regressive (ICAR) model; (2) the Besag, York, Mollier (BYM) model; (3) the independent random effects model; and (4) a spatial spline model. The models are compared on a huge data set from the Norwegian insurance company Gjensidige containing seven million observations of policyholders during the period 2011–2018. While Bayesian methods are most frequently used for inference in Gaussian Markov Random Field models, we take a frequentist approach and estimate the model parameters using Laplace approximated restricted maximum likelihood. Using the R package mgcv, we compare the different models for claim frequency, claim size and combined in a risk premium model in a comprehensive cross-validation study. Practical measures such as the loss ratio lift, double lift and Gini index are used to compare performance. Finally, we also compare mgcv with INLA and show that for reasonable big data sets we get identical estimates at a much lower computational cost. Journal: Scandinavian Actuarial Journal Pages: 216-233 Issue: 3 Volume: 2022 Year: 2022 Month: 03 X-DOI: 10.1080/03461238.2021.1951346 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1951346 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:3:p:216-233 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1958917_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zhengjun Jiang Author-X-Name-First: Zhengjun Author-X-Name-Last: Jiang Title: Banach contraction principle, q-scale function and ultimate ruin probability under a Markov-modulated classical risk model Abstract: Suppose that risk reserves of an insurance company are governed by a Markov-modulated classical risk model with parameters modulated by a finite-state irreducible Markov chain. The main purpose of this paper is to calculate ultimate ruin probability that ruin time, the first time when risk reserve is negative, is finite. We apply Banach contraction principle, q-scale functions and Markov property to prove that ultimate ruin probability is the fixed point of a contraction mapping in terms of q-scale functions and that ultimate ruin probability can be calculated by constructing an iterative algorithm to approximate the fixed point. Unlike Gajek and Rudź (Insurance: Mathematics and Economics, 80 (2018), 45–53), our paper uses q-scale functions to obtain more explicit Lipschitz constant in Banach contraction principle in our case so that proofs of several Lemmas and theorems in their Appendix are unnecessary and some of their assumptions are confirmed in our case. Journal: Scandinavian Actuarial Journal Pages: 234-243 Issue: 3 Volume: 2022 Year: 2022 Month: 03 X-DOI: 10.1080/03461238.2021.1958917 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1958917 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:3:p:234-243 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1966830_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Patrik Andersson Author-X-Name-First: Patrik Author-X-Name-Last: Andersson Author-Name: Mathias Lindholm Author-X-Name-First: Mathias Author-X-Name-Last: Lindholm Title: A note on pandemic mortality rates Abstract: This paper considers a population being affected by a mortality stress during a limited period of time, for example a pandemic. It has recently been suggested that the mortality stress during a pandemic can be viewed as a temporary shift in apparent age. We instead suggest to use a frailty based model where the baseline mortality rate is being stressed. This approach will in a natural way imply post-pandemic mortality rates at the population level. In particular, analytical results concerning the population mortality rate during and after a pandemic are derived. Under general assumptions it is shown that, compared to a non stressed scenario, the mortality is higher during the pandemic and lower after. These general results are exemplified for the Gompertz-Makeham law where more precise results can be obtained using its proportional frailty representation. The results are illustrated based on COVID-19 data for the Swedish population and we estimate the effect of the pandemic on the expected life time of an individual. Journal: Scandinavian Actuarial Journal Pages: 269-278 Issue: 3 Volume: 2022 Year: 2022 Month: 03 X-DOI: 10.1080/03461238.2021.1966830 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1966830 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:3:p:269-278 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1962962_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marcos Escobar-Anel Author-X-Name-First: Marcos Author-X-Name-Last: Escobar-Anel Author-Name: Markus Wahl Author-X-Name-First: Markus Author-X-Name-Last: Wahl Author-Name: Rudi Zagst Author-X-Name-First: Rudi Author-X-Name-Last: Zagst Title: Portfolio optimization with wealth-dependent risk constraints Abstract: Regulatory risk constraints as in the European Solvency II standard formula for insurance companies may lead to wealth-dependent constraints on the investment strategy. We develop two solution approaches for portfolio optimization problems in continuous time with wealth-dependent constraint sets. In the first approach, we reduce the optimization problem to an associate problem with constraints independent of wealth and a different utility function. The associate problem is then solved using known convex duality results. In the second approach, we use a change of control. We apply these results to Solvency II constraint sets and find that even for an investor with HARA utility who inherently reduces risk in times of distress, the constraints help to prevent the investor from taking too much risk in an optimistic market. Furthermore, we measure significant loss in utility and reduction in risk caused by the constraints, and we also evaluate the trade-off between these two effects. Journal: Scandinavian Actuarial Journal Pages: 244-268 Issue: 3 Volume: 2022 Year: 2022 Month: 03 X-DOI: 10.1080/03461238.2021.1962962 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1962962 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:3:p:244-268 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1971756_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yu Yuan Author-X-Name-First: Yu Author-X-Name-Last: Yuan Author-Name: Zhibin Liang Author-X-Name-First: Zhibin Author-X-Name-Last: Liang Author-Name: Xia Han Author-X-Name-First: Xia Author-X-Name-Last: Han Title: Robust reinsurance contract with asymmetric information in a stochastic Stackelberg differential game Abstract: In this paper, we determine a robust reinsurance contract from joint interests of the insurer and reinsurer under the framework of Stackelberg differential game. More specifically, the reinsurer is the leader of the game and decides on an optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses an optimal proportional reinsurance to purchase. In order to defend the large shocks of wealth process, a loss-dependent premium principle is applied to the insurer. Meanwhile, we incorporate model uncertainty into the reinsurer's controlled surplus due to the asymmetric information. Under the time-consistent mean-variance criterion, we derive the robust reinsurance contract explicitly by solving the coupled extended Hamilton–Jacobi–Bellman systems. It is interesting to prove that the optimal premium control for the reinsurer is determined by a time-adjusted variance principle. In addition, we find that the reinsurer would like to raise the reinsurance price to guard against the model uncertainty, which consequently decreases the insurer's reinsurance demand. Finally, further analyses are provided to show the necessity of considering the model uncertainty; otherwise, the reinsurance company will suffer a great loss of utility. Journal: Scandinavian Actuarial Journal Pages: 328-355 Issue: 4 Volume: 2022 Year: 2022 Month: 04 X-DOI: 10.1080/03461238.2021.1971756 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1971756 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:4:p:328-355 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1966831_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Christoph Hambel Author-X-Name-First: Christoph Author-X-Name-Last: Hambel Author-Name: Holger Kraft Author-X-Name-First: Holger Author-X-Name-Last: Kraft Author-Name: Claus Munk Author-X-Name-First: Claus Author-X-Name-Last: Munk Title: Solving life-cycle problems with biometric risk by artificial insurance markets Abstract: We study canonical consumption-savings problems of an individual involving uninsurable biometric risk. These problems are important in many applications from insurance economics and actuarial science. Since biometric risk is uninsurable, closed-form solutions do not exist and thus the problems must be approached by numerical methods. We propose a powerful approach where the solution is obtained by optimizing over a parametrized family of consumption strategies. In settings with mortality risk, critical illness risk, and habit formation, our solution method outperforms the well-established finite-difference approach both in run time and in precision. Our method also delivers a precision measure and closed-form representations of the optimal controls. Journal: Scandinavian Actuarial Journal Pages: 307-327 Issue: 4 Volume: 2022 Year: 2022 Month: 04 X-DOI: 10.1080/03461238.2021.1966831 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1966831 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:4:p:307-327 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1980430_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 Author-Name: David Pitt Author-X-Name-First: David Author-X-Name-Last: Pitt Author-Name: Han Li Author-X-Name-First: Han Author-X-Name-Last: Li Title: Dispersion modelling of mortality for both sexes with Tweedie distributions Abstract: Past mortality experience has shown that the variability in mortality levels is not constant and can be higher than what the usual Poisson assumption implies. This paper proposes two ways to tackle the heterogeneity often present in mortality data. First, an additional dispersion submodel is developed and combined with the mean model to perform a joint modelling of the mean and the dispersion. Moreover, a flexible group of distributions called the Tweedie family is adopted to model the number of deaths. Using Australian and other mortality data, the results of this study show that this Tweedie double modelling framework can generally improve the fitting performance and also leads to a more adequate allowance for longevity risk when valuing pension annuities. Journal: Scandinavian Actuarial Journal Pages: 356-374 Issue: 4 Volume: 2022 Year: 2022 Month: 04 X-DOI: 10.1080/03461238.2021.1980430 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1980430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:4:p:356-374 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1964590_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alexander Glauner Author-X-Name-First: Alexander Author-X-Name-Last: Glauner Title: Dynamic reinsurance in discrete time minimizing the insurer's cost of capital Abstract: In the classical static optimal reinsurance problem, the cost of capital for the insurer's risk exposure determined by a monetary risk measure is minimized over the class of reinsurance treaties represented by increasing Lipschitz retained loss functions. In this paper, we consider a dynamic extension of this reinsurance problem in discrete time which can be viewed as a risk-sensitive Markov Decision Process. The model allows for both insurance claims and premium income to be stochastic and operates with general risk measures and premium principles. We derive the Bellman equation and show the existence of a Markovian optimal reinsurance policy. Under an infinite planning horizon, the model is shown to be contractive and the optimal reinsurance policy to be stationary. The results are illustrated with examples where the optimal policy can be determined explicitly. Journal: Scandinavian Actuarial Journal Pages: 279-306 Issue: 4 Volume: 2022 Year: 2022 Month: 04 X-DOI: 10.1080/03461238.2021.1964590 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1964590 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:4:p:279-306 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1989025_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jamaal Ahmad Author-X-Name-First: Jamaal Author-X-Name-Last: Ahmad Title: Multivariate higher order moments in multi-state life insurance Abstract: It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such joint effects are less trivial. In this paper, we consider a multivariate payment process in multi-state life insurance, where the components are defined in terms of the same Markovian state process. The multivariate present value of future payments is introduced, and we derive differential equations and product integral representations of its conditional moments and moment generating function. Special attention is given to pair-wise covariances between two present values, where results closely connected to Hattendorff type of results for the variance are derived. The results are illustrated in a numerical example in a disability model. Journal: Scandinavian Actuarial Journal Pages: 399-420 Issue: 5 Volume: 2022 Year: 2022 Month: 05 X-DOI: 10.1080/03461238.2021.1989025 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1989025 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:5:p:399-420 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1992001_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Vanessa Hanna Author-X-Name-First: Vanessa Author-X-Name-Last: Hanna Author-Name: Peter Hieber Author-X-Name-First: Peter Author-X-Name-Last: Hieber Author-Name: Pierre Devolder Author-X-Name-First: Pierre Author-X-Name-Last: Devolder Title: Mixed participating and unit-linked life insurance contracts: design, pricing and optimal strategy Abstract: In many countries, the decline in interest rates has reduced the interest in traditional participating life insurance contracts with investment guarantees and has led to a shift to unit-linked policies without guarantees. We design a novel mixed insurance contract splitting premium payments between a participating and a unit-linked fund. An additional guarantee fee is applied on the unit-linked return in order to increase the investment guarantee of the participating fund. In a utility-based framework, using power utility and prospect theory as preference functions, we show that the mixed product is usually perceived more attractive than a full investment in either the unit-linked or the participating contract. The guarantee fee is beneficial for conservative investors interested in stronger protection against losses. This is also interesting from a marketing perspective: By the increase of the guarantee in the participating product, zero or negative guaranteed rates can be avoided. Journal: Scandinavian Actuarial Journal Pages: 421-446 Issue: 5 Volume: 2022 Year: 2022 Month: 05 X-DOI: 10.1080/03461238.2021.1992001 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1992001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:5:p:421-446 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1979639_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 Title: Hierarchical Bayesian modeling of multi-country mortality rates Abstract: As world populations age along with speedy internationalization, forecasting mortality for multiple countries or populations with similar socio-economic conditions or close cultural connections has become essential. We apply the hierarchical Bayesian theory to the random walk with drift model governing the dynamics of the logarithm of central death rates for each age and population. Using the mortality data for both genders of three developed countries for an age span 25–84 and a series of fitting age-year windows, and further extending the data set to include both genders of twenty countries, we conclude that the proposed hierarchical Bayesian framework can more accurately capture the mortality trends and overall outperforms the Lee–Carter model and its three extensions in mortality forecasting. Grouping both genders of the twenty countries in three ways, we find that the expected improvement rates per year in the logarithm of central death rate for all twenty countries converge to about 2% except for the US. Journal: Scandinavian Actuarial Journal Pages: 375-398 Issue: 5 Volume: 2022 Year: 2022 Month: 05 X-DOI: 10.1080/03461238.2021.1979639 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1979639 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:5:p:375-398 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1995781_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: J. Akahori Author-X-Name-First: J. Author-X-Name-Last: Akahori Author-Name: C. Constantinescu Author-X-Name-First: C. Author-X-Name-Last: Constantinescu Author-Name: Y. Imamura Author-X-Name-First: Y. Author-X-Name-Last: Imamura Author-Name: H. H. Pham Author-X-Name-First: H. H. Author-X-Name-Last: Pham Title: An application of risk theory to mortgage lending Abstract: Inspired by the double-debt problem in Japan where the mortgagor has to pay the remaining loan even if their house was destroyed by a catastrophic event, we model the lender's cash flow, by an exponential functional of a renewal-reward process. We propose an insurance add-on to the loan repayments and analyse the asymptotic behavior of the distribution of the first hitting time, which represents the probability of full repayment. We show that the finite-time probability of full loan repayment converges exponentially fast to the infinite-time one. In a few concrete scenarios, we calculate the exact form of the infinite-time probability and the corresponding premiums. Journal: Scandinavian Actuarial Journal Pages: 447-469 Issue: 5 Volume: 2022 Year: 2022 Month: 05 X-DOI: 10.1080/03461238.2021.1995781 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1995781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:5:p:447-469 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1998922_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Tim J. Boonen Author-X-Name-First: Tim J. Author-X-Name-Last: Boonen Author-Name: Yiying Zhang Author-X-Name-First: Yiying Author-X-Name-Last: Zhang Title: Bowley reinsurance with asymmetric information: a first-best solution Abstract: Bowley reinsurance solutions are reinsurance contracts for which the reinsurer optimally sets the pricing density while anticipating that the insurer will choose the optimal reinsurance indemnity given this pricing density. This Bowley solution concept of equilibrium reinsurance strategy has been revisited in the modern risk management framework by Boonen et al. [(2021). Bowley reinsurance with asymmetric information on the insurer's risk preferences. Scandinavian Actuarial Journal 2021, 623–644], where the insurer and reinsurer are both endowed with distortion risk measures but there is asymmetric information on the distortion risk measure of the insurer. In this article, we continue to study this framework, but we allow the premium principle to be more flexible. We call this solution the first-best Bowley solution. We provide first-best Bowley solutions in closed form under very general assumptions. We implement some numerical examples to illustrate the findings and the comparisons with the second-best solution. The main result is further extended to the case when both the reinsurer and the insurers have heterogeneous beliefs on the distribution functions of the underlying risk. Journal: Scandinavian Actuarial Journal Pages: 532-551 Issue: 6 Volume: 2022 Year: 2022 Month: 07 X-DOI: 10.1080/03461238.2021.1998922 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1998922 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:6:p:532-551 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1997795_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yuxin Zhou Author-X-Name-First: Yuxin Author-X-Name-Last: Zhou Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: Jonathan Ziveyi Author-X-Name-First: Jonathan Author-X-Name-Last: Ziveyi Author-Name: Mengyi Xu Author-X-Name-First: Mengyi Author-X-Name-Last: Xu Title: An innovative design of flexible, bequest-enhanced life annuity with natural hedging Abstract: There is a significant potential demand around the world for a flexible product to manage individual longevity risk. However, annuity markets remain thin, driven by factors including lack of pricing transparency, high product loadings, bequest motives, loss aversion, and the difficulty to hedge the risk. This paper proposes an individual retirement product to allow flexible management of longevity risk. The product combines a lifetime income with a flexible death benefit to meet individual bequest needs. It also benefits the issuers by lower mortality risk due to the natural hedging, and thus lower capital cost as a risk margin. We apply actuarial models that provide transparent pricing for interest rate and mortality risk, the construction of immunized bond portfolios, and the determination of a loading and solvency margin for systematic longevity risk. We also quantify the natural hedging benefits arising from the flexible inclusion of both survival benefits and death benefits. Journal: Scandinavian Actuarial Journal Pages: 488-509 Issue: 6 Volume: 2022 Year: 2022 Month: 07 X-DOI: 10.1080/03461238.2021.1997795 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1997795 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:6:p:488-509 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2002185_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stig Rosenlund Author-X-Name-First: Stig Author-X-Name-Last: Rosenlund Title: Hierarchical credibility pseudo-estimators Abstract: Jewell's credibility model with two hierarchical levels and three variance parameters is treated. Under some additional assumptions, new pseudo-estimators are deduced, i.e. estimators which are defined by expressions that contain the estimands themselves and which must be solved numerically, for the parameters for variation between groups within sector and for variation between sectors. A Tweedie model is assumed for conditional claim rates, with exponent either 1 or 2, where 1 is for conditionally Poisson claim frequencies and 2 is for mean claim severities. Simulation results, where some of the additional assumptions are violated, indicate that our new pseudo-estimators are preferable over previous pseudo-estimators and non-pseudo-estimators for many cases that can be identified. The new between-sectors estimator seems to be universally better than the previous estimators. The goodness-of-fit of an estimator is measured by the square root of its mean square error relative to the true parameter. Journal: Scandinavian Actuarial Journal Pages: 552-564 Issue: 6 Volume: 2022 Year: 2022 Month: 07 X-DOI: 10.1080/03461238.2021.2002185 File-URL: http://hdl.handle.net/10.1080/03461238.2021.2002185 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:6:p:552-564 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1984293_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fraser Daly Author-X-Name-First: Fraser Author-X-Name-Last: Daly Title: Gamma, Gaussian and Poisson approximations for random sums using size-biased and generalized zero-biased couplings Abstract: Let $ Y=X_1+\cdots +X_N $ Y=X1+⋯+XN be a sum of a random number of exchangeable random variables, where the random variable N is independent of the $ X_j $ Xj, and the $ X_j $ Xj are from the generalized multinomial model introduced by Tallis [(1962). The use of a generalized multinomial distribution in the estimation of correlation in discrete data. Journal of the Royal Statistical Society: Series B (Methodological) 24(2), 530–534]. This relaxes the classical assumption that the $ X_j $ Xj are independent. Motivated by applications in insurance, we use zero-biased coupling and its generalizations to give explicit error bounds in the approximation of Y by a Gaussian random variable in Wasserstein distance when either the random variables $ X_j $ Xj are centred or N has a Poisson distribution. We further establish an explicit bound for the approximation of Y by a gamma distribution in the stop-loss distance for the special case where N is Poisson. Finally, we briefly comment on analogous Poisson approximation results that make use of size-biased couplings. The special case of independent $ X_j $ Xj is given special attention throughout. As well as establishing results which extend beyond the independent setting, our bounds are shown to be competitive with known results in the independent case. Journal: Scandinavian Actuarial Journal Pages: 471-487 Issue: 6 Volume: 2022 Year: 2022 Month: 07 X-DOI: 10.1080/03461238.2021.1984293 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1984293 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:6:p:471-487 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1998921_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: Fractional inhomogeneous multi-state models in life insurance Abstract: In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix generalizations of their single-state counterparts, and the absorption times are matrix versions of well-known scalar distributions. A further advantage of this approach is that it allows extending the analysis to the non-Markovian case where sojourns are Mittag-Leffler distributed, and where the absorption times are fractional phase-type distributed. Considering deterministic time transforms gives rise to fractional inhomogeneous phase-type distributions as absorption times. The latter underlying processes are an example of a regime where not only the present but also the history of a policyholder influences its future evolution. The sub-exponential nature of stable distributions translates into the multi-state insurance model as a random longevity risk at any given state of the chain. Journal: Scandinavian Actuarial Journal Pages: 510-531 Issue: 6 Volume: 2022 Year: 2022 Month: 07 X-DOI: 10.1080/03461238.2021.1998921 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1998921 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:6:p:510-531 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1999316_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Salvatory R. Kessy Author-X-Name-First: Salvatory R. Author-X-Name-Last: Kessy Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Author-Name: Andrés M. Villegas Author-X-Name-First: Andrés M. Author-X-Name-Last: Villegas Author-Name: Jonathan Ziveyi Author-X-Name-First: Jonathan Author-X-Name-Last: Ziveyi Title: Mortality forecasting using stacked regression ensembles Abstract: Many alternative approaches for selecting mortality models and forecasting mortality have been proposed. The usual practice is to base forecasts on a single mortality model selected using in-sample goodness-of-fit measures. However, cross-validation measures are increasingly being used in model selection, and model combination methods are becoming a common alternative to using a single mortality model. We propose and assess a stacked regression ensemble that optimally combines different mortality models to reduce out-of-sample mean squared errors and mitigate model selection risk. Stacked regression uses a meta-learner to approximate horizon-specific weights by minimizing a cross-validation criterion for each forecasting horizon. The horizon-specific weights determine a mortality model combination customized to each horizon. We use 44 populations from the Human Mortality Database to compare the stacked regression ensemble with alternative methods. We show that, using one-year-ahead to 15-year-ahead out-of-sample mean squared errors, the stacked regression ensemble improves mortality forecast accuracy by 13% - 49% for males and 19% - 90% for females over individual mortality models. The stacked regression ensembles also have better predictive accuracy than other model combination methods, including Simple Model Averaging, Bayesian Model Averaging, and Model Confidence Set. We provide an R package, CoMoMo, that combines forecasts for Generalized-Age-Period-Cohort models. Journal: Scandinavian Actuarial Journal Pages: 591-626 Issue: 7 Volume: 2022 Year: 2022 Month: 08 X-DOI: 10.1080/03461238.2021.1999316 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1999316 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:7:p:591-626 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1998923_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zbigniew Palmowski Author-X-Name-First: Zbigniew Author-X-Name-Last: Palmowski Title: Ruin probabilities for risk process in a regime-switching environment Abstract: In this paper we give a few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider a few versions of the ruin time. Journal: Scandinavian Actuarial Journal Pages: 565-590 Issue: 7 Volume: 2022 Year: 2022 Month: 08 X-DOI: 10.1080/03461238.2021.1998923 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1998923 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:7:p:565-590 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2013308_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mark Kiermayer Author-X-Name-First: Mark Author-X-Name-Last: Kiermayer Title: Modeling surrender risk in life insurance: theoretical and experimental insight Abstract: Surrender poses one of the major risks to life insurance and a sound modeling of its true probability has direct implication on the risk capital demanded by the Solvency II directive. We add to the existing literature by performing extensive experiments that present highly practical results for various modeling approaches, including XGBoost, random forest, GLM and neural networks. Further, we detect shortcomings of prevalent model assessments, which are in essence based on a confusion matrix. Our results indicate that accurate label predictions and a sound modeling of the true probability can be opposing objectives. We illustrate this with the example of resampling. While resampling is capable of improving label prediction in rare event settings, such as surrender, and thus is commonly applied, we show theoretically and numerically that models trained on resampled data predict significantly biased event probabilities. Following a probabilistic perspective on surrender, we further propose time-dependent confidence bands on predicted mean surrender rates as a complementary assessment and demonstrate its benefit. This evaluation takes a very practical, going concern perspective, which respects that the composition of a portfolio, as well as the nature of underlying risk drivers might change over time. Journal: Scandinavian Actuarial Journal Pages: 627-658 Issue: 7 Volume: 2022 Year: 2022 Month: 08 X-DOI: 10.1080/03461238.2021.2013308 File-URL: http://hdl.handle.net/10.1080/03461238.2021.2013308 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:7:p:627-658 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2025892_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Johannes M. Schumacher Author-X-Name-First: Johannes M. Author-X-Name-Last: Schumacher Title: Utilitarian versus neutralitarian design of endowment fund policies Abstract: This paper addresses investment and spending policies of endowment funds aiming to generate a stable income stream in perpetuity. The standard academic approach to the design of such policies is based on optimization of utility aggregated over time. However, the explicit purpose of many funds to serve current and future generations ‘in equal measure’ suggests incorporation of a suitable notion of neutrality. The utilitarian and neutralitarian approaches are compared in two settings: one in which the preferences of individual generations are described by a standard CRRA utility function, and one in which these utility functions are modified by the introduction of a saturation level. Results are expressed in terms of the implied assumed interest rate (AIR), which reflects the apportionment of initially available capital to the time-0 values of individual future benefits. Under CRRA preferences, the neutralitarian point of view can be seen as a way of determining the discount factor that is used in the utilitarian method. When a saturation level is added, the neutralitarian and utilitarian policies are essentially different. The introduction of saturation generally induces a shift of value from earlier to later generations. Journal: Scandinavian Actuarial Journal Pages: 718-748 Issue: 8 Volume: 2022 Year: 2022 Month: 09 X-DOI: 10.1080/03461238.2022.2025892 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2025892 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:8:p:718-748 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2025145_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yuxuan Liu Author-X-Name-First: Yuxuan Author-X-Name-Last: Liu Author-Name: Zhengjun Jiang Author-X-Name-First: Zhengjun Author-X-Name-Last: Jiang Author-Name: Yixin Qu Author-X-Name-First: Yixin Author-X-Name-Last: Qu Title: Gambler's ruin problem in a Markov-modulated jump-diffusion risk model Abstract: When an insurance company's risk reserve is governed by a Markov-modulated jump-diffusion risk model, we study gambler's ruin problem in terms of two-sided ruin probability that the insurance company shall be ruined before its risk reserve reaches an upper barrier level $ b\in (0, \infty ) $ b∈(0,∞). We employ Banach contraction principle and q-scale functions to confirm the two-sided ruin probability to be the only fixed point of a contraction mapping and construct an iterative algorithm of approximating the two-sided ruin probability. We find that the two-sided ruin probability and Lipschitz constant in the contraction mapping depend on the upper barrier level b, premium rate per squared volatility, Markov intensity rate per squared volatility, Poisson intensity rate per squared volatility and the mean value of claim per unit of time. Finally, we present a numerical example with two regimes to show the efficiency of the iterative algorithm. Journal: Scandinavian Actuarial Journal Pages: 682-694 Issue: 8 Volume: 2022 Year: 2022 Month: 09 X-DOI: 10.1080/03461238.2021.2025145 File-URL: http://hdl.handle.net/10.1080/03461238.2021.2025145 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:8:p:682-694 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2020892_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jean Pinquet Author-X-Name-First: Jean Author-X-Name-Last: Pinquet Title: Hereditarity of potential matrices and positive affine prediction of nonnegative risks from mixture models Abstract: Nonnegative linear filtering of nonnegative risk variables necessitates positivity properties on the variance–covariance matrices of random effects, if experience rating is derived from mixture models. A variance–covariance matrix is a potential if it is nonsingular and if its inverse is diagonally dominant, with off-diagonal entries that are all nonpositive. We consider risk models with stationary random effects whose variance–covariance matrices are potentials. Positive credibility predictors of nonnegative risks are obtained from these mixture models. The set of variance–covariance matrices that are potentials is closed under extraction of principal submatrices. This strong hereditary property maintains the positivity of the affine predictor if the horizon is greater than one and if the history is lacunary. The specifications of the dynamic random effects presented in this paper fulfill the required positivity properties, and encompass the three possible levels for the length of memory in the mixing distribution. A case study discusses the possible strategies in the prediction of the pure premium from dynamic random effects. Journal: Scandinavian Actuarial Journal Pages: 659-681 Issue: 8 Volume: 2022 Year: 2022 Month: 09 X-DOI: 10.1080/03461238.2021.2020892 File-URL: http://hdl.handle.net/10.1080/03461238.2021.2020892 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:8:p:659-681 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2025891_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Stephen J. Richards Author-X-Name-First: Stephen J. Author-X-Name-Last: Richards Title: Modelling mortality by continuous benefit amount Abstract: Mortality levels vary by benefit amount, and a common simplification is to group by non-overlapping ranges of varying widths. However, this ignores the continuous nature of benefit amounts and leads to discretisation error, i.e. heterogeneity within benefit ranges and step jumps at range boundaries. Another drawback of discretisation is that fitted parameters are not easily extrapolated to values outside the range of the experience data. To address these shortcomings it is often better to model mortality continuously by benefit amount. In this paper we present a method of modelling mortality levels continuously by a financial covariate such as pension size. We split the task into (i) a transform function to address the presence of extreme benefit amounts in actuarial data sets, and (ii) a response function to model mortality. Using as few as two parameters, the method avoids discretisation error and extrapolates to amounts outside the range covered by the calibrating data set. We illustrate the method by applying it to seven international data sets of pensioners and annuitants. Journal: Scandinavian Actuarial Journal Pages: 695-717 Issue: 8 Volume: 2022 Year: 2022 Month: 09 X-DOI: 10.1080/03461238.2022.2025891 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2025891 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:8:p:695-717 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2034127_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric R. Ulm Author-X-Name-First: Eric R. Author-X-Name-Last: Ulm Title: Analytic valuation of GMDB options with utility based asset allocation Abstract: A number of analytic solutions have been found for Variable Annuity Guaranteed Minimum Death Benefit (GMDB) option values under a variety of mortality laws. To date, the solutions are for Risk-Neutral valuation only. Where policyholder decisions are allowed, it is assumed that they act to maximize the risk-neutral value of the GMDB. We examine situations where the asset allocation decisions are made to maximize expected utility rather than option value. We find analytic solutions for both return of premium and ratchet options at small values of bequest motive for a number of mortality laws. Journal: Scandinavian Actuarial Journal Pages: 816-840 Issue: 9 Volume: 2022 Year: 2022 Month: 10 X-DOI: 10.1080/03461238.2022.2034127 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2034127 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:9:p:816-840 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2030398_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Duni Hu Author-X-Name-First: Duni Author-X-Name-Last: Hu Author-Name: Hailong Wang Author-X-Name-First: Hailong Author-X-Name-Last: Wang Title: Robust reinsurance contract with learning and ambiguity aversion Abstract: We investigate the robust reinsurance demand and price under learning and ambiguity aversion. In the reinsurance contract, the insurer is ambiguity neutral and believes that he is perfectly informed, and the reinsurer is a Bayesian learner and is aware that even the filtered model is the best description of the data-generating process, might not forecast the future claims correctly. The ambiguity-averse reinsurer has a preference for reinsurance contract which is robust to model misspecification. Closed-form expressions for the robust reinsurance demand and price are derived. We find that both the reinsurer's one-sided learning and ambiguity aversion influence the structures and levels of the optimal reinsurance demand and price. Moreover, if the ambiguity-averse reinsurer specifies the suboptimal reinsurance contract as an ambiguity-neutral decision-maker, it will result in significant utility loss and the utility loss increases with ambiguity aversion level and Bayesian volatility. Journal: Scandinavian Actuarial Journal Pages: 794-815 Issue: 9 Volume: 2022 Year: 2022 Month: 10 X-DOI: 10.1080/03461238.2022.2030398 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2030398 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:9:p:794-815 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2028185_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Wenjun Jiang Author-X-Name-First: Wenjun Author-X-Name-Last: Jiang Title: Pareto-optimal insurance under heterogeneous beliefs and incentive compatibility Abstract: This paper studies the design of Pareto-optimal insurance under the heterogeneous beliefs of the insured and insurer. To accommodate a wide range of belief heterogeneity, we allow the likelihood ratio function to be non-monotone. To prevent the ex post moral hazard issue, the incentive compatibility condition is exogenously imposed to restrict the indemnity function. An implicit characterization of the optimal indemnity function is presented first by using the calculus of variations. Based on the point-wise maximizer to the problem, we partition the domain of loss into disjoint pieces and derive the parametric form of the optimal indemnity function over each piece through its implicit characterization. The main result of this paper generalizes those in the literature and provides insights for related problems. Journal: Scandinavian Actuarial Journal Pages: 775-793 Issue: 9 Volume: 2022 Year: 2022 Month: 10 X-DOI: 10.1080/03461238.2022.2028185 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2028185 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:9:p:775-793 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2026459_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ailing Gu Author-X-Name-First: Ailing Author-X-Name-Last: Gu Author-Name: Shumin Chen Author-X-Name-First: Shumin Author-X-Name-Last: Chen Author-Name: Zhongfei Li Author-X-Name-First: Zhongfei Author-X-Name-Last: Li Author-Name: Frederi G. Viens Author-X-Name-First: Frederi G. Author-X-Name-Last: Viens Title: Optimal reinsurance pricing with ambiguity aversion and relative performance concerns in the principal-agent model Abstract: This paper first studies the optimal reinsurance problems for two competitive insurers and then studies the optimal reinsurance premium pricing problem for their common reinsurer by using the dynamic programming technique. The two insurers are subject to common insurance systematic risk. Each purchases proportional or excess-of-loss reinsurance for risk control. They aim to maximize the expected utilities of their relative terminal wealth. With the insurers' optimal reinsurance strategies, the reinsurer decides the reinsurance premiums for each insurer, also aiming to maximize the expected utility of her terminal wealth. Thus, the optimal reinsurance pricing problem is formulated as a Stackelberg game between two competitive insurers and a reinsurer, where the reinsurer is the leader, and the insurers are followers. Besides, all three players take model ambiguity into account. We characterize the optimal strategies for the insurers and the reinsurer and provide some numerical examples to show the impact of competition and model ambiguity on the pricing of reinsurance contracts. Journal: Scandinavian Actuarial Journal Pages: 749-774 Issue: 9 Volume: 2022 Year: 2022 Month: 10 X-DOI: 10.1080/03461238.2022.2026459 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2026459 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2022:y:2022:i:9:p:749-774 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2075282_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: A. Y. Golubin Author-X-Name-First: A. Y. Author-X-Name-Last: Golubin Author-Name: V. N. Gridin Author-X-Name-First: V. N. Author-X-Name-Last: Gridin Title: Optimal insurance strategy in a risk process under a safety level imposed on the increments of the process Abstract: The problem of designing an optimal insurance strategy in a modification of the risk process with discrete time is investigated. This model introduces stage-by-stage probabilistic constraints (Value-at-Risk (VaR) constraints) on the insurer's capital increments during each stage. Also, the set of admissible insurances is determined by a safety level reflecting a ‘good’ or ‘bad’ capital increment at the previous stage. The mathematical expectation of the insurer's final capital is used as the objective functional. The total loss of the insurer at each stage is modeled by the Gaussian (normal) distribution with parameters depending on a seded loss function (or, in other words, an insurance policy) selected. In contrast to traditional dynamic optimization models for insurance strategies, the proposed approach allows to construct the value functions (and hence the optimal insurance policies) by simply solving a sequence of static insurance optimization problems. It is demonstrated that the optimal seded loss function at each stage depends on the prescribed value of the safety level: it is either a stop-loss insurance or conditional deductible insurance having a discontinuous point. In order to reduce ex post moral hazard, we also investigate the case, where both parties in an insurance contract are obligated to pay more for a larger realization of loss. This leads to that the optimal seeded loss functions are either stop-loss insurances or unconditional deductible insurances. Journal: Scandinavian Actuarial Journal Pages: 20-37 Issue: 1 Volume: 2023 Year: 2023 Month: 01 X-DOI: 10.1080/03461238.2022.2075282 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2075282 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:1:p:20-37 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2079996_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Marcus C. Christiansen Author-X-Name-First: Marcus C. Author-X-Name-Last: Christiansen Title: On the decomposition of an insurer's profits and losses Abstract: Current reporting standards for insurers require a decomposition of observed profits and losses in such a way that changes in the insurer's balance sheet can be attributed to specified risk factors. Generating such a decomposition is a non-trivial task because balance sheets generally depend on the risk factors in a non-linear way. This paper starts from an axiomatic perspective on profit and loss decompositions and finds that the axioms necessarily lead to infinitesimal sequential updating (ISU) decompositions, provided that the latter exist and are stable, whereas the current practice is rather to use sequential updating (SU) decompositions. The generality of the axiomatic approach makes the results useful also beyond insurance applications wherever profits and losses shall be additively decomposed in a risk-oriented manner. Journal: Scandinavian Actuarial Journal Pages: 51-70 Issue: 1 Volume: 2023 Year: 2023 Month: 01 X-DOI: 10.1080/03461238.2022.2079996 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2079996 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:1:p:51-70 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2061868_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Debbie Kusch Falden Author-X-Name-First: Debbie Kusch Author-X-Name-Last: Falden Author-Name: Anna Kamille Nyegaard Author-X-Name-First: Anna Kamille Author-X-Name-Last: Nyegaard Title: Reserve-dependent Management Actions in life insurance Abstract: In a set-up of with-profit life insurance including bonus, we study the calculation of the market reserve, where Management Actions such as investment strategies and bonus allocation strategies depend on the reserve itself. Since the amount of future bonus depends on the retrospective savings account, the introduction of Management Actions that depend on the prospective market reserve results in an entanglement of retrospective and prospective reserves. We study the complications that arise due to the interdependence between retrospective and prospective reserves, and characterize the market reserve by a partial differential equation (PDE). We reduce the dimension of the PDE in the case of linearity, and furthermore, we suggest an approximation of the market reserve based on the forward rate. The quality of the approximation is studied in a numerical example. Journal: Scandinavian Actuarial Journal Pages: 1-19 Issue: 1 Volume: 2023 Year: 2023 Month: 01 X-DOI: 10.1080/03461238.2022.2061868 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2061868 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:1:p:1-19 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2078221_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yuxuan Liu Author-X-Name-First: Yuxuan Author-X-Name-Last: Liu Author-Name: Zhengjun Jiang Author-X-Name-First: Zhengjun Author-X-Name-Last: Jiang Author-Name: Yiwen Zhang Author-X-Name-First: Yiwen Author-X-Name-Last: Zhang Title: q-scale function, Banach contraction principle, and ultimate ruin probability in a Markov-modulated jump–diffusion risk model Abstract: The paper investigates ultimate ruin probability, the probability that ruin time is finite, for an insurance company whose risk reserves follow a Markov-modulated jump–diffusion risk model. We use both the Banach contraction principle and q-scale functions to prove that ultimate ruin probability is the only fixed point of a contraction mapping and show that an iterative equation can be employed to calculate ultimate ruin probability by an iterative algorithm of approximating the fixed point. Using q-scale functions and the methodology from Gajek and Rudź [(2018). Banach contraction principle and ruin probabilities in regime-switching models. Insurance: Mathematics and Economics, 80, 45–53] applied to the Markov-modulated jump–diffusion risk model, we get a more explicit Lipschitz constant in the Banach contraction principle and conveniently verify some similar results of their appendix in our case. Journal: Scandinavian Actuarial Journal Pages: 38-50 Issue: 1 Volume: 2023 Year: 2023 Month: 01 X-DOI: 10.1080/03461238.2022.2078221 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2078221 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:1:p:38-50 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2081816_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ronald Richman Author-X-Name-First: Ronald Author-X-Name-Last: Richman Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Title: LocalGLMnet: interpretable deep learning for tabular data Abstract: Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep learning models is that their solutions are difficult to interpret and explain, and variable selection is not easily possible because deep learning models solve feature engineering and variable selection internally in a nontransparent way. Inspired by the appealing structure of generalized linear models, we propose a new network architecture that shares similar features as generalized linear models but provides superior predictive power benefiting from the art of representation learning. This new architecture allows for variable selection of tabular data and for interpretation of the calibrated deep learning model, in fact, our approach provides an additive decomposition that can be related to other model interpretability techniques. Journal: Scandinavian Actuarial Journal Pages: 71-95 Issue: 1 Volume: 2023 Year: 2023 Month: 01 X-DOI: 10.1080/03461238.2022.2081816 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2081816 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:1:p:71-95 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2090272_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Karim Barigou Author-X-Name-First: Karim Author-X-Name-Last: Barigou 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: Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation Abstract: This paper introduces new valuation schemes called actuarial-consistent valuations for insurance liabilities which depend on both financial and actuarial risks, which imposes that all actuarial risks are priced via standard actuarial principles. We propose to extend standard actuarial principles by a new actuarial-consistent procedure, which we call ‘two-step actuarial valuations’. In the case valuations are coherent, we show that actuarial-consistent valuations are equivalent to two-step actuarial valuations. We also discuss the connection with ‘two-step market-consistent valuations’ from Pelsser, A. & Stadje, M. [(2014). Time-consistent and market-consistent evaluations. Mathematical Finance 24(1), 25–65]. In particular, we discuss how the dependence structure between actuarial and financial risks impacts both actuarial-consistent and market-consistent valuations. Journal: Scandinavian Actuarial Journal Pages: 191-217 Issue: 2 Volume: 2023 Year: 2023 Month: 02 X-DOI: 10.1080/03461238.2022.2090272 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2090272 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:2:p:191-217 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2089050_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ling Wang Author-X-Name-First: Ling Author-X-Name-Last: Wang Author-Name: Mei Choi Chiu Author-X-Name-First: Mei Choi Author-X-Name-Last: Chiu Author-Name: Hoi Ying Wong Author-X-Name-First: Hoi Ying Author-X-Name-Last: Wong Title: Time-consistent mean-variance reinsurance-investment problem with long-range dependent mortality rate Abstract: This paper investigates the time-consistent mean-variance reinsurance-investment (RI) problem faced by life insurers. Inspired by recent findings that mortality rates exhibit long-range dependence (LRD), we examine the effect of LRD on RI strategies. We adopt the Volterra mortality model proposed in Wang et al. [(2021). Volterra mortality model: actuarial valuation and risk management with long-range dependence. Insurance: Mathematics and Economics 96, 1–14] to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with intensity represented by the stochastic mortality rate. Under the open-loop equilibrium mean-variance criterion, we derive explicit equilibrium RI controls and study the uniqueness of these controls in cases of constant and state-dependent risk aversion. We simultaneously resolve difficulties arising from unbounded non-Markovian parameters and sudden increases in the insurer's wealth process. While the exiting literature suggests that LRD has a significant effect on longevity hedging, we find that reinsurance is a risk management strategy that is robust to LRD. Journal: Scandinavian Actuarial Journal Pages: 123-152 Issue: 2 Volume: 2023 Year: 2023 Month: 02 X-DOI: 10.1080/03461238.2022.2089050 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2089050 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:2:p:123-152 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2089051_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Eric C. K. Cheung Author-X-Name-First: Eric C. K. Author-X-Name-Last: Cheung Author-Name: Hayden Lau Author-X-Name-First: Hayden Author-X-Name-Last: Lau Author-Name: Gordon E. Willmot Author-X-Name-First: Gordon E. Author-X-Name-Last: Willmot Author-Name: Jae-Kyung Woo Author-X-Name-First: Jae-Kyung Author-X-Name-Last: Woo Title: Finite-time ruin probabilities using bivariate Laguerre series Abstract: In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk model. Traditional general solutions to finite-time ruin problems are usually expressed in terms of infinite sums involving the convolutions related to the claim size distribution and their integrals, which can typically be evaluated only in special cases where the claims follow exponential or (more generally) mixed Erlang distribution. We propose to tackle the partial integro-differential equation satisfied by the finite-time ruin probability and develop a new approach to obtain a solution in terms of bivariate Laguerre series as a function of the initial surplus level and the time horizon for a large class of light-tailed claim distributions. To illustrate the versatility and accuracy of our proposed method which is easy to implement, numerical examples are provided for claim amount distributions such as generalized inverse Gaussian, Weibull and truncated normal where closed-form convolutions are not available in the literature. Journal: Scandinavian Actuarial Journal Pages: 153-190 Issue: 2 Volume: 2023 Year: 2023 Month: 02 X-DOI: 10.1080/03461238.2022.2089051 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2089051 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:2:p:153-190 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2086063_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Budhi Surya Author-X-Name-First: Budhi Author-X-Name-Last: Surya Author-Name: Wenyuan Wang Author-X-Name-First: Wenyuan Author-X-Name-Last: Wang Author-Name: Xianghua Zhao Author-X-Name-First: Xianghua Author-X-Name-Last: Zhao Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: Parisian excursion with capital injection for drawdown reflected Lévy insurance risk process Abstract: This paper discusses Parisian ruin problem under drawdown with capital injection when the underlying source of randomness of the surplus is modeled by a general Lévy insurance risk process. Capital injection is provided at the first instance the surplus drops below the drawdown level that is a pre-specified function of its current maximum. The capital is continuously injected to keep the surplus above the drawdown level until either it goes above its current maximum or a Parisian type ruin occurs, which is announced at the first time the surplus process has undergone an excursion below its current maximum for an independent exponential period of time consecutively since the most recent drawdown time. Some distributional identities concerning this excursion are presented. Firstly, we give the Parisian ruin probability and the joint Laplace transform (possibly killed at the first passage time above a fixed level for the surplus process) of the ruin time, the surplus position at ruin, and the total capital injection at ruin. Secondly, we obtain the q-potential measure of the surplus process killed at Parisian ruin. Finally, we give the expected present value of the total discounted capitals injected up to the Parisian ruin time. The results are derived using recent developments in fluctuation and excursion theory of spectrally negative Lévy process and are presented semi-explicitly in terms of the scale function of the Lévy process. Some numerical examples are given to facilitate the analysis of the impact of initial surplus and frequency of observation periods to the ruin probability and to the expected total discounted capital injection. Journal: Scandinavian Actuarial Journal Pages: 97-122 Issue: 2 Volume: 2023 Year: 2023 Month: 02 X-DOI: 10.1080/03461238.2022.2086063 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2086063 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:2:p:97-122 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2092419_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hamza Hanbali Author-X-Name-First: Hamza Author-X-Name-Last: Hanbali Author-Name: Daniël Linders Author-X-Name-First: Daniël Author-X-Name-Last: Linders Author-Name: Jan Dhaene Author-X-Name-First: Jan Author-X-Name-Last: Dhaene Title: Value-at-Risk, Tail Value-at-Risk and upper tail transform of the sum of two counter-monotonic random variables Abstract: The Value-at-Risk (VaR) of comonotonic sums can be decomposed into marginal VaRs at the same level. This additivity property allows to derive useful decompositions for other risk measures. In particular, the Tail Value-at-Risk (TVaR) and the upper tail transform of comonotonic sums can be written as the sum of their corresponding marginal risk measures. The other extreme dependence situation, involving the sum of two arbitrary counter-monotonic random variables, presents a certain number of challenges. One of them is that it is not straightforward to express the VaR of a counter-monotonic sum in terms of the VaRs of the marginal components of the sum. This paper generalizes the results derived in [Chaoubi, I., Cossette, H., Gadoury, S.-P. & Marceau, E. (2020). On sums of two counter-monotonic risks. Insurance: Mathematics and Economics 92, 47–60.] by providing decomposition formulas for the VaR, TVaR and the stop-loss transform of the sum of two arbitrary counter-monotonic random variables. Journal: Scandinavian Actuarial Journal Pages: 219-243 Issue: 3 Volume: 2023 Year: 2023 Month: 03 X-DOI: 10.1080/03461238.2022.2092419 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2092419 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:3:p:219-243 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2092892_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zuo Quan Xu Author-X-Name-First: Zuo Quan Author-X-Name-Last: Xu Title: Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory Abstract: This paper investigates a Pareto-optimal insurance problem, where the insured maximizes her rank-dependent utility preference and the insurer is risk-neutral and employs the mean-variance premium principle. To eliminate potential moral hazard issues, we only consider the so-called moral-hazard-free insurance contracts that obey the incentive compatibility constraint. The insurance problem is first formulated as a non-concave maximization problem involving Choquet expectation, then turned into a concave quantile optimization problem and finally solved by the calculus of variations method. The optimal contract is expressed by a semi-linear second-order double-obstacle ordinary differential equation with nonlocal operator. An effective numerical method is proposed to compute the optimal contract assuming the probability weighting function has a density. Also, we provide an example that is analytically solved. Journal: Scandinavian Actuarial Journal Pages: 269-289 Issue: 3 Volume: 2023 Year: 2023 Month: 03 X-DOI: 10.1080/03461238.2022.2092892 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2092892 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:3:p:269-289 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2094718_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Yuanying Guan Author-X-Name-First: Yuanying Author-X-Name-Last: Guan Author-Name: Andreas Tsanakas Author-X-Name-First: Andreas Author-X-Name-Last: Tsanakas Author-Name: Ruodu Wang Author-X-Name-First: Ruodu Author-X-Name-Last: Wang Title: An impossibility theorem on capital allocation Abstract: Two natural and potentially useful properties for capital allocation rules are top-down consistency and shrinking independence. Top-down consistency means that the total capital is determined by the aggregate portfolio risk. Shrinking independence means that the risk capital allocated to a given business line should not be affected by a proportional reduction of exposure in another business line. These two properties are satisfied by, respectively, the Euler allocation rule and the stress allocation rule. We prove an impossibility theorem that states that these two properties jointly lead to the trivial capital allocation based on the mean. When a subadditive risk measure is used, the same result holds for weaker versions of shrinking independence, which prevents the increase in risk capital in one line, when exposure to another is reduced. The impossibility theorem remains valid even if one assumes strong positive dependence among the risk vectors. Journal: Scandinavian Actuarial Journal Pages: 290-302 Issue: 3 Volume: 2023 Year: 2023 Month: 03 X-DOI: 10.1080/03461238.2022.2094718 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2094718 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:3:p:290-302 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2092891_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Sophie de Mol van Otterloo Author-X-Name-First: Sophie Author-X-Name-Last: de Mol van Otterloo Author-Name: Jennifer Alonso-García Author-X-Name-First: Jennifer Author-X-Name-Last: Alonso-García Title: A multi-state model for sick leave and its impact on partial early retirement incentives: the case of the Netherlands Abstract: We investigate the effect of part-time and full-time work on health using a Markov framework and generalized linear models to smooth the resulting crude rates. The Chapman-Kolmogorov equations are used for a general solution. We apply this model to assess a partial early retirement incentive in the Netherlands, known as ‘the generation pact’. The smoothed rates imply that working part time does not necessarily mean a better health for the elderly. In fact, men are healthier when working full time, while women fall sick more often when working full time but recover more often as well. However, when comparing the future rates of a person currently aged 50 working full time and using the generation pact, both the recovery and the morbidity rates drop when starting the generation pact. A stylized assessment of the costs associated yields that costs drop by half when using the generation pact. Journal: Scandinavian Actuarial Journal Pages: 244-268 Issue: 3 Volume: 2023 Year: 2023 Month: 03 X-DOI: 10.1080/03461238.2022.2092891 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2092891 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:3:p:244-268 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2097019_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 Author-Name: Jorge Yslas Author-X-Name-First: Jorge Author-X-Name-Last: Yslas Title: Phase-type mixture-of-experts regression for loss severities Abstract: The task of modeling claim severities is addressed when data is not consistent with the classical regression assumptions. This framework is common in several lines of business within insurance and reinsurance, where catastrophic losses or heterogeneous sub-populations result in data difficult to model. Their correct analysis is required for pricing insurance products, and some of the most prevalent recent specifications in this direction are mixture-of-experts models. This paper proposes a regression model that generalizes the latter approach to the phase-type distribution setting. More specifically, the concept of mixing is extended to the case where an entire Markov jump process is unobserved and where states can communicate with each other. The covariates then act on the initial probabilities of such underlying chain, which play the role of expert weights. The basic properties of such a model are computed in terms of matrix functionals, and denseness properties are derived, demonstrating their flexibility. An effective estimation procedure is proposed, based on the EM algorithm and multinomial logistic regression, and subsequently illustrated using simulated and real-world datasets. The increased flexibility of the proposed models does not come at a high computational cost, and the motivation and interpretation are equally transparent to simpler MoE models. Journal: Scandinavian Actuarial Journal Pages: 303-329 Issue: 4 Volume: 2023 Year: 2023 Month: 04 X-DOI: 10.1080/03461238.2022.2097019 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2097019 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:4:p:303-329 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2099296_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Meiqiao Ai Author-X-Name-First: Meiqiao Author-X-Name-Last: Ai Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Author-Name: Dan Zhu Author-X-Name-First: Dan Author-X-Name-Last: Zhu Title: Valuing variable annuities with path-dependent surrender guarantees under regime-switching Lévy models Abstract: Variable annuities with complex surrender features are nowadays increasingly popular for managing longevity risks. The study of their accurate pricing and sensitivity analysis is one of the main actuarial research topics. This paper studies the valuation problem of variable annuity contracts with guaranteed minimum maturity benefits on a set of predetermined discrete tenor dates under regime-switching Lévy models. Extending from existing vanilla payoffs, we consider the guaranteed minimum maturity benefits with lookback and geometric average features. We customise the dynamic programming principle to solve the corresponding optimal stopping problem, relying on some semi-analytical valuation formulae resulting from an acute Fourier cosine series expansion. Finally, numerical illustrations are provided to show the accuracy and efficiency of the proposed method. We also demonstrate the use of our proposed method in a range of sensitivity analysis exercises, which shed light on the pricing and risk management of complex variable annuity products. Journal: Scandinavian Actuarial Journal Pages: 330-358 Issue: 4 Volume: 2023 Year: 2023 Month: 04 X-DOI: 10.1080/03461238.2022.2099296 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2099296 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:4:p:330-358 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2108334_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Ghislain Léveillé Author-X-Name-First: Ghislain Author-X-Name-Last: Léveillé Author-Name: Ilie Radu Mitric Author-X-Name-First: Ilie Radu Author-X-Name-Last: Mitric Title: Conditional increments of aggregate discounted claims with a trend Abstract: We study the moments generating function, moments, distributions, VaR, and TVaR of conditional increments of aggregate discounted claims when the counting process is generated by a trend renewal process. The combined effect of the age process and trend is also examined. Journal: Scandinavian Actuarial Journal Pages: 388-410 Issue: 4 Volume: 2023 Year: 2023 Month: 04 X-DOI: 10.1080/03461238.2022.2108334 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2108334 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:4:p:388-410 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2104131_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Pintao Lyu Author-X-Name-First: Pintao Author-X-Name-Last: Lyu Author-Name: Johnny Siu-Hang Li Author-X-Name-First: Johnny Siu-Hang Author-X-Name-Last: Li Author-Name: Kenneth Q. Zhou Author-X-Name-First: Kenneth Q. Author-X-Name-Last: Zhou Title: Socioeconomic differentials in mortality: implications on index-based longevity hedges Abstract: In this paper, we address the mortality modeling needs for pension plan sponsors who wish to use index-based solutions to mitigate their longevity risk exposures. Specifically, we propose the three-way Li-Lee (TWLL) model, which enforces a certain extent of coherence between the population to which the index-based hedging instrument is linked and the population of pension plan members, and at the same time incorporates the empirical fact that mortality improvement rates of different socioeconomic subgroups in the pension plan are persistently different. We further develop a delta longevity hedging strategy that is compatible with the TWLL model. With the aid of real mortality data, we demonstrate that if persistent socioeconomic differentials in mortality improvement rates exist but are not considered in an index-based longevity hedge, the performance of the hedge could be compromised, and the extent of underperformance would depend on the distributions of pension plan members and pension amounts across different socioeconomic subgroups. This problem can be alleviated if the longevity hedge is calibrated on the basis of the TWLL model. Journal: Scandinavian Actuarial Journal Pages: 359-387 Issue: 4 Volume: 2023 Year: 2023 Month: 04 X-DOI: 10.1080/03461238.2022.2104131 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2104131 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:4:p:359-387 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2132181_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: The Editors Title: Correction Journal: Scandinavian Actuarial Journal Pages: 411-411 Issue: 4 Volume: 2023 Year: 2023 Month: 04 X-DOI: 10.1080/03461238.2022.2132181 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2132181 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:4:p:411-411 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2133625_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jae Youn Ahn Author-X-Name-First: Jae Author-X-Name-Last: Youn Ahn Author-Name: Himchan Jeong Author-X-Name-First: Himchan Author-X-Name-Last: Jeong Author-Name: Yang Lu Author-X-Name-First: Yang Author-X-Name-Last: Lu Title: A simple Bayesian state-space approach to the collective risk models Abstract: The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, natural disaster forecasting, as well as operational risk in banking regulation. This model, initially designed for cross-sectional data, has recently been adapted to a longitudinal context for both a priori and a posteriori ratemaking, through random effects specifications. However, the random effects are usually assumed to be static due to computational concerns, leading to predictive premiums that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effects processes. The model is based on Bayesian state-space models. It is associated with a simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. A real data application for auto insurance is proposed to show the performance of our method. Journal: Scandinavian Actuarial Journal Pages: 509-529 Issue: 5 Volume: 2023 Year: 2023 Month: 05 X-DOI: 10.1080/03461238.2022.2133625 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2133625 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:5:p:509-529 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2108335_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Wenyuan Wang Author-X-Name-First: Wenyuan Author-X-Name-Last: Wang Author-Name: Dmitry Muravey Author-X-Name-First: Dmitry Author-X-Name-Last: Muravey Author-Name: Yang Shen Author-X-Name-First: Yang Author-X-Name-Last: Shen Author-Name: Yan Zeng Author-X-Name-First: Yan Author-X-Name-Last: Zeng Title: Optimal investment and reinsurance strategies under 4/2 stochastic volatility model Abstract: This paper studies a mean-variance investment-reinsurance problem under a new stochastic volatility model, namely the 4/2 stochastic volatility model. Solving this problem requires a deep understanding of a class of parabolic partial differential equations (PPDEs). By the parametrix method and the integral transform method, we derive explicit solutions to the PPDEs in several special cases. Through the Lie symmetry analysis, we obtain a four-parameter family of the 4/2 stochastic volatility models such that the corresponding PPDEs have closed-form solutions. The efficient strategy and the efficient frontier of the mean-variance problem are represented by using the closed-form solutions to PPDEs. Numerical examples for the obtained efficient frontier are provided by Monto Carlo method. Journal: Scandinavian Actuarial Journal Pages: 413-449 Issue: 5 Volume: 2023 Year: 2023 Month: 05 X-DOI: 10.1080/03461238.2022.2108335 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2108335 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:5:p:413-449 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2111529_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alejandro Balbás Author-X-Name-First: Alejandro Author-X-Name-Last: Balbás Author-Name: Beatriz Balbás Author-X-Name-First: Beatriz Author-X-Name-Last: Balbás Author-Name: Raquel Balbás Author-X-Name-First: Raquel Author-X-Name-Last: Balbás Author-Name: Antonio Heras Author-X-Name-First: Antonio Author-X-Name-Last: Heras Title: Actuarial pricing with financial methods Abstract: The objective of this paper is twofold. On the one hand, the optimal combination of reinsurance and financial investment will be studied under a general framework. Indeed, there is no specific type of reinsurance contract, there is no specific dynamics of the involved financial instruments and the financial market does not have to be free of frictions. On the other hand, it will be pointed out how the optimal combination above may provide us with new premium principles making the insurer global risk vanish. The risk will be managed with a coherent risk measure, and the new premium principles will seem to reflect several properties, which are desirable from both the analytical and the economic perspectives. From the analytical viewpoint, the premium principles will be continuous, homogeneous and increasing. From the economic viewpoint, the premium principles will lead to cheaper prices with respect to both the insurance market and the financial one. In other words, the premium principles will make the insurer more competitive in prices under a null risk. General necessary and sufficient optimality conditions will be given, as well as closed forms for the solutions under appropriate assumptions. Several methods preventing unbounded optimization problems will warrant special attention, and one particular case will be more thoroughly studied, namely, the combination of the Black–Scholes–Merton pricing model with the conditional value at risk. Journal: Scandinavian Actuarial Journal Pages: 450-476 Issue: 5 Volume: 2023 Year: 2023 Month: 05 X-DOI: 10.1080/03461238.2022.2111529 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2111529 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:5:p:450-476 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2116725_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Benjamin Avanzi Author-X-Name-First: Benjamin Author-X-Name-Last: Avanzi Author-Name: Ping Chen Author-X-Name-First: Ping Author-X-Name-Last: Chen Author-Name: Lars Frederik Brandt Henriksen Author-X-Name-First: Lars Frederik Brandt Author-X-Name-Last: Henriksen Author-Name: Bernard Wong Author-X-Name-First: Bernard Author-X-Name-Last: Wong Title: On the surplus management of funds with assets and liabilities in presence of solvency requirements Abstract: In this paper, we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu [(2003). Geometric Brownian motion models for assets and liabilities: From pension funding to optimal dividends. North American Actuarial Journal 7(3), 37–56]. We determine what dividend strategy maximises the expected present value of dividends until ruin in two cases: (i) when shareholders won't cover surplus shortfalls and a solvency constraint [as in Paulsen (2003). Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics 7(4), 457–473] is consequently imposed and (ii) when shareholders are always to fund any capital deficiency with capital (asset) injections. In the latter case, ruin will never occur and the objective is to maximise the difference between dividends and capital injections. Developing and using appropriate verification lemmas, we show that the optimal dividend strategy is, in both cases, of barrier type. Both value functions are derived in closed form. Furthermore, the barrier is defined on the ratio of assets to liabilities, which mimics some of the dividend strategies that can be observed in practice by insurance companies. The existence and uniqueness of the optimal strategies are shown. Results are illustrated. Journal: Scandinavian Actuarial Journal Pages: 477-508 Issue: 5 Volume: 2023 Year: 2023 Month: 05 X-DOI: 10.1080/03461238.2022.2116725 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2116725 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:5:p:477-508 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2139630_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Corrado De Vecchi Author-X-Name-First: Corrado Author-X-Name-Last: De Vecchi Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Title: The impact of correlation on (Range) Value-at-Risk Abstract: The assessment of portfolio risk is often explicitly (e.g. the Basel III square root formula) or implicitly (e.g. credit risk models) driven by the marginal distributions of the risky components and their correlations. We assess the extent by which such practice is prone to model error. In the case of n = 2 risks, we investigate under which conditions the unconstrained Value-at-Risk (VaR) bounds (which are the maximum and minimum VaR for $ S=\sum _{i=1}^{n}X_i $ S=∑i=1nXi when only the marginal distributions of the $ X_i $ Xi are known) coincide with the (constrained) VaR bounds when in addition one has information on some measure of dependence (e.g. Pearson correlation or Spearman's rho). We find that both bounds coincide if the measure of dependence takes value in an interval that we explicitly determine. For probability levels used in risk management practice, we show that using correlation information has typically no effect on the highest possible VaR whereas it can affect the lowest possible VaR. In the case of a general sum of $ n \geqslant 2 $ n⩾2 risks, we derive Range Value-at-Risk (RVaR) bounds under an average correlation constraint and we show they are best-possible in the case of a sum of $ n\geqslant 3 $ n⩾3 standard uniformly distributed risks. Journal: Scandinavian Actuarial Journal Pages: 531-564 Issue: 6 Volume: 2023 Year: 2023 Month: 07 X-DOI: 10.1080/03461238.2022.2139630 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2139630 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:6:p:531-564 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2139631_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Xue Dong Author-X-Name-First: Xue Author-X-Name-Last: Dong Author-Name: Ximin Rong Author-X-Name-First: Ximin Author-X-Name-Last: Rong Author-Name: Hui Zhao Author-X-Name-First: Hui Author-X-Name-Last: Zhao Title: Non-zero-sum reinsurance and investment game with non-trivial curved strategy structure under Ornstein–Uhlenbeck process Abstract: This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, where we adopt the different classes of premium principles (including the expected value premium principle, the variance premium principle and the exponential premium principle) and each insurer aims to maximize the expected exponential utility of his terminal wealth relative to that of his competitor. Moreover, both insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks and can invest in a financial market consisting of a risk-free asset, a risky asset where the instantaneous rate of investment return follows an Ornstein-Uhlenbeck process which can reflect the changes of bull market and bear market. The optimal reinsurance strategy has a non-trivial structure which is distinguished from the conventional proportional and excess-of-loss reinsurance strategies. Furthermore, we derive the optimal reinsurance and investment strategies under the variance premium principle and expected value principle. In addition, we give another model which considers the correlation between risk model and financial market under the expected value principle. Finally, numerical analyses are provided to analyze the effects of model parameters on the optimal strategies under different cases. Journal: Scandinavian Actuarial Journal Pages: 565-597 Issue: 6 Volume: 2023 Year: 2023 Month: 07 X-DOI: 10.1080/03461238.2022.2139631 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2139631 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:6:p:565-597 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2141656_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: J. Lars Kirkby Author-X-Name-First: J. Lars Author-X-Name-Last: Kirkby Author-Name: Jean-Philippe Aguilar Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Aguilar Title: Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees Abstract: This work studies the valuation and optimal surrender of variable (equity-linked) annuities under a Lévy-driven equity market with mortality risk. We consider a practical periodic fee structure which can vary over time and is assessed as a proportion of the fund value. At maturity, the fund value is returned to the policyholder according to a guaranteed minimum accumulation benefit (GMAB). Mortality risk is also modeled discretely, and the contract offers a guaranteed minimum death benefit (GMBD) prior to maturity. The benefits accommodate caps on the growth of funds (in addition to the rising floor) to reduce the fee level and as a disincentive to early surrender. Interest rates are modeled via a deterministic discounting term structure, which can be calibrated (bootstrapped) to the rates market, according to market convention. An efficient and accurate valuation framework is developed, along with closed form pricing formulas in the case where policy surrender is not permitted. Numerous experiments are conducted to illustrate the interplay between contract parameters and the decision to surrender, and we provide an extensive analysis that investigates how to structure contracts to disincentivize early surrender. Journal: Scandinavian Actuarial Journal Pages: 624-654 Issue: 6 Volume: 2023 Year: 2023 Month: 07 X-DOI: 10.1080/03461238.2022.2141656 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2141656 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:6:p:624-654 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2139632_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jingyi Cao Author-X-Name-First: Jingyi Author-X-Name-Last: Cao Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Asymptotic analysis of a Stackelberg differential game for insurance under model ambiguity Abstract: We consider the problem of to which extent a diffusion process serves as a valid approximation of the classical Cramér-Lundberg (CL) risk process for a Stackelberg differential game between a buyer and a seller of insurance. We show that the equilibrium for the diffusion approximation equals the limit of the equilibrium for the scaled CL process, and it is nearly optimal for the pre-limit problem. Specifically, if the loss process follows a CL risk process and ambiguity is measured via entropic divergence, then the Stackelberg equilibrium of the diffusion approximation with squared-error divergence approximates the equilibrium for the former model to order $ \mathcal {O}\big (\frac {1}{\sqrt {n}}\big ) $ O(1n), in which we scale the CL model via n, as in Cohen and Young [(2020). Rate of convergence of the probability of ruin in the Cramér-Lundberg model to its diffusion approximation. Insurance: Mathematics and Economics 93: 333–340]. Journal: Scandinavian Actuarial Journal Pages: 598-623 Issue: 6 Volume: 2023 Year: 2023 Month: 07 X-DOI: 10.1080/03461238.2022.2139632 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2139632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:6:p:598-623 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2144432_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Wei Zhong Author-X-Name-First: Wei Author-X-Name-Last: Zhong Author-Name: Dan Zhu Author-X-Name-First: Dan Author-X-Name-Last: Zhu Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Title: Valuation of variable annuities under stochastic volatility and stochastic jump intensity Abstract: We present an efficient valuation approach for guaranteed minimum benefits embedded in variable annuity contracts, where the log price follows a jump-diffusion model with stochastic volatilities. In particular, we allow separate Cox-Ingersoll-Ross processes for the underlying volatility and the jump intensity, each correlated with the diffusion term of the spot price. To value the contract under such complex stochastic nature, we rely on the recent advances in the frame dual projection methods with the stochastic process approximated by its expectation. As a byproduct of the transparent analytical expression derived, we derive the associated Greeks that provide a practical basis for risk management. Numerical experiments demonstrate the accuracy and efficiency of the proposed method. Journal: Scandinavian Actuarial Journal Pages: 708-734 Issue: 7 Volume: 2023 Year: 2023 Month: 08 X-DOI: 10.1080/03461238.2022.2144432 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2144432 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:7:p:708-734 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2142157_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jingyi Cao Author-X-Name-First: Jingyi Author-X-Name-Last: Cao Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Title: Approximating the classical risk process by stable Lévy motion Abstract: The classical Cramér–Lundberg risk process is commonly used to model the surplus of an insurer; it characterizes the claim arrival process and the claim size random variable Y through a compound Poisson process, along with a constant rate of premium income. When $ \mathbb {E}(Y^2) \lt \infty $ E(Y2)<∞, the process can be approximated by a diffusion process, but that requirement eliminates many heavy-tailed claim models, such as the Pareto $ (\alpha, \theta ) $ (α,θ) with $ \alpha \le 2 $ α≤2. In this paper, we generalize the well known diffusion approximation by assuming that Y lies in the domain of attraction of an α-stable random variable, for $ 0 \lt \alpha \le 2 $ 0<α≤2. Then, we construct a sequence of classical Cramér–Lundberg risk processes and show that the sequence converges to an α-stable Lévy motion in the Skorokhod $ J_1 $ J1-topology. We prove this convergence by proving the pointwise convergence of the corresponding Laplace exponents of our processes, which to our knowledge, is a new result. To apply this convergence result, we show the convergence of a sequence of Gerber–Shiu distributions of exponential Parisian ruin, and we show the convergence of a sequence of payoff functions for barrier dividend strategies. Both of these applications provide new proofs of the stated limits. Journal: Scandinavian Actuarial Journal Pages: 679-707 Issue: 7 Volume: 2023 Year: 2023 Month: 08 X-DOI: 10.1080/03461238.2022.2142157 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2142157 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:7:p:679-707 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2142156_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Katia Colaneri Author-X-Name-First: Katia Author-X-Name-Last: Colaneri Author-Name: Julia Eisenberg Author-X-Name-First: Julia Author-X-Name-Last: Eisenberg Author-Name: Benedetta Salterini Author-X-Name-First: Benedetta Author-X-Name-Last: Salterini Title: Some optimisation problems in insurance with a terminal distribution constraint Abstract: In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. We set the initial capital to zero in order to verify whether the premia are sufficient to buy reinsurance and to manage the risk of incoming claims in such a way that the desired risk characteristics are achieved at some terminal time without external help (represented, for instance, by a positive initial capital). We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level α. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time. Journal: Scandinavian Actuarial Journal Pages: 655-678 Issue: 7 Volume: 2023 Year: 2023 Month: 08 X-DOI: 10.1080/03461238.2022.2142156 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2142156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:7:p:655-678 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2145233_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Jingyi Cao Author-X-Name-First: Jingyi Author-X-Name-Last: Cao Author-Name: Dongchen Li Author-X-Name-First: Dongchen Author-X-Name-Last: Li Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Author-Name: Bin Zou Author-X-Name-First: Bin Author-X-Name-Last: Zou Title: Stackelberg differential game for insurance under model ambiguity: general divergence Abstract: We solve a Stackelberg differential game between a buyer and a seller of insurance policies, in which both parties are ambiguous about the insurable loss. Both the buyer and seller maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a general divergence that measures the players' ambiguity, we obtain the Stackelberg equilibrium semi-explicitly. Our main results are that the optimal variance loading equals zero and that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability. Both of these important results generalize those we obtained in [Cao, J., Li, D., Young, V. R. & Zou, B. (2022). Stackelberg differential game for insurance under model ambiguity. Insurance: Mathematics and Economics, 106, 128–145.] under squared-error divergence. Journal: Scandinavian Actuarial Journal Pages: 735-763 Issue: 7 Volume: 2023 Year: 2023 Month: 08 X-DOI: 10.1080/03461238.2022.2145233 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2145233 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:7:p:735-763 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2161412_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 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 Author-Name: Guanxia Zhu Author-X-Name-First: Guanxia Author-X-Name-Last: Zhu Title: Insurance pricing in an equilibrium model Abstract: We develop a dynamic equilibrium model of insurance pricing in a competitive market consisting of heterogeneous insurance companies. The insurers have different beliefs on expected loss rate of an underlying risk process and the belief divergences are stochastic. The insurers select optimal insurance market shares to maximize their individual utilities. The equilibrium insurance price is formulated when the insurance market is cleared. We provide a general equilibrium framework with a continuum of insurers in the market and then solve for the equilibrium insurance price explicitly in the case of N insurers. We find that the stochastic heterogeneity brings extra volatility to insurance price and makes it dynamic. The mean-reverting divergences of insurers may explain cycles of insurance business documented by empirical studies. Compared to the previous literature of optimal insurance, this paper introduces an asset pricing framework of general equilibrium to the research of insurance pricing. Journal: Scandinavian Actuarial Journal Pages: 834-852 Issue: 8 Volume: 2023 Year: 2023 Month: 09 X-DOI: 10.1080/03461238.2022.2161412 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2161412 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:8:p:834-852 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2145577_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Pierre-O. Goffard Author-X-Name-First: Pierre-O. Author-X-Name-Last: Goffard Title: Sequential Monte Carlo samplers to fit and compare insurance loss models Abstract: Insurance loss distributions are characterized by a high frequency of small claim amounts and a lower, but not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the ‘body’ and the other for the ‘tail’ of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fit and compare the competing models. The method is validated via a simulation study and illustrated on an insurance loss dataset. Journal: Scandinavian Actuarial Journal Pages: 765-787 Issue: 8 Volume: 2023 Year: 2023 Month: 09 X-DOI: 10.1080/03461238.2022.2145577 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2145577 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:8:p:765-787 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2147862_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Brandon Garcia Flores Author-X-Name-First: Brandon Author-X-Name-Last: Garcia Flores Title: Optimal dividend bands revisited: a gradient-based method and evolutionary algorithms Abstract: We reconsider the study of optimal dividend strategies in the Cramér-Lundberg risk model. It is well-known that the solution of the classical dividend problem is in general a band strategy. However, the numerical techniques for the identification of the optimal bands available in the literature are very hard to implement and explicit numerical results are known for very few cases only. In this paper we put a gradient-based method into place which allows to determine optimal bands in more general situations. In addition, we adapt an evolutionary algorithm to this dividend problem, which is not as fast, but applicable in considerable generality, and can serve for providing a competitive benchmark. We illustrate the proposed methods in concrete examples, reproducing earlier results in the literature as well as establishing new ones for claim size distributions that could not be studied before. Journal: Scandinavian Actuarial Journal Pages: 788-810 Issue: 8 Volume: 2023 Year: 2023 Month: 09 X-DOI: 10.1080/03461238.2022.2147862 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2147862 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:8:p:788-810 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2161411_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Josef Anton Strini Author-X-Name-First: Josef Anton Author-X-Name-Last: Strini Author-Name: Stefan Thonhauser Author-X-Name-First: Stefan Author-X-Name-Last: Thonhauser Title: Time-inconsistent view on a dividend problem with penalty Abstract: We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the dividends and the penalty, which causes time-inconsistency. This allows to study different types of constraints. For the diffusion approximation of the classical surplus process we derive an explicit equilibrium dividend strategy and the associated value function. Inspired by duality arguments, we can identify a particular equilibrium strategy such that for a given initial surplus the imposed constraint is fulfilled. Furthermore, we illustrate our findings with a numerical example. Journal: Scandinavian Actuarial Journal Pages: 811-833 Issue: 8 Volume: 2023 Year: 2023 Month: 09 X-DOI: 10.1080/03461238.2022.2161411 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2161411 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:8:p:811-833 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2169632_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Alexander Schimmele Author-X-Name-First: Alexander Author-X-Name-Last: Schimmele Author-Name: Klaus D. Schmidt Author-X-Name-First: Klaus D. Author-X-Name-Last: Schmidt Title: A note on bivariate survival functions following a law of uniform seniority Abstract: In a recent paper published in this journal, Genest & Kolev (2021) studied bivariate survival functions following a law of uniform seniority in the sense that these bivariate survival functions can be represented by a univariate one. While in that paper it is assumed that the survival functions are continuous and strictly decreasing on their support, we show that these assumptions are redundant in certain places. We also present simplified proofs on some of its results. Journal: Scandinavian Actuarial Journal Pages: 907-915 Issue: 9 Volume: 2023 Year: 2023 Month: 10 X-DOI: 10.1080/03461238.2023.2169632 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2169632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:9:p:907-915 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2161413_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Bavo D. C. Campo Author-X-Name-First: Bavo D. C. Author-X-Name-Last: Campo Author-Name: Katrien Antonio Author-X-Name-First: Katrien Author-X-Name-Last: Antonio Title: Insurance pricing with hierarchically structured data an illustration with a workers' compensation insurance portfolio Abstract: Actuaries use predictive modeling techniques to assess the loss cost on a contract as a function of observable risk characteristics. State-of-the-art statistical and machine learning methods are not well equipped to handle hierarchically structured risk factors with a large number of levels. In this paper, we demonstrate the data-driven construction of an insurance pricing model when hierarchically structured risk factors, contract-specific as well as externally collected risk factors are available. We examine the pricing of a workers' compensation insurance product with a hierarchical credibility model [Jewell, W. S. (1975). The use of collateral data in credibility theory: A hierarchical model. Laxenburg: IIASA], Ohlsson's combination of a generalized linear and a hierarchical credibility model [Ohlsson, E. (2008). Combining generalized linear models and credibility models in practice. Scandinavian Actuarial Journal 2008(4), 301–314] and mixed models. We compare the predictive performance of these models and evaluate the effect of the distributional assumption on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models. For our case-study the Tweedie distribution is well suited to model and predict the loss cost on a contract. Moreover, incorporating contract-specific risk factors in the model improves the predictive performance and the risk differentiation in our workers' compensation insurance portfolio. Journal: Scandinavian Actuarial Journal Pages: 853-884 Issue: 9 Volume: 2023 Year: 2023 Month: 10 X-DOI: 10.1080/03461238.2022.2161413 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2161413 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:9:p:853-884 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2163512_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Zijia Wang Author-X-Name-First: Zijia Author-X-Name-Last: Wang Author-Name: Mohamed Amine Lkabous Author-X-Name-First: Mohamed Amine Author-X-Name-Last: Lkabous Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Title: A refracted Lévy process with delayed dividend pullbacks Abstract: The threshold dividend strategy, under which dividends are paid only when the insurer's surplus exceeds a pre-determined threshold, has received considerable attention in risk theory. However, in practice, it seems rather unlikely that an insurer will immediately pull back the dividend payments as soon as its surplus level drops below the dividend threshold. Hence, in this paper, we propose a refracted Lévy risk model with delayed dividend pullbacks triggered by a certain Poissonian observation scheme. Leveraging the extensive literature on fluctuation identities for spectrally negative Lévy processes, we obtain explicit expressions for two-sided exit identities of the proposed insurance risk process. Also, penalties are incorporated into the analysis of dividend payouts as a mechanism to penalize for the volatility of the dividend policy and account for an investor's typical preference for more stable cash flows. An explicit expression for the expected (discounted) dividend payouts net of penalties is derived. The criterion for the optimal threshold level that maximizes the expected dividend payouts is also discussed. Finally, several numerical examples are considered to assess the impact of dividend delays on ruin-related quantities. We numerically show that dividend strategies with more steady dividend payouts can be preferred (over the well-known threshold dividend strategy) when penalty fee become too onerous. Journal: Scandinavian Actuarial Journal Pages: 885-906 Issue: 9 Volume: 2023 Year: 2023 Month: 10 X-DOI: 10.1080/03461238.2022.2163512 File-URL: http://hdl.handle.net/10.1080/03461238.2022.2163512 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:9:p:885-906 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2175326_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Giovanni Cardillo Author-X-Name-First: Giovanni Author-X-Name-Last: Cardillo Author-Name: Paolo Giordani Author-X-Name-First: Paolo Author-X-Name-Last: Giordani 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 Author-Name: Alessandro Spelta Author-X-Name-First: Alessandro Author-X-Name-Last: Spelta Title: Mortality forecasting using the four-way CANDECOMP/PARAFAC decomposition Abstract: To design appropriate pension or insurance plans it is crucial to understand mortality heterogeneity across demographic features, such as age, gender, and country. To this aim, we propose a coherent mortality forecasting methodology, which leverages the four-way CANDECOMP/PARAFAC and Vector-Error Correction models. We examine how age groups, years, countries, and gender impact target variables, namely log-centered mortality rates and compositional transformation of mortality data using the Human Mortality Database. The CANDECOMP/PARAFAC model synthesizes the behavior of the target variables through a few latent components and highlights the evolution of the temporal patterns. These patterns are employed to forecast future trajectories of mortality with Vector-Error Correction models, which account for the non-stationarity of the series. We carry out Monte Carlo simulations to obtain the distributions of the time component over the forecasted period 2001–2015, and we evaluate the goodness of the prediction by computing the Root Mean Square Error and the Mean Absolute Error. Our analysis underlines that understanding mortality dynamics in a high-dimensional framework is crucial for demographic assessments and could help design appropriate pension plans that mitigate the burden of increased longevity. The paper provides two steps further on methodological developments in the field of mortality analysis and forecasting in a high-dimensional space by (i) offering a comprehensive picture of mortality data through the four-way decomposition and (ii) designing appropriate forecasting of mortality data which relies on the projection of the temporal component through Vector-Error Correction models. Journal: Scandinavian Actuarial Journal Pages: 916-932 Issue: 9 Volume: 2023 Year: 2023 Month: 10 X-DOI: 10.1080/03461238.2023.2175326 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2175326 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:9:p:916-932 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2191869_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Michel Dacorogna Author-X-Name-First: Michel Author-X-Name-Last: Dacorogna Author-Name: Marie Kratz Author-X-Name-First: Marie Author-X-Name-Last: Kratz Title: Managing cyber risk, a science in the making Abstract: Not a day goes by without news about a cyber attack. Fear spreads out and lots of wrong ideas circulate. This survey aims at showing how all these uncertainties about cyber can be transformed into manageable risk. After reviewing the main characteristics of cyber risk, we consider the three layers of cyber space: hardware, software and psycho-cognitive layer. We ask ourselves how is this risk different from others, how modelling has been tackled and needs to evolve, and what are the multi-facetted aspects of cyber risk management. This wide exploration pictures a science in the making and points out the questions to be solved for building a resilient society. Journal: Scandinavian Actuarial Journal Pages: 1000-1021 Issue: 10 Volume: 2023 Year: 2023 Month: 11 X-DOI: 10.1080/03461238.2023.2191869 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2191869 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:10:p:1000-1021 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_1978535_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Walther Neuhaus Author-X-Name-First: Walther Author-X-Name-Last: Neuhaus Title: Consistent development patterns Abstract: Traditional claim estimation in general insurance works with accident year cohorts and development patterns. For the impending International Financial Reporting Standard (IFRS) 17 Insurance Contracts and often for reinsurance purposes, claim estimates must be split by contract year. This paper proposes to add contract year as a cohort classifier and to adjust the development patterns accordingly. To this end, we use the continuous time models of Hesselager and Norberg. Having contract year as an additional cohort classifier, display of claim estimates by contract year and/or accident year becomes a simple matter of summation across the appropriate dimensions. The continuous time model also enables us to derive mutually consistent development patterns for discrete time intervals of different length, such as years and quarters. In addition to delivering consistent development patterns in discrete time, continuous time modelling offers the advantage of requiring only a fixed number of model parameters. Although most of the derivations in this paper are explained in terms of claim numbers, the mechanics can also be applied to claim payments. Journal: Scandinavian Actuarial Journal Pages: 933-945 Issue: 10 Volume: 2023 Year: 2023 Month: 11 X-DOI: 10.1080/03461238.2021.1978535 File-URL: http://hdl.handle.net/10.1080/03461238.2021.1978535 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:10:p:933-945 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2176251_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: M. Lindholm Author-X-Name-First: M. Author-X-Name-Last: Lindholm Author-Name: F. Lindskog Author-X-Name-First: F. Author-X-Name-Last: Lindskog Author-Name: J. Palmquist Author-X-Name-First: J. Author-X-Name-Last: Palmquist Title: Local bias adjustment, duration-weighted probabilities, and automatic construction of tariff cells Abstract: We study non-life insurance pricing and present a general procedure for constructing a distribution-free locally unbiased predictor of the risk premium based on any initially suggested predictor. The resulting predictor is piecewise constant, corresponding to a partition of the covariate space, and by construction auto-calibrated. Two key issues are the appropriate partitioning of the covariate space and the handling of randomly varying durations, acknowledging possible early termination of contracts. A basic idea in the present paper is to partition the predictions from the initial predictor, which as a by-product defines a partition of the covariate space. Two different approaches to create partitions are discussed in detail using (i) duration-weighted equal-probability binning, and (ii) binning by duration-weighted regression trees. Given a partitioning procedure, the size of the partition to be used is obtained using cross-validation. In this way we obtain an automatic data-driven tariffication procedure, where the number of tariff cells corresponds to the size of the partition. We illustrate the procedure based on both simulated and real insurance data, using both simple GLMs and GBMs as initial predictors. The resulting tariffs are shown to have a rather small number of tariff cells while maintaining or improving the predictive performance compared to the initial predictors. Journal: Scandinavian Actuarial Journal Pages: 946-973 Issue: 10 Volume: 2023 Year: 2023 Month: 11 X-DOI: 10.1080/03461238.2023.2176251 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2176251 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:10:p:946-973 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2181708_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Kristian Buchardt Author-X-Name-First: Kristian Author-X-Name-Last: Buchardt Author-Name: Christian Furrer Author-X-Name-First: Christian Author-X-Name-Last: Furrer Author-Name: Oliver Lunding Sandqvist Author-X-Name-First: Oliver Author-X-Name-Last: Lunding Sandqvist Title: Transaction time models in multi-state life insurance Abstract: In life insurance contracts, benefits and premiums are typically paid contingent on the biometric state of the insured. Due to delays between the occurrence, reporting, and settlement of changes to the biometric state, the state process is not fully observable in real-time. This fact implies that the classic multi-state models for the biometric state of the insured are not able to describe the development of the policy in real-time, which encompasses handling of incurred-but-not-reported and reported-but-not-settled claims. We give a fundamental treatment of the problem in the setting of continuous-time multi-state life insurance by introducing a new class of models: transaction time models. The relation between the transaction time model and the classic model is studied and a result linking the present values in the two models is derived. The results and their practical implications are illustrated for disability coverages, where we obtain explicit expressions for the transaction time reserve in specific models. Journal: Scandinavian Actuarial Journal Pages: 974-999 Issue: 10 Volume: 2023 Year: 2023 Month: 11 X-DOI: 10.1080/03461238.2023.2181708 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2181708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2023:y:2023:i:10:p:974-999 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2208583_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Guohui Guan Author-X-Name-First: Guohui Author-X-Name-Last: Guan Author-Name: Zongxia Liang Author-X-Name-First: Zongxia Author-X-Name-Last: Liang Author-Name: Yilun Song Author-X-Name-First: Yilun Author-X-Name-Last: Song Title: A Stackelberg reinsurance-investment game under α-maxmin mean-variance criterion and stochastic volatility Abstract: This paper investigates a Stackelberg game between an insurer and a reinsurer under the α-maxmin mean-variance criterion. The insurer can purchase per-loss reinsurance from the reinsurer. With the insurer's feedback reinsurance strategy, the reinsurer optimizes the reinsurance premium in the Stackelberg game. The financial market consists of cash and stock with Heston's stochastic volatility. Both the insurer and reinsurer maximize their respective α-maxmin mean-variance preferences in the market. The criterion is time-inconsistent and we derive the equilibrium strategies by the extended Hamilton-Jacobi-Bellman equations. Similar to the non-robust case in [Li, D. & Young, V. R. (2022). Stackelberg differential game for reinsurance: mean-variance framework and random horizon. Insurance: Mathematics and Economics 102, 42–55.], excess-of-loss reinsurance is the optimal form of reinsurance strategy for the insurer. The equilibrium investment strategy is determined by a system of Riccati differential equations. Besides, the equations determining the equilibrium reinsurance strategy and reinsurance premium rate are given semi-explicitly, which is simplified to an algebraic equation in a specific example. Numerical examples illustrate that the game between the insurer and reinsurer makes the insurance more radical when the agents become more ambiguity averse or risk averse. Furthermore, the level of ambiguity, ambiguity attitude, and risk attitude of the insurer (reinsurer) have similar effects on the equilibrium reinsurance strategy, reinsurance premium, and investment strategy. Journal: Scandinavian Actuarial Journal Pages: 28-63 Issue: 1 Volume: 2024 Year: 2024 Month: 01 X-DOI: 10.1080/03461238.2023.2208583 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2208583 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:1:p:28-63 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2208787_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: M. V. Boutsikas Author-X-Name-First: M. V. Author-X-Name-Last: Boutsikas Author-Name: D.-J. Economides Author-X-Name-First: D.-J. Author-X-Name-Last: Economides Author-Name: E. Vaggelatou Author-X-Name-First: E. Author-X-Name-Last: Vaggelatou Title: On the time and aggregate claim amount until the surplus drops below zero or reaches a safety level in a jump diffusion risk model Abstract: We consider a two-barrier renewal risk model assuming that insurer's income is modeled via a Brownian motion, and the surplus is inspected only at claim arrival times. We are interested in the joint distribution of the time, number of claims and the total claim amount until the surplus process falls below zero (ruin) or reaches a safety level. We obtain a general formula for the respective joint generating function which is expressed via the distributions of the undershoot (deficit at ruin) and the overshoot (surplus exceeding safety level). We offer explicit results in the classical Poisson model, and we also study a more general renewal model assuming mixed Erlang distributed claim amounts and inter-arrival times. Our methodology is based on tilted measures and Wald's likelihood ratio identity. We finally illustrate the applicability of our theoretical results by presenting appropriate numerical examples in which we derive the distributions of interest and compare them with the ones estimated using Monte Carlo simulation. Journal: Scandinavian Actuarial Journal Pages: 64-88 Issue: 1 Volume: 2024 Year: 2024 Month: 01 X-DOI: 10.1080/03461238.2023.2208787 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2208787 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:1:p:64-88 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2197442_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Martin Bladt Author-X-Name-First: Martin Author-X-Name-Last: Bladt Author-Name: Christian Furrer Author-X-Name-First: Christian Author-X-Name-Last: Furrer Title: Expert Kaplan–Meier estimation Abstract: The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the product-limit estimator in two different ways with distinct interpretations. Strong uniform consistency is proved for both cases under certain assumptions on the kind of contamination and the quality of expert information, which sheds light on the techniques and decisions that practitioners may take. The nuances of the techniques are discussed – also with a view towards semi-parametric estimation – and they are illustrated using simulated and real-world insurance data. Journal: Scandinavian Actuarial Journal Pages: 1-27 Issue: 1 Volume: 2024 Year: 2024 Month: 01 X-DOI: 10.1080/03461238.2023.2197442 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2197442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:1:p:1-27 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2209858_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Yichun Chi Author-X-Name-First: Yichun Author-X-Name-Last: Chi Author-Name: Yuxia Huang Author-X-Name-First: Yuxia Author-X-Name-Last: Huang Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Title: An insurer's optimal strategy towards a new independent business Abstract: In this paper, we investigate the optimal decision making of an insurer towards a new insurable business, whose risk is independent of the existing risk faced by the insurer. We assume that the insurer, with the objective of maximizing the expected utility of its final wealth, together with the solvency constraint and the availability of reinsurance as a risk transfer mechanism, is deciding if it is viable to underwrite a new insurance business risk. If this new business is underwritten, it is shown that a stop-loss reinsurance contract is optimal when the solvency risk is quantified by the conditional value at risk. If the regulatory regime changes to the value at risk, the optimal reinsurance form becomes more complicated; it can be either stop-loss or two-layer under the assumption that the new risk has a strictly decreasing probability density function. Numerical examples are provided to illuminate the insurer's decision making and the optimal form of the reinsurance strategy. Journal: Scandinavian Actuarial Journal Pages: 89-107 Issue: 1 Volume: 2024 Year: 2024 Month: 01 X-DOI: 10.1080/03461238.2023.2209858 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2209858 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:1:p:89-107 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2234914_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Tsz Chai Fung Author-X-Name-First: Tsz Chai Author-X-Name-Last: Fung Author-Name: Himchan Jeong Author-X-Name-First: Himchan Author-X-Name-Last: Jeong Author-Name: George Tzougas Author-X-Name-First: George Author-X-Name-Last: Tzougas Title: Soft splicing model: bridging the gap between composite model and finite mixture model Abstract: Considerations of both the heavy-tail phenomenon and multi-modality of a claim severity distribution have been challenging in the actuarial literature and practices. In this article, we develop a novel class of soft splicing models that bridges the gap between pre-existing methods for handling the issues above. The proposed method is flexible enough to incorporate tail-heaviness and multi-modality with computational efficiency and nests finite mixture models and splicing models as its special and/or limiting cases. The soft splicing model is also more robust in extrapolating the tail-heaviness of distribution subject to model contamination. According to simulation studies and real insurance claim data analyses, it is shown that the proposed soft splicing model provides superior goodness-of-fit and more accurate estimates of tail risk measures than both finite mixture and composite models. Journal: Scandinavian Actuarial Journal Pages: 168-197 Issue: 2 Volume: 2024 Year: 2024 Month: 02 X-DOI: 10.1080/03461238.2023.2234914 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2234914 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:2:p:168-197 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2220219_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Xia Han Author-X-Name-First: Xia Author-X-Name-Last: Han Author-Name: David Landriault Author-X-Name-First: David Author-X-Name-Last: Landriault Author-Name: Danping Li Author-X-Name-First: Danping Author-X-Name-Last: Li Title: Optimal reinsurance contract in a Stackelberg game framework: a view of social planner Abstract: In this paper, we consider an optimal reinsurance contract under a mean-variance criterion in a Stackelberg game theoretical framework. The reinsurer is the leader of the game and decides on an optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses an optimal per-loss reinsurance to purchase. The objective of the insurer is to maximize a given mean-variance criterion, while the reinsurer adopts the role of social planner balancing its own interests with those of the insurer. That is, we assume that the reinsurer determines the reinsurance premium by maximizing a weighted sum of the insurer's and reinsurer's mean-variance criteria. Under the general mean-variance premium principle, we derive the optimal reinsurance contract by solving the extended Hamilton–Jacobi–Bellman (HJB) systems. Moreover, we provide an intuitive way to set the weight of each party in the reinsurer's objective. Finally, we consider some special cases to illustrate our main results. Journal: Scandinavian Actuarial Journal Pages: 124-148 Issue: 2 Volume: 2024 Year: 2024 Month: 02 X-DOI: 10.1080/03461238.2023.2220219 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2220219 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:2:p:124-148 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2218859_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Jun Wang Author-X-Name-First: Jun Author-X-Name-Last: Wang Author-Name: Lihong Wen Author-X-Name-First: Lihong Author-X-Name-Last: Wen Author-Name: Lu Xiao Author-X-Name-First: Lu Author-X-Name-Last: Xiao Author-Name: Chaojie Wang Author-X-Name-First: Chaojie Author-X-Name-Last: Wang Title: Time-series forecasting of mortality rates using transformer Abstract: Predicting mortality rates is a crucial issue in life insurance pricing and demographic statistics. Traditional approaches, such as the Lee-Carter model and its variants, predict the trends of mortality rates using factor models, which explain the variations of mortality rates from the perspective of ages, gender, regions, and other factors. Recently, deep learning techniques have achieved great success in various tasks and shown strong potential for time-series forecasting. In this paper, we propose a modified Transformer architecture for predicting mortality rates in major countries around the world. Through the multi-head attention mechanism and positional encoding, the proposed Transformer model extracts key features effectively and thus achieves better performance in time-series forecasting. By using empirical data from the Human Mortality Database, we demonstrate that our Transformer model has higher prediction accuracy of mortality rates than the Lee-Carter model and other classic neural networks. Our model provides a powerful forecasting tool for insurance companies and policy makers. Journal: Scandinavian Actuarial Journal Pages: 109-123 Issue: 2 Volume: 2024 Year: 2024 Month: 02 X-DOI: 10.1080/03461238.2023.2218859 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2218859 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:2:p:109-123 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2232816_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Jackie Li Author-X-Name-First: Jackie Author-X-Name-Last: Li Title: Bayesian joint modelling of life expectancy and healthy life expectancy and valuation of retirement village contract Abstract: Life expectancy and healthy life expectancy are both important indicators of population wellbeing, reflecting the expected length of life and duraiton of healthy living respectively. While extensive research has focused on projecting life expectancy, very few have investigated the projection and simulation of healthy life expectancy and examined its potential applications. In this paper, we establish a Bayesian approach to jointly model life expectancy and healthy life expectancy. We apply this approach to the population data of various countries, demonstrating its ability to provide accurate forecasts, generate probability intervals to capture future uncertainty, and estimate missing data values. We then illustrate an application of the Bayesian model in valuing a retirement village contract. Many Australian seniors choose retirement villages for the community support they offer, transitioning to aged care facilities as their health declines. The value of the accommodation service depends on the resident’s length of stay, which can be approximated by healthy life expectancy. The proposed Bayesian model can produce a sampled distribution of the contract’s net present value, providing a useful risk management tool for retirement village operators. Our findings emphasise the importance of considering healthy life expectancy in policies on public health and retirement.  Journal: Scandinavian Actuarial Journal Pages: 149-167 Issue: 2 Volume: 2024 Year: 2024 Month: 02 X-DOI: 10.1080/03461238.2023.2232816 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2232816 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:2:p:149-167 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2241193_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Meiqiao Ai Author-X-Name-First: Meiqiao Author-X-Name-Last: Ai Author-Name: Yunyun Wang Author-X-Name-First: Yunyun Author-X-Name-Last: Wang Author-Name: Zhimin Zhang Author-X-Name-First: Zhimin Author-X-Name-Last: Zhang Author-Name: Dan Zhu Author-X-Name-First: Dan Author-X-Name-Last: Zhu Title: Valuation of variable annuities with guaranteed minimum maturity benefits and periodic fees Abstract: This paper focuses on the valuation of variable annuities with a guaranteed minimum maturity benefit under a regime-switching Lévy model. The model allows policyholders to surrender their annuities and receive a surrender benefit at predetermined tenor times before maturity. Additionally, we consider a state-dependent periodic fee structure where fees are deducted from the policyholder's account if it exceeds a certain level at discrete time points. Incorporating this fee structure, the Fourier cosine series expansion method based on characteristic functions is employed to determine the values and optimal surrender strategies for variable annuity contracts. Finally, we provide a comprehensive set of numerical examples to demonstrate and assess the effectiveness of our approach thoroughly. Journal: Scandinavian Actuarial Journal Pages: 252-278 Issue: 3 Volume: 2024 Year: 2024 Month: 03 X-DOI: 10.1080/03461238.2023.2241193 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2241193 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:3:p:252-278 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2239533_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Oma Coke Author-X-Name-First: Oma Author-X-Name-Last: Coke Author-Name: Mario Ghossoub Author-X-Name-First: Mario Author-X-Name-Last: Ghossoub Author-Name: Michael B. Zhu Author-X-Name-First: Michael B. Author-X-Name-Last: Zhu Title: Pareto-optimal insurance with an upper limit on the insurer's exposure Abstract: We examine the problem of determining Pareto-optimal (PO) insurance contracts when the insurer imposes an ex ante upper limit on disbursement. The problem is similar in spirit to that of Cummins & Mahul (2004), but it extends it in two directions: first, we use the more general and more flexible class of distortion premium principles; and second, we allow for heterogeneity in beliefs between the insurer and the insured. We unify the settings of Ghossoub (2019a, 2019b), and we adapt the approaches therein to encompass the case of a policy limit. First, we show that PO contracts are those that result from a budget-constrained optimization problem for the DM. We then provide a closed-form characterization of optimal contracts. Our result is similar in spirit to that of Cummins & Mahul (2004), who show that when policy limits are introduced to Arrow's model, PO contracts are limited deductible contracts. While Ghossoub (2019a, 2019b) shows that variable deductible contracts are optimal, the results of the present paper indicate that limited variable deductible contracts are optimal when policy limits are present. We illustrate our results via numerical examples. Journal: Scandinavian Actuarial Journal Pages: 227-251 Issue: 3 Volume: 2024 Year: 2024 Month: 03 X-DOI: 10.1080/03461238.2023.2239533 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2239533 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:3:p:227-251 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2234916_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Thomas Bernhardt Author-X-Name-First: Thomas Author-X-Name-Last: Bernhardt Author-Name: Ge Qu Author-X-Name-First: Ge Author-X-Name-Last: Qu Title: Wealth heterogeneity in a closed pooled annuity fund Abstract: The stability of income payments in a pooled annuity fund is studied. In those funds, members receive a fluctuating income depending on their experienced mortality in exchange for their pension savings. The focus is on describing the influence of different initial savings on the ability of the fund to provide a stable income in retirement. Because of this, members coincide in their characteristics except for their initial savings. We identify a term, which we dub ‘implied number of homogeneous members’, that directly links the initial savings to the size of the income fluctuations. Our main contribution is the analysis of this term and the development of a criterion to answer the question of whether or not a given group of same-aged people should pool their funds together. Journal: Scandinavian Actuarial Journal Pages: 199-226 Issue: 3 Volume: 2024 Year: 2024 Month: 03 X-DOI: 10.1080/03461238.2023.2234916 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2234916 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:3:p:199-226 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2246743_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Mario V. Wüthrich Author-X-Name-First: Mario V. Author-X-Name-Last: Wüthrich Author-Name: Johanna Ziegel Author-X-Name-First: Johanna Author-X-Name-Last: Ziegel Title: Isotonic recalibration under a low signal-to-noise ratio Abstract: Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to restore auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to an explainable pricing system because the resulting isotonically recalibrated regression function has a low complexity. Journal: Scandinavian Actuarial Journal Pages: 279-299 Issue: 3 Volume: 2024 Year: 2024 Month: 03 X-DOI: 10.1080/03461238.2023.2246743 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2246743 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:3:p:279-299 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2256508_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Yang Yang Author-X-Name-First: Yang Author-X-Name-Last: Yang Author-Name: Yahui Fan Author-X-Name-First: Yahui Author-X-Name-Last: Fan Author-Name: Kam Chuen Yuen Author-X-Name-First: Kam Author-X-Name-Last: Chuen Yuen Title: Ruin in a continuous-time risk model with arbitrarily dependent insurance and financial risks triggered by systematic factors Abstract: This paper is devoted to asymptotic analysis for a continuous-time risk model with the insurance surplus process and the log-price process of the investment driven by two dependent jump-diffusion processes. We take into account arbitrary dependence between the insurance claims and their corresponding investment return jumps caused by a sequence of systematic factors, whose arrival times constitute a renewal counting process. Under the framework of regular variation, we obtain a simple and unified asymptotic formula for the finite-time ruin probability as the initial wealth becomes large. It turns out that, in the weakly dependent case, the tails of the claims determine the exact decay rate of the finite-time ruin probability while the investment return jumps only contribute to the coefficient of the asymptotic formula; however, in the strongly dependent case, they both produce essential impacts on the finite-time ruin probability which is under-estimated in the weakly dependent case. Journal: Scandinavian Actuarial Journal Pages: 361-382 Issue: 4 Volume: 2024 Year: 2024 Month: 04 X-DOI: 10.1080/03461238.2023.2256508 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2256508 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:4:p:361-382 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2255399_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Jingyi Cao Author-X-Name-First: Jingyi Author-X-Name-Last: Cao Author-Name: Dongchen Li Author-X-Name-First: Dongchen Author-X-Name-Last: Li Author-Name: Virginia R. Young Author-X-Name-First: Virginia R. Author-X-Name-Last: Young Author-Name: Bin Zou Author-X-Name-First: Bin Author-X-Name-Last: Zou Title: Stackelberg reinsurance chain under model ambiguity Abstract: In this paper, we consider a continuous-time version of a reinsurance chain, which is sequentially formed by n+1 companies, with the first company being the primary insurer and the rest being reinsurers. Because of possible model misspecification, all companies are ambiguous about the original risk of the primary insurer. We model each reinsurance contracting problem as a Stackelberg game, in which the assuming reinsurer acts as the leader while the ceding company is the follower. Reinsurance is priced using the mean-variance premium principle and all companies are risk neutral under their own beliefs. We obtain equilibrium indemnities, premium loadings, and distortions in closed form, all of which are proportional to the original risk, with the corresponding proportions decreasing along the chain. We also show that the reinsurance chain with ambiguity aversions in increasing order is optimal from the perspectives of both selfish individual companies and an unselfish central planner. Journal: Scandinavian Actuarial Journal Pages: 329-360 Issue: 4 Volume: 2024 Year: 2024 Month: 04 X-DOI: 10.1080/03461238.2023.2255399 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2255399 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:4:p:329-360 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2257405_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Benjamin Avanzi Author-X-Name-First: Benjamin Author-X-Name-Last: Avanzi Author-Name: Hayden Lau Author-X-Name-First: Hayden Author-X-Name-Last: Lau Author-Name: Mogens Steffensen Author-X-Name-First: Mogens Author-X-Name-Last: Steffensen Title: Optimal reinsurance design under solvency constraints Abstract: We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the $ \mathbb {P} $ P and $ \mathbb {Q} $ Q measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated. Journal: Scandinavian Actuarial Journal Pages: 383-416 Issue: 4 Volume: 2024 Year: 2024 Month: 04 X-DOI: 10.1080/03461238.2023.2257405 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2257405 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:4:p:383-416 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2251197_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Kira Henshaw Author-X-Name-First: Kira Author-X-Name-Last: Henshaw Author-Name: Michel Mandjes Author-X-Name-First: Michel Author-X-Name-Last: Mandjes Author-Name: Corina Constantinescu Author-X-Name-First: Corina Author-X-Name-Last: Constantinescu Title: A stochastic model of group wealth responses to insurance mechanisms in low-income communities Abstract: This study addresses the group-based nature of financial vulnerability in the low-income environment. Adopting a highly flexible stochastic dissemination model, we assess the impact of insurance on the resilience of a low-income group to wealth shocks. For this purpose, the transient wealth of a group of interacting uninsured and insured agents is considered. The model is extended to capture four types of transaction events: external arrivals, internal redistributions, wealth losses and premium payments. Risk-sharing mechanisms, mitigating the impact of financial losses that are otherwise uninsured, are widespread in low-income communities. Our modelling of redistribution events captures the wealth transactions associated with these mechanisms, alongside the purchase of commodities and services from within the group. Through this set-up, we present a method for incorporating the high level of wealth interaction characteristic of the low-income setting in the assessment of the effectiveness of insurance. The model is underlined by an exogenously evolving Markov background process that represents the state of the economy. To analyse the distribution of wealth jointly with the state of the background process, a system of coupled differential equations for the joint transient distribution of agent wealth is derived, and is reduced to a linear system of differential equations through consideration of the moments of agent wealth. Sensitivity analysis is performed to establish the impact of the system's structure and stochastic dynamics on the wealth of the group. The probability of falling below the poverty line is then determined through application of a normal approximation and the impact of insurance in reducing this probability considered under varying levels of subsidisation. Journal: Scandinavian Actuarial Journal Pages: 301-328 Issue: 4 Volume: 2024 Year: 2024 Month: 04 X-DOI: 10.1080/03461238.2023.2251197 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2251197 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:4:p:301-328 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2264555_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Zied Chaieb Author-X-Name-First: Zied Author-X-Name-Last: Chaieb Author-Name: Domenico De Giovanni Author-X-Name-First: Domenico Author-X-Name-Last: De Giovanni Author-Name: Djibril Gueye Author-X-Name-First: Djibril Author-X-Name-Last: Gueye Title: Two hybrid models for dependent death times of couple: a common shock approach Abstract: We combine two recent credit risk models with the Marshall–Olkin setup to capture the dependence structure of bivariate survival functions. The main advantage of this approach is to handle fatal shock events in the dependence structure since these two credit risk models allow one to match the time of death of an individual with a catastrophe time event. We also provide a methodology for adding other sources of dependency to our approach. In such a setup, we derive the no-arbitrage prices of some common life insurance products for coupled lives. We demonstrate the performance of our method by investigating Sibuya's dependence function. Calibration is done on the data of joint life contracts from a Canadian company. Journal: Scandinavian Actuarial Journal Pages: 440-462 Issue: 5 Volume: 2024 Year: 2024 Month: 05 X-DOI: 10.1080/03461238.2023.2264555 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2264555 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:5:p:440-462 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2258135_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Julie Huyghe Author-X-Name-First: Julie Author-X-Name-Last: Huyghe Author-Name: Julien Trufin Author-X-Name-First: Julien Author-X-Name-Last: Trufin Author-Name: Michel Denuit Author-X-Name-First: Michel Author-X-Name-Last: Denuit Title: Boosting cost-complexity pruned trees on Tweedie responses: the ABT machine for insurance ratemaking Abstract: This paper proposes a new boosting machine based on forward stagewise additive modeling with cost-complexity pruned trees. In the Tweedie case, it deals directly with observed responses, not gradients of the loss function. Trees included in the score progressively reduce to the root-node one, in an adaptive way. The proposed Adaptive Boosting Tree (ABT) machine thus automatically stops at that time, avoiding to resort to the time-consuming cross validation approach. Case studies performed on motor third-party liability insurance claim data demonstrate the performances of the proposed ABT machine for ratemaking, in comparison with regular gradient boosting trees. Journal: Scandinavian Actuarial Journal Pages: 417-439 Issue: 5 Volume: 2024 Year: 2024 Month: 05 X-DOI: 10.1080/03461238.2023.2258135 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2258135 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:5:p:417-439 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2274096_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a 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: Zhaojie Ren Author-X-Name-First: Zhaojie Author-X-Name-Last: Ren Author-Name: Yilun Song Author-X-Name-First: Yilun Author-X-Name-Last: Song Title: Optimal mix among PAYGO, EET and individual savings Abstract: In order to deal with the aging problem, the pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the ‘Samuelson-Aaron’ criterion to age-dependent preference orderings. Under the baseline model, we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort's population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts' weight in the government's decision-making. The optimal mix is the comprehensive result of the two effects. Journal: Scandinavian Actuarial Journal Pages: 463-505 Issue: 5 Volume: 2024 Year: 2024 Month: 05 X-DOI: 10.1080/03461238.2023.2274096 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2274096 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:5:p:463-505 Template-Type: ReDIF-Article 1.0 # input file: SACT_A_2275276_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Kaixin Yan Author-X-Name-First: Kaixin Author-X-Name-Last: Yan Author-Name: Shuanming Li Author-X-Name-First: Shuanming Author-X-Name-Last: Li Author-Name: Aili Zhang Author-X-Name-First: Aili Author-X-Name-Last: Zhang Title: Valuing equity-linked annuities under high-water mark fee structure Abstract: This paper studies the valuation of equity-linked investment products embedded with a high-water mark (HWM) fee structure. Under the HWM fee structure, the insurance company charges threshold fees at a constant rate from the policyholder's account whenever the account value is lower than a pre-specified level, and levies HMW fees at another constant rate whenever the account is hitting new record highs that are higher than another pre-specified level. The dynamics of the logarithmic value of the policyholder's account, before fees, is assumed to follow either a two-sided jump-diffusion process with double exponential jumps, or a down-ward jump-diffusion process with exponential jumps. For the two-sided jump-diffusion model with HWM fees, using the Wiener–Hopf factorisation theorem and the duality lemma, we derive an explicit expression for its potential measure. For the down-ward jump-diffusion model with both threshold fees and HWM fees, we are facilitated with the excursion theory to derive an explicit expression of the potential measure. Using the above newly derived potential measures, we are able to obtain formulas for valuing the equity-linked annuity under the HWM fee structure. Finally, we illustrate our results with some numerical examples. Journal: Scandinavian Actuarial Journal Pages: 506-531 Issue: 5 Volume: 2024 Year: 2024 Month: 05 X-DOI: 10.1080/03461238.2023.2275276 File-URL: http://hdl.handle.net/10.1080/03461238.2023.2275276 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:sactxx:v:2024:y:2024:i:5:p:506-531