Measuring the Impact of a Dependence Among Insured Lifelengths

Actuaries usually compute multiple life premiums based on the unrealistic assumption of independence of the lifelengths of insured persons. Many clinical studies, however, have demonstrated dependence of the lifetimes of paired lives such as husband and wife. In this respect, the present article tries to give an answer to the following question: does this simplifying hypothesis constitute a real financial danger for the insurance company? The answer turns out to be affirmative: this dependence materially affects the values of annuities and insurances involving multiple lives. In order to quantify the impact of a possible dependence on the amount of premium charged for annuities, insurances and widow's pension, we resort here on the Frechet bounds, Markov processes and some copula models. These techniques are applied to classical insurance contracts issued to married couples and illustrated on NIS data as well as on observations from Brussels city.

[1]  M. Fréchet Sur les tableaux de correlation dont les marges sont donnees , 1951 .

[2]  Ph. Pluvinage Remarque au sujet de la note précédente , 1958 .

[3]  E. Lehmann Some Concepts of Dependence , 1966 .

[4]  Jan M. Hoem,et al.  Markov Chain Models in Life Insurance , 1969 .

[5]  C. M. Parkes,et al.  Broken Heart: A Statistical Study of Increased Mortality among Widowers , 1969, British medical journal.

[6]  Kanti V. Mardia,et al.  Families of Bivariate Distributions , 1970 .

[7]  Jan M. Hoem,et al.  Inhomogeneous Semi-Markov Processes, Select Actuarial Tables, and Duration-Dependence in Demography , 1972 .

[8]  J M Hoem,et al.  A Markov chain model of working life tables. , 1977, Scandinavian actuarial journal.

[9]  O. Aalen,et al.  Actuarial values of payment streams , 1978 .

[10]  Marie-Christine Aulas,et al.  A — Statistiques démographiques , 1982 .

[11]  S. Haberman Decrement tables and the measurement of morbidity: II , 1983 .

[12]  H. R. Waters,et al.  An approach to the study of multiple state models , 1984 .

[13]  C. Genest,et al.  The Joy of Copulas: Bivariate Distributions with Uniform Marginals , 1986 .

[14]  H. Wolthuis,et al.  Stochastic models for life contingencies , 1986 .

[15]  Christian Genest,et al.  Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données , 1986 .

[16]  Jacques F. Carrii,et al.  THE BOUNDS OF BIVARIATE DISTRIBUTIONS THAT LIMIT THE VALUE OF LAST-SURVIVOR ANNUITIES , 1986 .

[17]  I. Olkin,et al.  Families of Multivariate Distributions , 1988 .

[18]  H. Ramlau-Hansen Hattendorff's Theorem: A Markov chain and counting process approach , 1988 .

[19]  Harry H. Panjer,et al.  AIDS: SURVIVAL ANALYSIS OF PERSONS TESTING HIV + , 1988 .

[20]  H. Ramlau-Hansen The emergence of profit in life insurance , 1988 .

[21]  Select mortality and other durational effects modelled by partially observed Markov chains. , 1990 .

[22]  Hans U. Gerber Life Insurance Mathematics , 1990 .

[23]  C. Jagger,et al.  Death after marital bereavement--is the risk increased? , 1991, Statistics in medicine.

[24]  H. Ramlau-Hansen Distribution of Surplus in Life Insurance , 1991, ASTIN Bulletin.

[25]  Kenneth G. Manton,et al.  INTERVENTION EFFECTS AMONG A COLLECTION OF RISKS , 1991 .

[26]  Christian Max Møller Numerical evaluation of Markov transition probabilities based on the discretized product integral , 1992 .

[27]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .

[28]  J. Carriére DEPENDENT DECREMENT THEORY , 1994 .

[29]  Marc Goovaerts,et al.  Dependency of Risks and Stop-Loss Order , 1996, ASTIN Bulletin.

[30]  Jan Dhaene,et al.  On the dependency of risks in the individual life model , 1997 .

[31]  B. Jones A stochastic population model for high demand CCRCs , 1995 .

[32]  HIV, AIDS, Markov Processes, and Health andDisability Insurance , 1995 .

[33]  E. Pitacco Actuarial models for pricing disability benefits: Towards a unifying approach , 1995 .

[34]  Transient results for a high demand CCRC model , 1996 .

[35]  Emiliano A. Valdez,et al.  Annuity Valuation with Dependent Mortality , 1996 .

[36]  A. Müller Stop-loss order for portfolios of dependent risks , 1997 .

[37]  Bruce L. Jones,et al.  Methods for the Analysis of CCRC Data , 1997 .

[38]  B. Jones Stochastic Models for Continuing Care Retirement Communities , 1997 .

[39]  Jan Dhaene,et al.  A Note on Dependencies in Multiple Life Statuses , 2006 .

[40]  M. Denuit,et al.  Stochastic product orderings, with applications in actuarial sciences , 1997 .

[41]  Emiliano A. Valdez,et al.  Understanding Relationships Using Copulas , 1998 .

[42]  Christian Genest,et al.  “Understanding Relationships Using Copulas,” by Edward Frees and Emiliano Valdez, January 1998 , 1998 .

[43]  Steven Haberman,et al.  Actuarial Models for Disability Insurance , 2018 .

[44]  M. Denuit,et al.  Sur la hauteur du chargement implicite contenu dans l'hypothèse d'indépendance : l'assurance "solde restant dû" , 1999 .

[45]  M. Denuit,et al.  A class of bivariate stochastic orderings, with applications in actuarial sciences , 1999 .

[46]  Michel Denuit,et al.  Premium calculation with dependent time-until-death random variables : the widow's pension , 1999 .

[47]  M. Denuit,et al.  Stochastic Orderings of Convex-Type for Discrete Bivariate Risks , 1999 .

[48]  J. Carriére Bivariate Survival Models for Coupled Lives , 2000 .

[49]  N. Bäuerle,et al.  Modeling and Comparing Dependencies in Multivariate Risk Portfolios , 1998, ASTIN Bulletin.