Insurance contracts portfolios with heterogeneous insured ages. (English) Zbl 1075.62094

Summary: We consider two portfolios: one of \(m\) endowment insurance contracts and one of \(m\) whole life insurance contracts. We introduce the majorization order and Schur functions. We assume that the owners of the portfolios are of different ages at issue time and are exposed to a common life-distribution. We study the effect of the aging heterogeneity on the premiums and on the death benefits of the insurance contracts. We show that the premiums paid in both contracts and the death benefit awarded in the whole life contract are Schur functions. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for some distribution functions used frequently in the actuarial sciences.


62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
60E15 Inequalities; stochastic orderings
Full Text: DOI


[1] Arnold, B.C., 1987. Lecture Notes in Statistics. Springer-Verlag, Berlin Heidelberg.
[2] Dahan, M.; Frostig, E.; Langberg, N. A., Life insurance policies with statistical heterogenous population, Scandinavian Actuarial Journal, 3, 212-222, (2002) · Zbl 1039.91037
[3] Dahan, M.; Frostig, E.; Langberg, N. A., Analysis of heterogenous endowment policies under fractional approximations, Insurance: Mathematics and Economics, 33, 3, 567-584, (2003) · Zbl 1103.91360
[4] Dahan, M., Frostig, E., Langberg, N.A., 2004. Insurance contracts portfolios with heterogenous parametric life distributions. Scandinavian Actuarial Journal, to appear. · Zbl 1144.91024
[5] Marshall, A.W., Olkin, I., 1979. Inequalities: Theory of Majorization and its Applications. Academic Press, Inc., New York. · Zbl 0437.26007
[6] Spreeuw, J., 1998. Majorization order applied to a system of mortality profit distribution. In: Paper Presented at the Second International Congress on Insurance: Mathematics and Economics, vol. 4.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.