×

Analysis of heterogeneous endowment policies portfolios under fractional approximations. (English) Zbl 1103.91360

Summary: In this paper we consider heterogeneous portfolios of endowment insurance policies with a 12 months maturation time. We apply majorization order, Schur functions, and fractional approximations to study the effects of statistical heterogeneity on the premium, on the death benefit and on the survival benefit of the endowment contract. We obtain upper and lower bounds for the premium and the benefits, and under the power approximation we derive some monotone properties of the premium and the benefits.

MSC:

91B30 Risk theory, insurance (MSC2010)
62E10 Characterization and structure theory of statistical distributions
62E17 Approximations to statistical distributions (nonasymptotic)
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Arnold, B.C., 1987. Lecture Notes in Statistics. Springer, Berlin.
[2] Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbit, C.J., 1986. Actuarial Mathematics. The Society of Actuaries, Itasca, IL.
[3] Dahan, M.; Frostig, E.; Langberg, N.A., Comparison for life insurance policies with heterogeneous population, Scandinavian actuarial journal, 3, 2, 212-222, (2002) · Zbl 1039.91037
[4] Jones, B.L., Mereu, J.A., 2000. A family of fractional age assumptions. Insurance: Mathematics and Economics 27. · Zbl 0973.62094
[5] Jones, B.L., Mereu, J.A., 2002. A critique of fractional age assumptions. Insurance: Mathematics and Economics 30. · Zbl 1033.62103
[6] Marshall, A.W., Olkin, I., 1979. Inequalities: Theory of Majorization and its Applications. Academic Press, New York. · Zbl 0437.26007
[7] Neill, A., 1977. Life Contingencies. Heinmann, London.
[8] 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.