Analysis of heterogeneous endowment policies portfolios under fractional approximations

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.