Upper and Lower Bounds of Present Value Distributions of Life Insurance Contracts with Disability Related Benefi ts

The distribution function of the present value of a cash fl ow can be approximated by means of a distribution function of a random variable, which is also the present value of a sequence of payments, but has a simpler structure. The corresponding random variable has the same expectation as the random variable corresponding to the original distribution function and is a stochastic upper bound of convex order. A sharper upper bound and a nontrivial lower bound can be obtained if more information about the risk is available. In this paper, it will be shown that such an approach can be adopted for some life insurance contracts under Markov assumptions, with disability related benefi ts. The quality of the approximation will be investigated by comparing the distribution obtained with the one derived from the algorithm presented in the paper by Hesselager and Norberg (1996).