On the Dividend Problem in a Risk Model with Delayed Claims

Abstract

In this paper, a discrete time risk model with dividend payments is considered, in which the occurrences of the claims may be delayed. A system of differential equations with certain boundary conditions for the expected present value of dividend payments prior to ruin is derived and solved. Moreover, the closed form expressions are given when the claim size distributions belong to the rational family. The qualitative properties of ruin probabilities for this risk model are also obtained. Numerical results are provided to illustrate the applicability of the main result.