On the discounted penalty function in a discrete time renewal risk model with general interclaim times

Abstract

In this paper a discrete time renewal risk model with arbitrary interclaim times is discussed. We show that the expected discounted penalty function satisfies a recursive formula. In particular, the probability generating function of the time of ruin, as a function of the initial surplus, has a compound geometric tail. When the claim amounts follow a geometric distribution, explicit expression for the Gerber-Shiu function can be obtained for the specially chosen penalty function. The constant claim amounts and mixed geometric claim amounts are also examined.