A class of Sparre Andersen risk process

Abstract

In this paper, we investigate a renewal risk model in which the distribution of the interclaim times is a mixture of two Erlang distributions. First, the Laplace transform and the defective renewal equation for the Gerber-Shiu function are derived. Then, two asymptotic results for the Laplace transform of the time of ruin are given when the initial surplus tends to infinity for the light-tailed claims and heavy-tailed claims, respectively. Finally, an explicit expression for the Gerber-Shiu function is given.

Keywords

Sparre Andersen risk process / Gerber-Shiu function / Laplace transform / asymptotic / defective renewal equation