Note on stability of the ruin time density in a Sparre Andersen risk model with exponential claim sizes

Abstract

. In this note, the Sparre Andersen risk process with exponential claim sizes is considered. We derive upper bounds for deviations of the ruin time density when approximating the inter-claim time distribution. In particular, we treat approximation by means of empirical densities. In actuarial theory the significance of ruin probability is well-known (see Additionally, in certain the ruin time distribution has to estimated. problem arises, for in the cases of sudden natural when the of claims