Recursive Calculation of Ruin Probabilities at or Before Claim Instants for Non-Identically Distributed Claims

Abstract

In this paper, we consider a continuous time risk process for which the claim number process extends the classical Poisson process, and the claim sizes are independent, Erlang random variables, but not necessarily identically distributed. For this process, we obtain recursive formulas that allow us to evaluate the ruin probability at or before a certain claim instant. We illustrate the resulting algorithm in a numerical study.

Keywords: continuous time risk process, ruin probability, extensions of the Poisson process, nonhomogeneous claim sizes, Erlang distribution, mixture of exponentials distribution