The density of the time to ruin for a sparre andersen process with erlang arrivals and exponential claims

Abstract

We derive expressions for the density of the time to ruin given that ruin occurs in a Sparre Andersen model in which individual claim amounts are exponentially distributed and inter-arrival times are distributed as Erlang(n, β). We provide numerical illustrations of finite time ruin probabilities, as well as illustrating features of the density functions. © 2005 Taylor & Francis Group, LLC.