The Maximum Surplus before Ruin in a Generalized Erlang(n) Risk Process Perturbed by Diffusion

In this paper, we discuss a renewal risk process (Sparre Andersen risk model) perturbed by diffusion in which the claim inter-arrival times are generalized Erlang(n) distributed. The approach used is similar to that of Albrecher, et al.\,(2005), decomposing a generalized Erlang(n) random variable into an independent sum of n exponential random variables. Integro-differential equations with certain boundary conditions for the distribution of the maximum surplus before ruin are obtained. The special case where the claim size distribution is a K_m distribution is considered.