The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence

Abstract

<p style='text-indent:20px;'>We consider a compound Poisson risk process perturbed by a Brownian motion through using a potential measure where the claim sizes depend on inter-claim times via the Farlie-Gumbel-Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for the distribution of the maximum surplus before ruin. This distribution can be calculated through the probability that the surplus process attains a given level from the initial surplus without first falling below zero. The explicit expressions for this distribution are derived when the claim amounts are exponentially distributed.