Gerber-Shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times

In this paper, we consider a compound Poisson risk model perturbed by a Brownian motion. We construct the bivariate cumulative distribution function of the claim size and interclaim time by Farlie-Gumbel-Morgenstern copula. The integro-differential equations and the Laplace transforms for the Gerber-Shiu functions are obtained. We also show that the Gerber-Shiu functions satisfy some defective renewal equations. For exponential claims, some explicit expressions are obtained, and numerical examples for the ruin probabilities are also given.