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.