On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation

Abstract

In this paper, we consider a Sparre Andersen risk model where the interclaim time and claim size follow some bivariate distribution. Assuming that the risk model is also perturbed by a jump-diffusion process, we study the Gerber-Shiu functions when ruin is due to a claim or the jump-diffusion process. By using a q-potential measure, we obtain some integral equations for the Gerber-Shiu functions, from which we derive the Laplace transforms and defective renewal equations. When the joint density of the interclaim time and claim size is a finite mixture of bivariate exponentials, we obtain the explicit expressions for the Gerber-Shiu functions. © 2011 Springer Science+Business Media, LLC.