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

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 qpotential 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.