On the Threshold Dividend Strategy for a Generalized Jump-Diffusion Risk Model

In this paper, we generalize the Cramer-Lundberg risk model perturbed by diffusion to incorporate jumps due to the surplus investment return and to relax the positive loading condition. Assuming that the surplus process has exponential upward and arbitrary downward jumps, we analyze the expected discounted penalty (EDP) function of Gerber and Shiu (1998) under the threshold dividend strategy. We derive an integral equation for the EDP function and subsequently obtain an explicit analytical expression for the EDP function by solving the integral equation. Finally, phase-type downward jumps are considered and a matrix representation of the EDP function is presented