The compound Poisson process perturbed by a diffusion with a threshold dividend strategy

Abstract

In this paper, we consider the compound Poisson process perturbed by a diffusion in the presence of the so-called threshold dividend strategy. Within this framework, we prove the twice continuous differentiability of the expected discounted value of all dividends until ruin. We also derive integro-differential equations for the expected discounted value of all dividends until ruin and obtain explicit expressions for the solution to the equations. Along the same line, we establish explicit expressions for the Laplace transform of the time of rain and the Laplace transform of the aggregate dividends until ruin. In the case of exponential claims, some examples are provided. Copyright © 2008 John Wiley & Sons, Ltd.