The Gerber-Shiu discounted penalty function with a threshold stratregy for classical risk model perturbed by diffusion

In this paper, the classical risk model perturbed by diffusion is considered in presence of a constant dividend barrier. We study the Gerber-Shiu discounted penalty function. Two integro-differential equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results of discounted penalty function are obtained.