The Gerber-Shiu function in the perturbed compound Poisson Gamma Omega model with a dividend barrier

Abstract

In this paper, the perturbed compound Poisson Gamma Omega model with a barrier dividend strategy is studied. Using the strong Markov property and Taylor formula, the integro-differential equations for the Gerber-Shiu expected discounted penalty functions are derived. The explicit solutions of the Gerber-Shiu expected discounted penalty functions are also obtained when the claim size is exponentially distributed. Furthermore, a numerical example is presented to illustrate some properties of the function.