The Gerber-Shiu Penalty Functions for a Perturbed Risk Model with Two Classes of Risks and a Threshold Dividend Strategy

In this paper, we study the perturbed risk model with two classes of claims and a threshold dividend strategy. We assume that the two claim counting processes are, respectively, Poisson and renewal process with generalized Erlang(2) inter-claim times. Integro-differential equations and certain boundary conditions satisfied by the Gerber-Shiu penalty functions are derived in terms of matrices. Finally, we show that the closed form for the Gerber-Shiu penalty functions can be expressed by the Gerber-Shiu penalty functions without dividend payments and the matrix composed of two linearly independent solutions to the corresponding homogeneous integro-differential equations.