The Gerber-Shiu Penalty Function for a Risk Process with Two Classes of Claims under a Multi-layer Dividend Strategy

In this paper we consider a risk model with two classes of insurance risks in the presence of a multi-layer dividend startegy. We assume that the two claim counting processes are, respectively, Poisson and Sparre Andersen with generalized Erlang(2) claim inter-arrival times. We derive an integro-differential equation system for the Gerber-Shiu functions for surplus-dependent premium rates and as a special case we obtain an integro-differential equation system for the multi-layer risk model. The solution of the above system is given in terms of the linearly independent solutions to the associated homogeneous integro-differential equation system. The analysis of this homogeneous integro-differential systems is considered using Laplace transforms. Then we provide a recursive approach to obtain the general solution of the Gerber-Shiu functions.