Abstract Samos Act 2010.dvi
نویسنده
چکیده
In this paper we consider a risk model with two classes of insurance risks in the presence of multiple thresholds. 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 system for the Gerber-Shiu functions for surplus-dependent premium rates and a piecewise integro-differential system in the multi-threshold case. Then we solve the above system in terms of the linearly independent solutions to the associated homogeneous system of the initial integro-differential equation system. An analysis of this homogeneous integro-differential systems is done using Laplace transforms. Then we provide a recursive approach to obtain the general solution of the Gerber-Shiu functions. Finally, to illustrate the solution procedure, explicit expressions for the two types Laplace transforms of the time to ruin and the ruin probabilities are given when the claim sizes are exponentially distributed.
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