The Gerber-Shiu discounted penalty function in the risk process with phase-type interclaim times

In this paper, we consider the Gerber-Shiu discounted penalty function for the Sparre Anderson risk process in which the interclaim times have a phase-type distribution. By the Markov property of a joint process composed of the risk process and the underlying Markov process, we provide a new approach to prove the systems of integro-differential equations for the Gerber-Shiu functions. Closed form expressions for the Gerber-Shiu functions are obtained when the claim amount distribution is from the rational family. Finally we compute several numerical examples intended to illustrate the main results.

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