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The Gerber-Shiu discounted penalty function in the risk process with phase-type interclaim times |
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| Authors: | Min Song Rong Wu |
| Institution: | a Department of Finance, College of Economics, Nankai University, Tianjin 300071, PR China b Department of Finance, School of Business, Renmin University of China, Beijing 100872, PR China c School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China d Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, N6A 5B7, Canada |
| Abstract: | 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. |
| Keywords: | Gerber-Shiu discounted penalty function Phase-type distribution Sparre Anderson risk process Time of ruin Markov process |
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