| Ruin Probabilities of a Surplus Process Described by PDMPs |
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| 作者姓名： | Jing-min He Rong Wu Hua-yue Zhang |
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| 作者单位： | Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10571092） and the Research Fund for the Doctorial Program of Higher Education. |
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| 摘 要： | In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process （PDMP）. An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed.
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| 关 键 词： | 马尔可夫过程 破产概率 积分微分方程 剩余过程 |
| 收稿时间： | 2006-10-21 |
| 修稿时间： | 2007-04-11 |
Ruin probabilities of a surplus process described by PDMPs |
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| Jing-min He Rong Wu Hua-yue Zhang.Ruin Probabilities of a Surplus Process Described by PDMPs[J].Acta Mathematicae Applicatae Sinica,2008,24(1):117-128. |
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| Authors: | Jing-min He Rong Wu Hua-yue Zhang |
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| Institution: | (1) Department of Mathematics and LPMC, Nankai University, Tianjin, 300071, China |
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| Abstract: | In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process
(PDMP). An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed
into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that
in Asmussen and Nielsen2], the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and
its upper bounds when the claim-size is exponentially distributed.
Supported by the National Natural Science Foundation of China (No. 10571092) and the Research Fund for the Doctorial Program
of Higher Education. |
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| Keywords: | Ruin probability piecewise deterministic Markov process integro-differential equation volterra equation |
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