Ruin Probabilities of a Surplus Process Described by PDMPs  

作　　者：Jing-min He Rong Wu Hua-yue Zhang 

机构地区：[1]Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第1期117-128,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 10571092) ;the Research Fund for the Doctorial Program of Higher Education.

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.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.

关 键 词：Ruin probability piecewise deterministic Markov process integro-differential equation volterra equation 

分 类 号：O211.62[理学—概率论与数理统计]