Ruin Probabilities of a Surplus Process Described by PDMPs

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

作者机构：Department of Mathematics and LPMC Nankai University Tianjin 300071 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2008年第24卷第1期

页      面：117-128页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

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

主　　题：Ruin probability piecewise deterministic Markov process integro-differential equation volterra equation 

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.