On the Gerber-Shiu Discounted Penalty Function for a Surplus Process Described by PDMPs  

作　　者：Jing Min HE Rong WU 

机构地区：[1]College of Science, Tianjin University of Technology, Tianjin 300384, P. R. China [2]School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第5期951-962,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10926161, 10901086, 10871102);National Basic Research Program of China (973 Program) 2007CB814905;the Research Fund for the Doctorial Program of Higher Education

摘　　要：In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process （PDMP）. We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process.In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process （PDMP）. We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process.

关 键 词：Gerber-Shiu discounted penalty function piecewise deterministic Markov process ulti- mate ruin probability Volterra integral equation 

分 类 号：O211.6[理学—概率论与数理统计] TP273.4[理学—数学]