Ruin Probabilities for a Risk Model with Two Classes of Claims  

作　　者：Tong Ling LV Jun Yi GUO Xin ZHANG 

机构地区：[1]Department of Mathematics, China Agricultural University, Beijing 100083, 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9期1749-1760,共12页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10871102);National Basic Research Program of China (973 Program) 2007CB814905

摘　　要：In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.

关 键 词：Markov vector process piecewise-deterministic Markov process （PDMP） infinitesimal generator exponential martingale ruin probability 

分 类 号：O211.67[理学—概率论与数理统计] TN929.5[理学—数学]