Ruin Probabilities in the Risk Process with Random Income  

作　　者：Zhen-hua Bao Zhong-xing Ye 

机构地区：[1]School of Mathematics, Liaoning Normal University, Dalian 116029, China [2]Department of mathematics, Shanghai Jiaotong University, Shanghai 200240, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第2期195-202,共8页应用数学学报（英文版）

基　　金：National Basic Research Program of China(973 Program No.2007CB814903);the National Natural Science Foundation of China(No.70671069)

摘　　要：We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.

关 键 词：Beekman convolution formula Defective renewal equation Ruin probability Zero-truncated geo-metric distribution 

分 类 号：F830.59[经济管理—金融学] O211[理学—概率论与数理统计]