理赔次数为复合Poisson-Geometric过程的风险模型  

A Risk Model with Claim Numbers Following the Compound Poisson-Geometric Process

作　　者：赵金娥[1] 王贵红 龙瑶[1] 

机构地区：[1]红河学院数学学院,云南蒙自661100 [2]玉溪农业职业技术学院计科系,云南玉溪653106

出　　处：《西南大学学报（自然科学版）》2013年第3期78-83,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161020);云南省科技厅自然科学研究基金资助项目(2008CD186);云南省教育厅科研基金资助项目(2011C121)

摘　　要：对保费收入为复合Poisson过程,而理赔次数为复合Poisson-Geometric过程的风险模型进行研究,给出了生存概率满足的积分方程及其在指数分布下的具体表达式,并运用鞅方法得出了破产概率满足的Lundberg不等式和一般公式,同时导出有限时间内生存概率的偏积分—微分方程.In this article, a risk model is considered, for which the premium income follows the compound Poisson process and the claim numbers is a compound Poisson-Geometric process. The integral equation of the survival probability and its explicit formula under exponential distribution of the survival probability are derived. By applying the martingale approach, the Lundberg inequality and the formula of the ruin probability are obtained. Meanwhile, a partial integral-differential equation is derived of the survival prob- ability with finite time.

关 键 词：POISSON-GEOMETRIC过程 鞅 破产概率 LUNDBERG不等式 积分方程 

分 类 号：O211.67[理学—概率论与数理统计]