带干扰的Erlang(2)风险模型破产概率的分解  

A DECOMPOSITION OF THE RUIN PROBABILITY FOR THE ERLANG(2) RISK PROCESS PERTURBED BY DIFFUSION

作　　者：陈志英[1,2] 胡亦钧[2] 

机构地区：[1]龙岩学院数学系,福建龙岩364000 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2009年第3期319-324,共6页Journal of Mathematics

基　　金：国家自然科学基金(10671149)

摘　　要：本文研究了带干扰的Erlang(2)风险模型的破产概率.利用延迟更新方法以及全概率公式,获得了积分表达式、二次连续可微性以及微分方程,并且讨论了索赔额分布为指数分布时的情形.In this paper, the authors consider the ruin probabilities of the Erlang（2） risk process perturbed by diffusion. We decompose the ruin probability into two parts： the ruin probability caused by oscillation and the ruin probability caused by a claim. We drive the integral equation satisfied by them and prove their twice continuous differentiability. Also differential equations they satisfied are obtained. And we discuss the explicit expressions when the claim is an exponential distribution.

关 键 词：ERLANG(2)风险模型 破产概率 积分表达式 微分方程 

分 类 号：O211.6[理学—概率论与数理统计]