非时齐复合Poisson风险模型的破产特征量分析  

On the Analysis of Ruin-Related Quantities in the Nonhomogeneous Compound Poisson Risk Model

作　　者：邓迎春 李满 黄娅[2] 周杰明 Deng Yingchun;Li Man;Huang Ya;Zhou Jieming(Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education)&School of Mathematics and Statistics,Hunan Normal University,Changsha 410081;School of Business,Hunan Normal University,Changsha 410081)

机构地区：[1]计算与随机数学教育部重点实验室&湖南师范大学数学与统计学院,长沙410081 [2]湖南师范大学商学院,长沙410081

出　　处：《数学物理学报（A辑）》2020年第2期501-514,共14页Acta Mathematica Scientia

基　　金：湖南省哲学社会科学基金(17YBA290)。

摘　　要：该文将经典风险模型推广到非时齐复合Poisson风险模型.首先,运用经典方法和时变方法,计算了该模型下的破产特征量,且得到了更新方程的解析表达式.其次,定义了时变后相应模型的一个广义的Gerber-Shiu函数,验证了时变方法对非时齐Poisson风险模型的有效性.最后,当单次索赔量服从指数分布时,计算了相应的破产概率和Gerber-Shiu函数.In this paper,the classical risk model is extended to nonhomogeneous compound Poisson risk model.Firstly,both the classical method and the time-varying method are used to calculate the ruin-related quantities for this model,and the analytical expression of the renewal equation is obtained.Secondly,for the time-varying model,the generalized Gerber-Shiu function is defined,which is to verify the effectiveness of the time-varying method for the nonhomogeneous compound Poisson risk model.Finally,when each claim follows an exponentially distribution,the corresponding ruin probability and Gerber-Shiu function are calculated.

关 键 词：破产概率 时变方法 非时齐Poisson过程 GERBER-SHIU函数 更新方程 

分 类 号：O211.6[理学—概率论与数理统计] O212.7[理学—数学]