复合Poisson-Geometric风险模型下带混合保费和投资的Gerber-Shiu折现惩罚函数  

Gerber-Shiu discounted penalty function for compound Poisson-Geometric risk model with mixed premium and investment

作　　者：覃利华 QIN Lihua(School of Mathematics,Physics and Electronic Information Engineering,Guangxi Normal University for Nationlities,Chongzuo 532200,China)

机构地区：[1]广西民族师范学院,数理与电子信息工程学院,广西崇左532200

出　　处：《高师理科学刊》2022年第12期6-14,共9页Journal of Science of Teachers＇College and University

基　　金：广西高校中青年教师科研基础能力提升项目(2021KY0767)——保险精算中保险风险模型破产概率计算与算法研究;广西民族师范学院科研经费资助项目(2021YB054)。

摘　　要：在考虑到保费收入和通货膨胀等随机因素的干扰,以及保险公司将多余资本用于投资来提高其赔付能力的基础上,对经典风险模型进行推广,建立混合保费收取下带投资和扰动的双复合Poisson-Geometric过程的双险种风险模型.在该模型中,随机保费收入服从复合Poisson过程,理赔过程服从复合Poisson-Geometric过程.应用全概率公式,推导了该模型Gerber-Shiu折现罚金函数满足的更新方程,进而得到破产时盈余惩罚期望、破产时刻赤字分布函数和破产概率满足的更新方程,并当保费、理赔过程服从特定指数分布时,得到破产概率满足的微分方程.Taking into account the interference of random factors such as premium income and inflation,as well as the fact that insurance companies use excess capital for investment to improve their compensation ability,the classic risk mode was extended,and a double risk model of bicompound Poisson-Geometric process with investment and disturbance under mixed premium collection is built.In this model,random premium income follows compound Poisson process and claims process follows compound Poisson-Geometric process.The updated equations of the Gerber-Shiu discount penalty function of this model are derived by using the total probability formula,and then the updated equations of the earnings penalty expectation,the deficit distribution function at the time of bankruptcy and the bankruptcy probability are obtained.The differential equations of the bankruptcy probability are obtained when the premium and claims process obey the specific exponential distribution.

关 键 词：复合POISSON-GEOMETRIC过程 破产概率 更新方程 混合保费 

分 类 号：O211.6[理学—概率论与数理统计]