带有投资收益率和双保费复合Poisson-Geometric风险模型的研究  

Research on Compound Poisson-Geometric Risk Modelwith Investment Rate of Return and Double Premium

作　　者：覃利华 黄鸿君 洪小萍 QIN Li-hua;HUANG Hong-jun;HONG Xiao-ping(School of Mathematics,Physics and Electronic Information Engineering,Guangxi Minzu Normal University,Chongzuo 532200,Guangxi,China;School of Education Science,Guangxi Minzu Normal University,Chongzuo 532200,Guangxi,China;School of Economics and Management,Guangxi Minzu Normal University,Chongzuo 532200,Guangxi,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 [2]广西民族师范学院教育科学学院,广西崇左532200 [3]广西民族师范学院经济与管理学院,广西崇左532200

出　　处：《兰州文理学院学报（自然科学版）》2024年第4期13-19,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：广西高校中青年教师科研基础能力提升项目(2023KY0792);广西教育科学“十四五”规划2023年度专项项目(2023ZJY846);广西民族师范学院科研经费资助项目(2022YB019)。

摘　　要：研究了保费收入为线性增长和随机保费的风险模型,且随机保费的保单数服从复合Poisson过程,理赔次数服从复合Poisson-Geometric过程.应用全概率公式和积分变换公式,推导了该模型Gerber-Shiu折现罚金函数满足的更新方程,并当随机保费、理赔过程均服从特定指数分布时,得到了该模型破产概率的解析解,最后通过数值模拟对理论进行了分析验证.The risk model of linear increase and random premium was studied,the numbers of policies with random premium followed the compound Poisson process and the claim numbers followed a compound Poisson-Geometric process.Defective renewal equation of the Gerber-Shiu discounted penalty function was given by the method of total expectation and integral transformation formula.At last,an example was given that the premium amounts and claim amounts follow exponential distribution,and the differential equation for the ruin probability was derived.Finally,numerical simulation was given to verify the theoretical analysis.

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

分 类 号：O211.5[理学—概率论与数理统计]