马氏链环境中带随机收入的复合二项风险模型  

Compound Binomial Risk Model with Random Income in Markov Chain Environment

作　　者：肖临 Lin XIAO(China-ASEAN Institute of Statistics,Guangai University of Finance and Economics,530003,P.R.China;Guangri Education Performance Evaluation Studies&Collaborative Innovation Center,Key Research Institute of Humanities and Social Sciences in Universities of Guangri,Nanning 530003,P.R.China)

机构地区：[1]广西财经学院中国-东盟统计学院,南宁530003 [2]广西高校人文社科重点研究基地广西教育绩效评价研究协同创新中心,南宁530003

出　　处：《数学学报（中文版）》2022年第6期1067-1082,共16页Acta Mathematica Sinica：Chinese Series

基　　金：统计学广西一流学科建设项目(桂教科研(2022)1号);广西财经大数据重点实验室资助;湖南省社科基金一般项目(16YBA239);广西社科基金一般项目(18BTJ001);2020年度陆海经济一体化协同创新中心研究项目(2020C06);广西跨境电商智能信息处理重点实验室(2020C005);海陆经济一体化与海上丝绸之路建设研究协同中心研究项目(2019YB14)。

摘　　要：本文考虑精算模型受环境过程Θ,保费收入计数过程η,索赔计数过程I,索赔额过程B影响,建立马氏链环境中带随机收入的复合二项风险模型,简称MRICM,给出其特征五元组;证明了存在概率空间(Ω,F,P),及定义在其上的MRICM(Θ,η,I,B),它的特征五元组与给定的重合,并得出有限时间和无限时间条件破产概率的递推方程.In this paper,I consider that the actuarial model is affected by the environmental process,premium income counting process n,claim counting process I and the claim process B,and establish a compound binomial risk model with random income in Markov chain environment,which is called MRICM,for short.The characteristic five-tuple set is given.It is proved that there exists a probabilistic space(2,,P),and MRICM(O,n,I,B)defined on it,and its characteristic five-tuple set coincides with the given one.The recursive equations of conditional ruin probability for finite time and infinite time are obtained.

关 键 词：马氏链环境 复合二项风险模型 随机收入 破产概率 递推方程 

分 类 号：O211.63[理学—概率论与数理统计]