马氏链环境中带随机收入的复合二项风险模型

肖临

数学学报 ›› 2022, Vol. 65 ›› Issue (6) : 1067-1082.

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数学学报 ›› 2022, Vol. 65 ›› Issue (6) : 1067-1082. DOI: 10.12386/A20190054
论文

马氏链环境中带随机收入的复合二项风险模型

    肖临
作者信息 +

Compound Binomial Risk Model with Random Income in Markov Chain Environment

    Lin XIAO
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文章历史 +

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ΩFP,及定义在其上的MRICMΘηIB,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.

Abstract

In this paper, I consider that the actuarial model is affected by the environmental process Θ, premium income counting process η, 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 (Ω,F,P), and MRICM(Θ,η,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

Key words

Markov chain environment / compound binomial risk model / stochastic income / ruin probability / recursive equation

引用本文

导出引用
肖临. 马氏链环境中带随机收入的复合二项风险模型. 数学学报, 2022, 65(6): 1067-1082 https://doi.org/10.12386/A20190054
Lin XIAO. Compound Binomial Risk Model with Random Income in Markov Chain Environment. Acta Mathematica Sinica, Chinese Series, 2022, 65(6): 1067-1082 https://doi.org/10.12386/A20190054

参考文献

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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)
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