| 非时齐复合Poisson风险模型的破产特征量分析 |
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| 引用本文： | 邓迎春,李满,黄娅,周杰明.非时齐复合Poisson风险模型的破产特征量分析[J].数学物理学报(A辑),2020(2):501-514. |
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| 作者姓名： | 邓迎春 李满 黄娅 周杰明 |
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| 作者单位： | 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;湖南师范大学商学院 |
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| 基金项目： | 湖南省哲学社会科学基金(17YBA290)。 |
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| 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.
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| 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 |
On the Analysis of Ruin-Related Quantities in the Nonhomogeneous Compound Poisson Risk Model |
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| Deng Yingchun,Li Man,Huang Ya,Zhou Jieming.On the Analysis of Ruin-Related Quantities in the Nonhomogeneous Compound Poisson Risk Model[J].Acta Mathematica Scientia,2020(2):501-514. |
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| Authors: | Deng Yingchun Li Man Huang Ya Zhou Jieming |
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| Institution: | (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) |
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| Abstract: | 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. |
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| Keywords: | Ruin probability Time-varying method Nonhomogeneous Poisson process Gerber-Shiu function Renewal equation |
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