| 索赔次数为复合Poisson-Geometric过程的风险模型及破产概率 |
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| 引用本文： | 毛泽春,刘锦萼.索赔次数为复合Poisson-Geometric过程的风险模型及破产概率[J].应用数学学报,2005,28(3):419-428. |
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| 作者姓名： | 毛泽春 刘锦萼 |
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| 作者单位： | 1. 湖北大学商学院金融系,武汉,430062;山东经济学院概率统计与保险精算研究所,济南,250014
2. 山东经济学院概率统计与保险精算研究所,济南,250014 |
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| 基金项目： | 国家自然科学基金（10471076号）,山东省自然科学基金（Y2004A05,Y2004A07号）,山东省社科规划研究（04BJJ31号）资助项目 |
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| 摘 要： | 本文引入一类复合Poisson-Geometric分布,这类分布包括两个参数,是普通Poisson分布的一种推广,并在保险中有其实际的应用背景;基于此分布产生一个计数过程,称之为复合Poisson-Geometric过程.本文着重研究了索赔次数为复合Poisson-Geometric过程的风险模型,这种模型是经典风险模型的一个推广.针对此模型,本文给出了破产概率公式及更新方程.作为特例,当索赔额服从指数分布时,给出了破产概率的显式表达式.
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| 关 键 词： | 复合Poisson-Geometric过程 索赔过程 破产概率 更新方程 |
| 收稿时间： | 2002-5-31 |
| 修稿时间： | 2002-5-31 |
A RISK MODEL AND RUIN PROBABILITY WITH COMPOUND POISSON-GEOMETRIC PROCESS |
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| Mao Zechun,LIU JINE.A RISK MODEL AND RUIN PROBABILITY WITH COMPOUND POISSON-GEOMETRIC PROCESS[J].Acta Mathematicae Applicatae Sinica,2005,28(3):419-428. |
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| Authors: | Mao Zechun LIU JINE |
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| Abstract: | A distribution of claim numbers in insurance has been introduced, which include two parameters and is a generalization of Poisson's. It can be used to describe an extra zero claim numbers, so it is significant to apply the distribution in insurance practice. Based on this distribution, a stochastic counting process with independent and stationary increments can be generated in our paper. A risk model with the counting process has been studied. The ruin probability formula and the renewal equation have been given. Some important results on classical risk model with poisson process are the special cases in this paper. |
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| Keywords: | compound poisson-geometric process claims process ruin probability renewal equation |
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