个体风险模型的复合Poisson逼近

北京大学学报（自然科学版）

个体风险模型的复合Poisson逼近

李贤德¹,杨静平²

¹北京大学概率统计学系，北京，100871；²北京大学金融数学系，北京，100871

收稿日期:2000-06-09 出版日期:2001-09-20 发布日期:2001-09-20

Compound Poisson Approximation of Individual Risk Models

LI Xiande¹，YANG Jingping²

¹Department of Probability and Statistics, Peking University, Beijing, 100871; ²Department of Financial Mathematics, Peking University, Beijing, 100871

Received:2000-06-09 Online:2001-09-20 Published:2001-09-20

摘要/Abstract

摘要： 具体讨论个体风险模型的复合Poisson逼近。引入了3个准则，在这3个准则下，分别讨论Poisson参数的选取。证明了个体风险模型为一复合二项分布模型；在3种准则下，讨论了参数的计算，并给出参数的计算公式；对指数分布和Pareto分布，给出计算结果。

关键词: 个体风险模型, 复合Poisson分布, 索赔量

Abstract: Individual risk models' approximation by Compound Poisson approximation is discussed. Three principles are presented, and the optimal choice of Poisson parameters under the three principles is discussed. It is proved that the individual risk model is also a compound binomial model; And formulas on the calculation of the optimal parameters are given. For two distributions, Exponential and Pareto, calculating results are given.

Key words: Individual risk model, Compound Poisson Distribution, Severity

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