基于污染Gamma分布的聚合风险模型及其在风险分类中的应用

卢志义;刘乐平;孟生旺

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (2) : 174-183.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (2) : 174-183. DOI: 10.12341/jssms10124
论文

基于污染Gamma分布的聚合风险模型及其在风险分类中的应用

    卢志义(1), 刘乐平(1)(2), 孟生旺(2)
作者信息 +

Collective Risk Model Based on the Contaminated GammaDistribution and Its Application in Risk Classfication

    LU Zhiyi(1), LIU Leping;(1)(2), MENG Shengwang(2)
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文章历史 +

摘要

分析了污染Gamma分布及其性质,
讨论了基于污染Gamma分布的聚合风险模型.
对模型的概率特性和参数估计进行了分析,
并对该模型在风险分类中的应用进行了讨论.
为克服索赔总量的分布函数在计算上的困难,
利用同单调性理论得到了随机凸序意
义下索赔总量随机变量S的随机上界Sc, 对
Sc的分布函数及限额损失保费进行了讨论.
通过一个例子对所述结论的有效性进行验证.

Abstract

The contaminated Gamma distribution and its
properties are analyzed. The collective risk model based on
contaminated Gamma distribution is put forward and its probability
character is considered. Then the application of the model in risk
classification is discussed. To overcome the difficulty in
calculating the distribution function of claim amount S, a stochastic
upper bound Sc of S in the sense of stochastic convex order is
obtained by using the comonotonicity theory. The distribution function
of Sc and stop-loss premium are discussed. A numerical examples
is given to illustrate the validity of the proposed method.

关键词

污染Gamma分布 / 聚合风险模型 / 风险分类 / 同单调性 / 随机凸界.

Key words

Contaminated Gamma distribution / collective risk model / risk classification / comonotonicity / stochastic convex bounds.

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卢志义 , 刘乐平 , 孟生旺. 基于污染Gamma分布的聚合风险模型及其在风险分类中的应用. 系统科学与数学, 2009, 29(2): 174-183. https://doi.org/10.12341/jssms10124
LU Zhiyi , LIU Leping. Collective Risk Model Based on the Contaminated GammaDistribution and Its Application in Risk Classfication. Journal of Systems Science and Mathematical Sciences, 2009, 29(2): 174-183 https://doi.org/10.12341/jssms10124
中图分类号： 62P05   
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