| 上部同单调随机变量和的度量 |
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| 引用本文： | 荀立,盛丹姝,王德辉.上部同单调随机变量和的度量[J].吉林大学学报(理学版),2012,50(6):1057-1063. |
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| 作者姓名： | 荀立 盛丹姝 王德辉 |
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| 作者单位： | 1. 吉林大学 数学学院, 长春 130012,2. 长春工业大学 基础科学学院, 长春 130012 |
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| 基金项目： | 国家自然科学基金(批准号:10971081;11071126;J1030101) |
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| 摘 要： | 应用分布函数的反函数法和上部同单调随机向量的性质, 计算不同Young函数下Pareto分布与指数分布随机变量和的Haezendonck-Goovaerts风险度量, 得到了保单组合风险的上部同单调临界点及理赔总量的停止损失保费和Haezendonck-Goovaerts度量的表达式, 并运用R软件对Haezendonck-Goovaerts度量进行了数值模拟.
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| 关 键 词： | 上部同单调 停止损失保费 Haezendonck-Goovaerts风险度量 尾部凸序 Pareto分布 |
| 收稿时间： | 2012-02-07 |
Measure on the Sum of Upper Comonotonic Random Variables |
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| XUN Li,SHEND Dan-shu,WANG De-hui.Measure on the Sum of Upper Comonotonic Random Variables[J].Journal of Jilin University: Sci Ed,2012,50(6):1057-1063. |
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| Authors: | XUN Li SHEND Dan-shu WANG De-hui |
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| Institution: | 1. College of Mathematics, Jilin University, Changchun 130012, China;2. School of Basic Science, Changchun University of Technology, Changchun 130012, China |
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| Abstract: | We computed the Haezendonck Goovaerts risk measure of the sum of random variables with Pareto and exponential marginal distributions on different Young functions, using the inverse function of the distribution function and the properties of upper comonotonic random vector. The upper comonotonic thresholds of the portfolio risks were given. We established a transparent expression for the stop loss premium and Haezendonck Goovaerts risk measure of the total claim. We also analyzed the properties of the natural estimators of Haezendonck Goovaerts risk measures by means of numerical simulations with the help of R. |
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| Keywords: | upper comonotonicity stop loss premium Haezendonck-Goovaerts risk measure tail convex order Pareto distribution |
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