上部同单调随机变量和的度量  

Measure on the Sum of Upper Comonotonic Random Variables

作　　者：荀立[1,2] 盛丹姝[1] 王德辉[1] 

机构地区：[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

出　　处：《吉林大学学报（理学版）》2012年第6期1057-1063,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10971081;11071126;J1030101)

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.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.

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 

分 类 号：O213[理学—概率论与数理统计]