上部同单调随机变量和的度量

Measure on the Sum of Upper Comonotonic Random Variables

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.