标题： 两类反向相关的风险之和的畸变风险度量 显示英文标题

标题： Distortion risk measures of sums of two counter-monotonic risks

摘要： 本文将证明，在某些条件下，对于任意固定的畸变函数 $g$，两个反向单调风险之和的畸变风险测度可以表示为涉及的边缘分布的两个相关畸变风险测度之和，其中一个与原始畸变函数 $g$相关，另一个与 $g$的对偶畸变函数相关。 这一结果推广了 \cite{Chaoubi et al. (2020)}和 \cite{HLD}中的一些工作，因为畸变风险测度类包含了VaR和TVaR的风险测度作为特例。 显示英文摘要

摘要： In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals involved, one associated to the original distortion function $g$ and the other associated to the dual distortion function of $g$. This result extends some of the work in \cite{Chaoubi et al. (2020)} and \cite{HLD} since the class of distortion risk measures includes the risk measure of VaR and TVaR as special cases.