标题： 部分共单调性与畸变风险度量 显示英文标题

标题： Partial comonotonicity and distortion riskmetrics

摘要： 我们建立了失真风险度量子类与相依结构之间的联系，并确保其可加性。 提出了一种新的正相依性概念，称为部分单调性，它包含了现有的单调性和单点集中性的概念。 对于两个随机变量，与第三个随机变量单调相关并不意味着它们彼此单调相关；相反，这定义了部分单调性的一个实例。 部分单调性的任何特定实例都通过在这种相依结构下的可加性唯一地刻画了一类失真风险度量。 这一结果的一个含义是使用单点集中性来表征期望短缺（Expected Shortfall）。 显示英文摘要

摘要： We establish a connection between subclasses of distortion riskmetrics and dependence structures, ensuring their additivity. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing concepts of comonotonicity and single-point concentration. For two random variables, being comonotonic with a third one does not imply that they are comonotonic; instead, this defines an instance of partial comonotonicity. Any specific instance of partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity under this dependence structure. An implication of this result is the characterization of the Expected Shortfall using single-point concentration.