离散分布的加权通用风险价值超可加性

中文摘要 AI 辅助

加权通用风险价值超可加性（WUVS）概念由Chen等人（2026）近期提出，作为对以下问题的推广：对于某些无限均值分布，独立同分布随机变量的凸组合是否能在随机意义上支配父分布。在本文短注中，我们证明对于离散分布，除共单调情形外，WUVS性质基本上不可能成立。由此推论，对于具有无限均值的离散分布，独立同分布随机变量的凸组合也永远不可能在随机意义上支配父分布。这解决了Müller（2025）中提出的一个开放问题。

英文摘要

The concept of weighted universal Value-at-Risk superadditivity (WUVS) was recently introduced by Chen et al. (2026) as a generalization of the question whether for some infinite mean distributions convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. In this short note we prove that the property WUVS can basically never hold for discrete distributions except for the case of comonotonicity. This implies as a corollary that for discrete distributions with infinite mean it can also never hold that convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. This settles an open problem mentioned in Müller (2025).

发表机构

• University of Siegen（锡根大学）

机构由 AI 辅助整理，请以论文原文为准。