In this paper, we provide a new property of value at risk (VaR), which is a standard risk measure that is widely used in quantitative financial risk management. We show that the subadditivity of VaR for given loss random variables holds for any confidence level if and only if those are comonotonic. This result also gives a new equivalent condition for the comonotonicity of random vectors.

翻译：本文探讨了风险价值（VaR）的一个新性质，该风险度量是量化金融风险管理中广泛采用的标准工具。我们证明，对于给定的损失随机变量，其VaR在任意置信水平下均满足次可加性，当且仅当这些随机变量具有同单调性。该结论同时为随机向量同单调性提供了一个新的等价条件。