A Note on Subadditivity of Value at Risks (VaRs): A New Connection to Comonotonicity
Risk Management
2025-10-24 v2 Probability
Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2509.12558,
title = {A Note on Subadditivity of Value at Risks (VaRs): A New Connection to Comonotonicity},
author = {Yuri Imamura and Takashi Kato},
journal= {arXiv preprint arXiv:2509.12558},
year = {2025}
}
Comments
5 pages