Partial comonotonicity and distortion riskmetrics
Risk Management
2026-03-16 v3
Abstract
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. 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.
Keywords
Cite
@article{arxiv.2506.07472,
title = {Partial comonotonicity and distortion riskmetrics},
author = {Muqiao Huang},
journal= {arXiv preprint arXiv:2506.07472},
year = {2026}
}