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arXiv · 2506.07472

Partial comonotonicity and distortion riskmetrics

Muqiao Huang
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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.

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Muqiao Huang. 2025-06-09. Partial comonotonicity and distortion riskmetrics. https://arxiv.org/abs/2506.07472

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