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Partial comonotonicity and distortion riskmetrics

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  • Muqiao Huang

Abstract

We establish a connection between subclasses of distortion riskmetrics and dependence structures, ensuring their additivity. 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.

Suggested Citation

  • Muqiao Huang, 2025. "Partial comonotonicity and distortion riskmetrics," Papers 2506.07472, arXiv.org, revised Jun 2025.
    • Handle: RePEc:arx:papers:2506.07472
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