Partial comonotonicity and distortion riskmetrics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911510401384448 |
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| author | Huang, Muqiao |
| author_facet | Huang, Muqiao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial comonotonicity and distortion riskmetrics Huang, Muqiao Risk Management 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. |
| title | Partial comonotonicity and distortion riskmetrics |
| topic | Risk Management |
| url | https://arxiv.org/abs/2506.07472 |