A Note on Subadditivity of Value at Risks (VaRs): A New Connection to Comonotonicity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918166311993344 |
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| author | Imamura, Yuri Kato, Takashi |
| author_facet | Imamura, Yuri Kato, Takashi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on Subadditivity of Value at Risks (VaRs): A New Connection to Comonotonicity Imamura, Yuri Kato, Takashi Risk Management Probability Statistics Theory 91G70, 62P05 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. |
| title | A Note on Subadditivity of Value at Risks (VaRs): A New Connection to Comonotonicity |
| topic | Risk Management Probability Statistics Theory 91G70, 62P05 |
| url | https://arxiv.org/abs/2509.12558 |