Distortion risk measures of sums of two counter-monotonic risks
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929747093618688 |
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| author | Huang, Chunle |
| author_facet | Huang, Chunle |
| contents | In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals involved, one associated to the original distortion function $g$ and the other associated to the dual distortion function of $g$. This result extends some of the work in \cite{Chaoubi et al. (2020)} and \cite{HLD} since the class of distortion risk measures includes the risk measure of VaR and TVaR as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distortion risk measures of sums of two counter-monotonic risks Huang, Chunle Mathematical Finance Probability In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals involved, one associated to the original distortion function $g$ and the other associated to the dual distortion function of $g$. This result extends some of the work in \cite{Chaoubi et al. (2020)} and \cite{HLD} since the class of distortion risk measures includes the risk measure of VaR and TVaR as special cases. |
| title | Distortion risk measures of sums of two counter-monotonic risks |
| topic | Mathematical Finance Probability |
| url | https://arxiv.org/abs/2503.05256 |