First order Martingale model risk and semi-static hedging
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915595827544064 |
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| author | Sauldubois, Nathan Touzi, Nizar |
| author_facet | Sauldubois, Nathan Touzi, Nizar |
| contents | We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our results extend the findings of Bartl, Drapeau, Obloj \& Wiesel \cite{bartl2021sensitivity} and Bartl \& Wiesel \cite{bartlsensitivityadapted} by introducing the minimization of the distributionally robust problem with respect to semi-static hedging strategies. We provide explicit characterizations of the model risk (first order) optimal semi-static hedging strategies. The distributional robustness is analyzed both in terms of the adapted Wasserstein metric and the more relevant standard Wasserstein metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First order Martingale model risk and semi-static hedging Sauldubois, Nathan Touzi, Nizar Mathematical Finance Optimization and Control Probability 49K45, 49Q22 We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our results extend the findings of Bartl, Drapeau, Obloj \& Wiesel \cite{bartl2021sensitivity} and Bartl \& Wiesel \cite{bartlsensitivityadapted} by introducing the minimization of the distributionally robust problem with respect to semi-static hedging strategies. We provide explicit characterizations of the model risk (first order) optimal semi-static hedging strategies. The distributional robustness is analyzed both in terms of the adapted Wasserstein metric and the more relevant standard Wasserstein metric. |
| title | First order Martingale model risk and semi-static hedging |
| topic | Mathematical Finance Optimization and Control Probability 49K45, 49Q22 |
| url | https://arxiv.org/abs/2410.06906 |