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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2307.07165 |
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| _version_ | 1866911855828533248 |
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| author | Bouchard, Bruno Tan, Xiaolu Wang, Jixin |
| author_facet | Bouchard, Bruno Tan, Xiaolu Wang, Jixin |
| contents | We provide an Itô's formula for $C^1$-functionals of flows of conditional marginal distributions of continuous semimartingales. This is based on the notion of weak Dirichlet process, and extends the $C^1$-Itô's formula in Gozzi and Russo (2006) to this context. As the first application, we study a class of McKean-Vlasov optimal control problems, and establish a verification theorem which only requires $C^1$-regularity of its value function, which is equivalently the (viscosity) solution of the associated HJB master equation. It goes together with a novel duality result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07165 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A $C^1$-Itô's formula for flows of semimartingale distributions Bouchard, Bruno Tan, Xiaolu Wang, Jixin Probability We provide an Itô's formula for $C^1$-functionals of flows of conditional marginal distributions of continuous semimartingales. This is based on the notion of weak Dirichlet process, and extends the $C^1$-Itô's formula in Gozzi and Russo (2006) to this context. As the first application, we study a class of McKean-Vlasov optimal control problems, and establish a verification theorem which only requires $C^1$-regularity of its value function, which is equivalently the (viscosity) solution of the associated HJB master equation. It goes together with a novel duality result. |
| title | A $C^1$-Itô's formula for flows of semimartingale distributions |
| topic | Probability |
| url | https://arxiv.org/abs/2307.07165 |