Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918260516061184 |
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| author | Jarni, Imane Laayoun, Ayoub Missaoui, Badr |
| author_facet | Jarni, Imane Laayoun, Ayoub Missaoui, Badr |
| contents | In this work, we investigate the multidimensional Skorokhod problem for càdlàg processes, where the reflection is subject to a minimality condition depending on the law of the solution. We then apply these results to establish existence and uniqueness for multidimensional McKean-Vlasov stochastic differential equations with mean reflection. Finally, we address the existence of optimal relaxed controls for such equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control Jarni, Imane Laayoun, Ayoub Missaoui, Badr Probability In this work, we investigate the multidimensional Skorokhod problem for càdlàg processes, where the reflection is subject to a minimality condition depending on the law of the solution. We then apply these results to establish existence and uniqueness for multidimensional McKean-Vlasov stochastic differential equations with mean reflection. Finally, we address the existence of optimal relaxed controls for such equations. |
| title | Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control |
| topic | Probability |
| url | https://arxiv.org/abs/2512.19932 |