Conditional McKean-Vlasov control
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908580760780800 |
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| author | Carmona, René Tangpi, Ludovic Zhang, Kaiwen |
| author_facet | Carmona, René Tangpi, Ludovic Zhang, Kaiwen |
| contents | Conditional McKean-Vlasov control problems involve controlling McKean-Vlasov diffusions where the interaction occurs through the law of the state process conditionally on it staying in a domain. Introduced by Lions in his 2016 lectures at the Collège de France, these problems have notable applications, particularly in systemic risk. We establish well-posedness and provide a general characterization of optimal controls using a new Pontryagin maximum principle in the probabilistic weak formulation. Unlike the classical approach based on forward-backward systems, our results connect the control problem to a generalized McKean-Vlasov backward stochastic differential equation (BSDE). We illustrate our framework with two applications: a version of the Schrödinger problem with killing, and a construction of equilibria in potential mean field games via McKean-Vlasov control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conditional McKean-Vlasov control Carmona, René Tangpi, Ludovic Zhang, Kaiwen Probability Optimization and Control Conditional McKean-Vlasov control problems involve controlling McKean-Vlasov diffusions where the interaction occurs through the law of the state process conditionally on it staying in a domain. Introduced by Lions in his 2016 lectures at the Collège de France, these problems have notable applications, particularly in systemic risk. We establish well-posedness and provide a general characterization of optimal controls using a new Pontryagin maximum principle in the probabilistic weak formulation. Unlike the classical approach based on forward-backward systems, our results connect the control problem to a generalized McKean-Vlasov backward stochastic differential equation (BSDE). We illustrate our framework with two applications: a version of the Schrödinger problem with killing, and a construction of equilibria in potential mean field games via McKean-Vlasov control. |
| title | Conditional McKean-Vlasov control |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2510.06543 |