{"ID":2858507,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.06543","arxiv_id":"2510.06543","title":"Conditional McKean-Vlasov control","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.06543","url_pdf":"https://arxiv.org/pdf/2510.06543v1","authors":"[\"René Carmona\",\"Ludovic Tangpi\",\"Kaiwen Zhang\"]","published":"2025-10-08T00:45:15Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}