Conditional McKean-Vlasov control

René Carmona; Ludovic Tangpi; Kaiwen Zhang

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arXiv · 2510.06543

Conditional McKean-Vlasov control

René Carmona·Ludovic Tangpi·Kaiwen Zhang

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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 Coll\`ege 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 Schr\"odinger problem with killing, and a construction of equilibria in potential mean field games via McKean-Vlasov control.

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René Carmona, Ludovic Tangpi, Kaiwen Zhang. 2025-10-08. Conditional McKean-Vlasov control. https://arxiv.org/abs/2510.06543

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