Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control

Imane Jarni; Ayoub Laayoun; Badr Missaoui

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arXiv · 2512.19932

Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control

Imane Jarni·Ayoub Laayoun·Badr Missaoui

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Abstract

In this work, we investigate the multidimensional Skorokhod problem for c\`adl\`ag 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.

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Imane Jarni, Ayoub Laayoun, Badr Missaoui. 2025-12-22. Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control. https://arxiv.org/abs/2512.19932

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