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Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control (2512.19932v1)
Published 22 Dec 2025 in math.PR
Abstract: 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.
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