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

2025/12/22 by Imane Jarni, Jarni, Imane, Ayoub Laayoun +3
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2512.19932

openalex publication_date 2025/12/22 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28

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.

Citations

• Mean reflected stochastic differential equations with two constraints
• Forward and Backward Stochastic Differential Equations with normal constraint in law

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