Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control
Probability
2025-12-24 v1
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.
Cite
@article{arxiv.2512.19932,
title = {Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control},
author = {Imane Jarni and Ayoub Laayoun and Badr Missaoui},
journal= {arXiv preprint arXiv:2512.19932},
year = {2025}
}