One-dimensional McKean–Vlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients

Abstract

In this article, we investigate three classes of equations: the McKean–Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean–Vlasov stochastic variational inequality (MVSVI), and the coupled forward–backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness, in terms of the existence and uniqueness of a strong solution, for these three classes in their general forms. Importantly, we consider stochastic coefficients with locally Hölder continuity and employ different strategies to achieve that for each class.