Backward multivalued McKean-Vlasov SDEs and associated variational inequalities

TL;DR

This paper establishes existence, uniqueness, and continuous dependence of solutions for backward multivalued McKean-Vlasov SDEs and links these solutions to viscosity solutions of nonlocal variational inequalities.

Contribution

It introduces the first comprehensive analysis of backward multivalued McKean-Vlasov SDEs and connects their solutions to variational inequalities.

Findings

Proved existence and uniqueness of solutions.

Demonstrated continuous dependence on terminal values.

Provided probabilistic interpretation of viscosity solutions.

Abstract

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it is presented that their solutions depend continuously on the terminal values. Finally, we give a probabilistic interpretation for viscosity solutions of nonlocal quasi-linear parabolic variational inequalities.