Well-Posedness of Generalized Mean-Reflected McKean-Vlasov Backward Stochastic Differential Equations

TL;DR

This paper establishes the existence and uniqueness of solutions for a new class of mean-reflected McKean-Vlasov BSDEs, combining mean reflection constraints with generalized integrals.

Contribution

It introduces a novel framework for mean-reflected McKean-Vlasov BSDEs and proves key theoretical properties using penalization and approximation techniques.

Findings

Proved existence of solutions under the new framework

Established uniqueness via stability estimates

Developed a penalization method for solutions

Abstract

This paper investigates a class of generalized mean-reflected McKean-Vlasov type backward stochastic differential equations (BSDEs). Our new framework combines a mean reflection constraint on the solution's expectation with a generalized integral with respect to a continuous non-decreasing process. We establish the existence and uniqueness of the solution. The uniqueness is derived via stability estimates, while the existence is proved by employing a penalization method combined with a smooth approximation of the obstacle.