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

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.