Mean-field reflected backward stochastic differential equations

In this paper, mean-field reflected backward stochastic differential equations (MF-RBSDEs, for short) are introduced and studied. We prove the existence and uniqueness of solutions for MF-RBSDEs under the Lipschitz condition by a fixed point argument. Under monotone assumptions for coefficients, we show a comparison theorem for MF-RBSDEs. We finally get an existence and a comparison theorem of the minimal solution when the coefficients are continuous, non-decreasing in y′ and have a linear growth.