Well-posedness of mean-field type forward–backward stochastic differential equations

Being motivated by a recent pioneer work Carmona and Delarue (2013), in this article, we propose a broad class of natural monotonicity conditions under which the unique existence of the solutions to Mean-Field Type (MFT) Forward–Backward Stochastic Differential Equations (FBSDE) can be established. Our conditions provided here are consistent with those normally adopted in the traditional FBSDE (without the interference of a mean-field) frameworks, and give a generic explanation on the unique existence of solutions to common MFT-FBSDEs, such as those in the linear-quadratic setting; besides, the conditions are ‘optimal’ in a certain sense that can elaborate on how their counter-example in Carmona and Delarue (2013) just fails to ensure its well-posedness. Finally, a stability theorem is also included.