Well-Posedness for a Class of Mean-Field-Type Forward-Backward Stochastic Differential Equations and Classical Solutions of Related Master Equations

In this paper, we study a class of mean-field-type forward-backward stochastic differential equations. We propose a class of monotonicity conditions, under which we show the uniformly Lipschitz continuity of the decoupling field and obtain the existence and uniqueness of solution. We further provide a representation result for the solution and the decoupling field. Finally, we obtain the regularity of the decoupling field and establish global well-posedness of classical solutions to related master equations.