This paper considers a forward-backward stochastic differential equation (FBSDE) which is a system of the type
for . Under some technical conditions like Lipschitz, linear growth, or measurability and a simple and very natural monotonicity condition on and , the authors prove results on existence and uniqueness of a solution . Furthermore, they establish a priori estimates and continuous dependence upon a parameter. Finally, they connect FBSDEs to systems of quasilinear parabolic PDEs of second order. Using their purely probabilistic approach, they prove the existence of viscosity solutions of the PDE.