The wellposedness of FBSDEs

Abstract

In this paper we investigate the wellposedness of a class of Forward-Backward SDEs. Compared to the existing methods in the literature, our result has the following features: (i) arbitrary time duration; (ii) random coefficients; (iii) (possibly) degenerate forward diffusion; and (iv) no monotonicity condition. As a trade off, we impose some assumptions on the derivatives of the coefficients. A comparison theorem is also proved under the same conditions. This work is motivated by studying numerical methods for FBSDEs.