The Wellposedness of FBSDEs (II)

TL;DR

This paper extends the well-posedness results of forward-backward stochastic differential equations (FBSDEs) to high dimensions, relaxing key conditions and allowing for more general, possibly degenerate, and random coefficients over arbitrary time durations.

Contribution

It significantly broadens the class of FBSDEs for which well-posedness can be established, removing previous restrictions like monotonicity and degeneracy.

Findings

Established well-posedness for high-dimensional FBSDEs

Allowed for arbitrary time durations and random coefficients

Handled possibly degenerate forward diffusions

Abstract

This paper is a continuation of \cite{zhang}, in which we established the wellposedness result and a comparison theorem for a class of one dimensional Forward-Backward SDEs. In this paper we extend the wellposedness result to high dimensional FBSDEs, and weaken the key condition in \cite{zhang} significantly. 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.