Solvability of one kind of forward-backward stochastic difference equations

Abstract

In this article, we consider the solvability problems for the fully coupled forward-backward stochastic difference equations (FBSΔEs). On one hand, we provide the necessary and sufficient condition for the solvability of the linear FBSΔEs. On the other hand, under the assumption that the coefficients satisfy the monotonicity condition, we investigate the existence and uniqueness theorems for the general non linear FBSΔEs.

KEYWORDS:

• Forward-backward stochastic difference equations
• martingale representation theorem
• continuation method

Additional information

Funding

Shaolin Ji research is supported by NSF (No. 11571203). Haodong Liu research is supported by NSF (No. 12201593).