Solvability of General Linear Forward and Backward Stochastic Difference Equations

摘要

In this paper, we consider a class of general linear forward and backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient condition for the existence of a unique solution to FBSDEs is given in terms of a Riccati equation. The result is applied to the linear quadratic optimal control problem for systems with stochastic multiplicative noises.