Abstract
This paper studies linear quadratic (LQ) control of forward and backward stochastic difference system (FBSDS). There are two main contributions: first, the equivalent condition is obtained for the solvability of optimal control of FBSDS with multi-multiplicative noises under complete information and the analytic solution is also stated by the proposed Riccati equation. Second, the result of complete information is deduced to the situation of incomplete information, that is, the equivalent conditions of solvability and analytical solution are obtained based on Riccati equation. The main technique we use is to solve the forward–backward stochastic difference equations (FBSDEs) originated from maximum principle (MP).
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