LQ control of Itô stochastic system with asymmetric information

Abstract

This paper is concerned with the linear quadratic (LQ) optimal control problem for the stochastic system under asymmetric information structure. The system contains two controllers and multiplicative noises where each controller has its own information generated by part of the noises. The main contribution is to give the explicitly optimal controllers via Riccati equations. Through the stochastic maximum principle, the solvability of the optimal control problem is reduced to that of corresponding forward and backward stochastic differential equations (FBSDEs). The innovation of this paper is to establish the relationship between forward and backward processes under the general asymmetric information.