A Linear Quadratic Stackelberg Game of Backward Stochastic Differential Equations with Partial Information

Abstract

The paper is concerned with a linear quadratic (LQ) Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the leader is a sub-σ-algebra of that of the follower which is a kind of new feature of asymmetric information. By the maximum principle, the state feedback representation for the optimal control of the follower is first given via two Riccati equations. Then two new high-dimensional Riccati equations, a backward stochastic differential filtering equation (BSDFE) and a stochastic differential filtering equation (SDFE) are introduced to represent the state estimate feedback for the optimal control of the leader.