Maximum principle for partially observed leader–follower stochastic differential game

Abstract

AbstractThis paper deals with the optimal control problem for partially observed leader–follower stochastic differential game. By virtue of the classical variational method and Girsanov's theorem, the stochastic maximum principles for the follower under one type of partially observed case and for the leader under the complete information structure are derived. As applications, two partially observed cases are considered for the linear–quadratic models. Then by the stochastic filtering technique, the optimal feedback controls for the follower and the leader are represented by the new stochastic Riccati equations.