A stackelberg game of backward stochastic differential equations with partial information

Abstract

<p style='text-indent:20px;'>This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the follower is a sub-<inline-formula><tex-math id="M1">\begin{document}$ \sigma $\end{document}</tex-math></inline-formula>-algebra of that of the leader. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. The state estimate feedback representation for the optimal control of the follower is first given via two Riccati equations. Then the leader's problem is formulated as an optimal control problem of FBSDE. Four high-dimensional Riccati equations are introduced to represent the state estimate feedback for the optimal control of the leader. Theoretic results are applied to a pension fund management problem of two players in the financial market.</p>

Maximum principle for partially observed leader–follower stochastic differential game

“…They obtained necessary and sufficient conditions of the optimality for the follower and the leader in the full information. Reference [22] focused on the Stackelberg game of backward stochastic differential equations with partial information. It is natural to discuss the leader–follower stochastic differential game under more partially observed cases, which is more important and technologically demanding in its filtering procedure.…”