  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-$\sigma$-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.
