  This paper is concerned with a Stackelberg game of backward stochastic
differential equations (BSDEs), where the coefficients of the backward system
and the cost functionals are deterministic, and the control domain is convex.
Necessary and sufficient conditions of the optimality for the follower and the
leader are first given for the general problem, by the stochastic maximum
principles of BSDEs and forward-backward stochastic differential equations
(FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs
is investigated under standard assumptions. The state 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 with the control-independent diffusion term. Two
high-dimensional Riccati equations are introduced to represent the state
feedback for the optimal control of the leader. The solvability of the four
Riccati equations are discussed. Theoretic results are applied to an optimal
consumption rate problem of two players in the financial market.
