  This paper obtains the maximum principle for both stochastic (global)
open-loop and stochastic (global) closed-loop Stackelberg differential games.
For the closed-loop case, we use the theory of controlled forward-backward
stochastic differential equations to derive the maximum principle for the
leader's optimal strategy. In the special case of the open-loop linear
quadratic Stackelberg game, we consider the follower's Hamiltonian system as
the leader's state equation, derive the related stochastic Riccati equation,
and show the existence and uniqueness of the solution to the Riccati equation
under appropriate assumptions. However, for the closed-loop linear quadratic
Stackelberg game, we can write the related Riccati equation consisting of
forward-backward stochastic differential equations, while leaving the existence
of its solution as an open problem.
