  This paper is concerned with the closed-loop solvability of one kind of
linear-quadratic Stackelberg stochastic differential game, where the
coefficients are deterministic. The notion of the closed-loop solvability is
introduced, which require to be independent of the initial state. The
follower's problem is solved first, and the closed-loop optimal strategy is
characterized by a Riccati equation, together with an adapted solution to a
linear backward stochastic differential equation. Then the necessary conditions
of the existence of the leader's nonanticipating closed-loop optimal strategy
is obtained via a system of cross-coupled Riccati equations. The sufficiency is
open since the completion-of-square method is invalid.
