  In this paper, we consider a linear quadratic stochastic two-person zero-sum
differential game. The controls for both players are allowed to appear in both
drift and diffusion of the state equation. The weighting matrices in the
performance functional are not assumed to be definite/non-singular. A necessary
and sufficient condition for the existence of a closed-loop saddle point is
established in terms of the solvability of a Riccati differential equation with
certain regularity. It is possible that the closed-loop saddle point fails to
exist, and at the same time, the corresponding Riccati equation admits a
solution (which does not have needed regularity). Also, we will indicate that
the solution of the Riccati equation may be non-unique.
