  The paper studies the open-loop saddle point and the open-loop lower and
upper values, as well as their relationship for two-person zero-sum stochastic
linear-quadratic (LQ, for short) differential games with deterministic
coefficients. It derives a necessary condition for the finiteness of the
open-loop lower and upper values and a sufficient condition for the existence
of an open-loop saddle point. It turns out that under the sufficient condition,
a strongly regular solution to the associated Riccati equation uniquely exists,
in terms of which a closed-loop representation is further established for the
open-loop saddle point. Examples are presented to show that the finiteness of
the open-loop lower and upper values does not ensure the existence of an
open-loop saddle point in general. But for the classical deterministic LQ game,
these two issues are equivalent and both imply the solvability of the Riccati
equation, for which an explicit representation of the solution is obtained.
