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JIMO

An open-loop two-person zero-sum linear quadratic (LQ for short)
stochastic differential game is considered. The controls for both
players are allowed to appear in both the drift and diffusion of the
state equation, the weighting matrices in the payoff/cost functional
are not assumed to be definite/non-singular, and the cross-terms
between two controls are allowed to appear. A forward-backward
stochastic differential equation (FBSDE, for short) and a
generalized differential Riccati equation are introduced, whose
solvability leads to the existence of the open-loop saddle points
for the corresponding two-person zero-sum LQ stochastic differential
game, under some additional mild conditions. The main idea is a
thorough study of general two-person zero-sum LQ games in Hilbert
spaces.

keywords:
Hilbert method.
,
open-loop controls
,
Stochastic games
,
linear-quadratic
,
saddle points

## Year of publication

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