SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 1804-1829, January 2021.
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) 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.

中文翻译：

---

两人零和随机线性二次微分对策

SIAM控制与优化杂志，第59卷，第3期，第1804-1829页，2021年1月。
本文研究了具有确定性系数的两人零和随机线性二次方程（LQ）微分对策的开环鞍点和开环下限值和上限值，以及它们的关系。它得出了开环下限值和上限值的有限性的必要条件，以及开环鞍点存在的充分条件。事实证明，在充分条件下，唯一存在对相关Riccati方程的强正则解，由此进一步为开环鞍点建立了闭环表示。实例表明，开环下限值和上限值的有限性通常不能确保开环鞍点的存在。但是对于经典的确定性LQ游戏，