In this talk we study 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. We derive 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. We present examples 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, we obtain the equivalence of these two issues and an explicit representation of the solution to the Riccati equation.

会议网址：https://meeting.tencent.com/s/nJtWuX2Dgo0y

会议ID：685 345 876