Lecture on "Closed-Loop Strategies in Stochastic Linear-Quadratic Problems"
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Lecture on "Closed-Loop Strategies in Stochastic Linear-Quadratic Problems"
DateandTime: 2017-06-14 09:10:29

Speaker: Sun Jing-Rui, Doctor of Philosophy, The National University of Singapore, Singapore

Date: June 14, 2017

Time: 2:30 pm-3:30 pm

Location: Room 1238, Block B, Zhixin Building, Central Campus

Sponsor: the School of Mathematics


In stochastic differential games, open-loop controls depend on the initial state as well as all the information, including those of the opponent, over the whole time duration. This makes open-loop controls practically infeasible. In this talk, we introduce closed-loop strategies for stochastic linear-quadratic (LQ) problems, which are non-anticipating and hence more meaningful and convenient to use in reality. We begin with LQ control problems, carefully illustrate the relationship between open-loop and closed-loop solvabilities, and provide characterizations of the existence of open-loop optimal controls and closed-loop optimal strategies. Then we consider stochastic LQ two-person differential games. Besides characterizing open-loop and closed-loop Nash equilibria, we find several interesting but unexpected facts: 1) The existence of an open-loop Nash equilibrium is not equivalent to that of a closed-loop Nash equilibrium. 2) The outcome of a closed-loop Nash equilibrium is different from the closed-loop representation of an open-loop Nash equilibrium. 3) For the case of zero-sum differential games, the closed-loop representation of open-loop saddle points coincides with the outcome of the corresponding closed-loop saddle point as long as both exist.


Sun Jing-Rui is a Doctor of Philosophy at The National University of Singapore in Singapore. His research interests fall into the fields of applied mathematics and probability theory.

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Edited by: Zhang Xinyuan

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