Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability

Sun Jingrui; Wang Hanxiao

doi:10.3934/mcrf.2020026

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2021, Volume 11, Issue 1: 47-71. Doi: 10.3934/mcrf.2020026

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Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability

Sun Jingrui^1, and
Wang Hanxiao^2, ,

1.
Department of Mathematics, Southern University of Science and Technology, Shenzhen Guangdong 518055, China
2.
School of Mathematical Sciences, Fudan University, Shanghai 200433, China

^* Corresponding author: Hanxiao Wang
^* Corresponding author: Hanxiao Wang

Received: May 31, 2019

Revised: December 31, 2019

Early access: May 2020

Published: February 2021

The first author is supported by NSFC Grant 11901280

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Abstract

This paper is concerned with mean-field stochastic linear-quadratic (MF-SLQ, for short) optimal control problems with deterministic coefficients. The notion of weak closed-loop optimal strategy is introduced. It is shown that the open-loop solvability is equivalent to the existence of a weak closed-loop optimal strategy. Moreover, when open-loop optimal controls exist, there is at least one of them admitting a state feedback representation, which is the outcome of a weak closed-loop optimal strategy. Finally, an example is presented to illustrate the procedure for finding weak closed-loop optimal strategies.

Keywords:

Mean-field stochastic differential equation,
linear-quadratic optimal control,
open-loop solvability,
weak closed-loop solvability,
state feedback.

Mathematics Subject Classification: Primary: 93E20; Secondary: 49N10, 49N35.

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References

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