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March 2022 McKean–Vlasov optimal control: The dynamic programming principle
Mao Fabrice Djete, Dylan Possamaï, Xiaolu Tan
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Ann. Probab. 50(2): 791-833 (March 2022). DOI: 10.1214/21-AOP1548

Abstract

We study the McKean–Vlasov optimal control problem with common noise which allow the law of the control process to appear in the state dynamics under various formulations: strong and weak ones, Markovian or non-Markovian. By interpreting the controls as probability measures on an appropriate canonical space with two filtrations, we then develop the classical measurable selection, conditioning and concatenation arguments in this new context, and establish the dynamic programming principle under general conditions.

Funding Statement

F. Djete acknowledges support from the région Île-de-France.
X. Tan acknowledges support from CUHK startup grant and CUHK Faculty of Science Direct Grant 2019-2020. This work also benefited from support of the ANR project PACMAN ANR–16–CE05–0027.

Acknowledgments

We are grateful to two anonymous reviewers for useful comments and suggestions.

Most parts of this work had been finished when M. F. Djete and X. Tan were still at University of Paris–Dauphine, whose support is greatly acknowledged.

Citation

Download Citation

Mao Fabrice Djete. Dylan Possamaï. Xiaolu Tan. "McKean–Vlasov optimal control: The dynamic programming principle." Ann. Probab. 50 (2) 791 - 833, March 2022. https://doi.org/10.1214/21-AOP1548

Information

Received: 1 March 2020; Revised: 1 May 2021; Published: March 2022
First available in Project Euclid: 24 March 2022

Digital Object Identifier: 10.1214/21-AOP1548

Subjects:
Primary: 49L20 , 93E20
Secondary: 60H30 , 60K35

Keywords: dynamic programming principle , McKean–Vlasov optimal control , measurable selection

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 2 • March 2022
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