MCKEAN-VLASOV OPTIMAL CONTROL: THE DYNAMIC PROGRAMMING PRINCIPLE

Mao Fabrice Djete; Dylan Possamaï; Xiaolu Tan

doi:10.1214/21-AOP1548

MCKEAN-VLASOV OPTIMAL CONTROL: THE DYNAMIC PROGRAMMING PRINCIPLE

Mao Fabrice Djete
, Dylan Possamaï
, Xiaolu Tan

École Polytechnique
ETH Zurich
The Chinese University of Hong Kong

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	791-833
Number of pages	43
Journal	Annals of Probability
Volume	50
Issue number	2
DOIs	https://doi.org/10.1214/21-AOP1548
Publication status	Published - 1 Mar 2022
Externally published	Yes

Keywords

McKean-Vlasov optimal control
dynamic programming principle
measurable selection

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10.1214/21-AOP1548

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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.",

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KW - McKean-Vlasov optimal control

KW - dynamic programming principle

KW - measurable selection

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ER -

MCKEAN-VLASOV OPTIMAL CONTROL: THE DYNAMIC PROGRAMMING PRINCIPLE

Abstract

Keywords

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