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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	791-833
Nombre de pages	43
journal	Annals of Probability
Volume	50
Numéro de publication	2
Les DOIs	https://doi.org/10.1214/21-AOP1548
état	Publié - 1 mars 2022
Modification externe	Oui

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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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MCKEAN-VLASOV OPTIMAL CONTROL: THE DYNAMIC PROGRAMMING PRINCIPLE

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