Extended mean field control problems: stochastic maximum principle and transport perspective

Acciaio, Beatrice, Backhoff-Veraguas, J. and Carmona, Rene (2019) Extended mean field control problems: stochastic maximum principle and transport perspective. SIAM Journal on Control and Optimization, 57 (6). 3666 - 3693. ISSN 0363-0129

Text (Extend mean field control problems) - Accepted Version Download (426kB)

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Abstract

We study mean field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufficient forms, which extend the known conditions to this general framework. We suggest a variational approach for a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme.

Item Type:	Article
Official URL:	https://epubs.siam.org/loi/sjcodc
Additional Information:	© 2019 Society for Industrial and Applied Mathematics
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	04 Oct 2019 16:27
Last Modified:	16 Apr 2024 17:51
URI:	http://eprints.lse.ac.uk/id/eprint/101877

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