McKean-Vlasov optimal control: the dynamic programming principle
Optimization and Control
2020-03-25 v2 Probability
Abstract
We study the McKean-Vlasov optimal control problem with common noise in various formulations, namely the strong and weak formulation, as well as the Markovian and non-Markovian formulations, and allowing for the law of the control process to appear in the state dynamics. 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.
Cite
@article{arxiv.1907.08860,
title = {McKean-Vlasov optimal control: the dynamic programming principle},
author = {Mao Fabrice Djete and Dylan Possamaï and Xiaolu Tan},
journal= {arXiv preprint arXiv:1907.08860},
year = {2020}
}
Comments
33 pages