McKean–Vlasov optimal control: The dynamic programming principle

By Mao Fabrice Djete, Dylan Possamaï, Xiaolu Tan. Annals of Probability, 2019

94 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1e4296bef7db63644de186d9e4af54955ce9e975

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Citations in the corpus

Optimal control of path-dependent McKean–Vlasov SDEs in infinite-dimension (2020, background): “[66], [27], [32], and the reference monographs [10] and [23].”
Superposition and mimicking theorems for conditional McKean–Vlasov equations (2020, background): “The few recent papers on mean field control with common noise, such as [60, 28] have proposed various notions of admissible controls, usually with the goal of deriving a dynamic programming principle and an associated Hamilton-Jacobi-Bellman equation.”
Mean–field moral hazard for optimal energy demand response management (2019, background): “This is proved in a setting with common noise by Djete, Possamaï, and Tan (2019, 2020).”