Controlled diffusion Mean Field Games with common noise, and McKean-Vlasov second order backward SDEs

2020/05/15 by Adrien Barrasso, Barrasso, Adrien, Nizar Touzi +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60H10 #60H30 #91A15 #93E03 #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2005.07542

openalex publication_date 2020/05/15 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider a mean field game with common noise in which the diffusion coefficients may be controlled. We prove existence of a weak relaxed solution under some continuity conditions on the coefficients. We then show that, when there is no common noise, the solution of this mean field game is characterized by a McKean-Vlasov type second order backward SDE.

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