CONTROLLED DIFFUSION MEAN FIELD GAMES WITH COMMON NOISE AND MCKEAN–VLASOV SECOND ORDER BACKWARD SDEs

A. Barrasso; N. Touzi

doi:10.1137/S0040585X97T990654

CONTROLLED DIFFUSION MEAN FIELD GAMES WITH COMMON NOISE AND MCKEAN–VLASOV SECOND ORDER BACKWARD SDEs

A. Barrasso, N. Touzi

Finance and Risk Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	613-639
Number of pages	27
Journal	Theory of Probability and its Applications
Volume	66
Issue number	4
DOIs	https://doi.org/10.1137/S0040585X97T990654
State	Published - 2022

Keywords

Nash equilibrium
exterior noise
mean field game
stochastic control

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1137/S0040585X97T990654

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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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author = "A. Barrasso and N. Touzi",

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AU - Barrasso, A.

AU - Touzi, N.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Nash equilibrium

KW - exterior noise

KW - mean field game

KW - stochastic control

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SP - 613

EP - 639

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 4

ER -

CONTROLLED DIFFUSION MEAN FIELD GAMES WITH COMMON NOISE AND MCKEAN–VLASOV SECOND ORDER BACKWARD SDEs

Abstract

Keywords

ASJC Scopus subject areas

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