2017/07/28 by Saran Ahuja, Weiluo Ren, Ahuja, Saran +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1707.09090
arxiv created 2017/07/28 · openalex publication_date 2017/07/28 · arxiv updated 2017/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose solution can be obtained through a coupled system of partial differential equations. We characterize the first order approximation via linear mean-field forward-backward stochastic differential equations whose solution is a centered Gaussian process with respect to the common noise. The first order approximate strategy can be described as follows: at time t ∈ [0,T], applying the original MFG optimal strategy for a sub game over [t,T] with the initial being the current state and distribution. We then show that this strategy gives an approximate Nash equilibrium of order ε2.