2021/07/19 by Minyi Huang, Huang, Minyi, Xuwei Yang +1
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2107.09168
openalex publication_date 2021/07/19 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28
This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The rescaling technique is further used for performance estimates, establishing an O(1/N)-Nash equilibrium for the obtained decentralized strategies.