2020/12/31 by Minyi Huang, Huang, Minyi, Xuwei Yang +1 · 1 citation
Economics, Econometrics and Finance · Medicine · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2012.15468
openalex publication_date 2020/12/31 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28
This paper studies asymptotic solvability of a linear quadratic (LQ) mean field social optimization problem with controlled diffusions and indefinite state and control weights. Starting with an N-agent model, 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 decentralized control obtained from the mean field limit ensures a bounded optimality loss in minimizing the social cost having magnitude O(N), which implies an optimality loss of O(1/N) per agent. We further quantify the efficiency gain of the social optimum with respect to the solution of the mean field game.