2024/11/28 by Yu Si, Si, Yu, Jingtao Shi +1
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2411.18891
This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of N weakly coupled linear backward stochastic differential equation. Different from the fixed-point approach commonly used to address large population problems, we first directly apply the maximum principle and decoupling techniques to solve a multi-agent problem, obtaining a centralized optimal strategy. Then, by letting N tend to infinity, we establish a decentralized optimal strategy. Subsequently, we prove that the decentralized optimal strategy constitutes an ε-Nash equilibrium for this game. Finally, we provide a numerical example to simulate our results.