Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Jiaxuan Ye: Convergence of the equilibrium measure for the LQG Mean Field Game with a Common Noise

Speaker: Jiaxuan Ye, Illinois Institute of Technology.

Title: Convergence of the equilibrium measure for the LQG Mean Field Game with a Common Noise.

Abstract: The convergence rate of equilibrium measures of N-player Games with Brownian common noise to its asymptotic Mean Field Game system is known as 1/9 with respect to 1-Wasserstein distance, obtained by the monograph [Cardaliaguet, Delarue, Lasry, Lions (2019)]. In this work, we study the convergence of the N-player LQG game with a Markov chain or a Brownian motion as the common noise towards its asymptotic Mean Field Game. The approach relies on an explicit coupling of the optimal trajectory of the N-player game driven by N-dimensional Brownian motion and the Mean Field Game counterpart driven by one-dimensional Brownian motion. As a result, the convergence rate is 1/2 with respect to the 2-Wasserstein distance.

 

Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar