2025/11/19 by Li, Yuchen, Liang, Zongxia, Yu, Xiang
Decision Sciences · Economics, Econometrics and Finance · #91A06 #91A07 #91A16 #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.2511.15176
openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28
This paper studies the mean field game (MFG) and N-player game on relative performance portfolio management with two heterogeneous populations. In addition to the Brownian idiosyncratic and common noise, the first population invests in assets driven by idiosyncratic Poisson jump risk, while the second population invests in assets subject to Poisson common noise. We establish the characterization of the mean-field equilibrium (MFE) in MFG with two populations as well as the Nash equilibrium in the N1+N2-player game. Furthermore, we prove the convergence of the Nash equilibrium in the N1+N2-player game to the MFE as the number of players in two populations tends to infinity. We also discuss some impacts on MFE by the Poisson idiosyncratic risk and Poisson common noise in the context of relative performance, compensated by some numerical examples and financial implications.