Mean-Field Game of Relative Performance Portfolio for Two Populations with Poisson Common Noise

Fuente: arXiv
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Autori principali: Li, Yuchen, Liang, Zongxia, Yu, Xiang
Natura: Preprint
Pubblicazione: 2025
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author Li, Yuchen
Liang, Zongxia
Yu, Xiang
author_facet Li, Yuchen
Liang, Zongxia
Yu, Xiang
contents 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 $N_1+N_2$-player game. Furthermore, we prove the convergence of the Nash equilibrium in the $N_1+N_2$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_15176
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mean-Field Game of Relative Performance Portfolio for Two Populations with Poisson Common Noise
Li, Yuchen
Liang, Zongxia
Yu, Xiang
Optimization and Control
91A16, 91A06, 91A07
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 $N_1+N_2$-player game. Furthermore, we prove the convergence of the Nash equilibrium in the $N_1+N_2$-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.
title Mean-Field Game of Relative Performance Portfolio for Two Populations with Poisson Common Noise
topic Optimization and Control
91A16, 91A06, 91A07
url https://arxiv.org/abs/2511.15176