Mean-Field Game of Relative Performance Portfolio for Two Populations with Poisson Common Noise
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908665210994688 |
|---|---|
| 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 |