Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2412.03070 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910726668419072 |
|---|---|
| author | Liang, Zongxia Zhang, Keyu Zhuang, Yaqi |
| author_facet | Liang, Zongxia Zhang, Keyu Zhuang, Yaqi |
| contents | We investigate stochastic utility maximization games under relative performance concerns in both finite-agent and infinite-agent (graphon) settings. An incomplete market model is considered where agents with power (CRRA) utility functions trade in a common risk-free bond and individual stocks driven by both common and idiosyncratic noise. The Nash equilibrium for both settings is characterized by forward-backward stochastic differential equations (FBSDEs) with a quadratic growth generator, where the solution of the graphon game leads to a novel form of infinite-dimensional McKean-Vlasov FBSDEs. Under mild conditions, we prove the existence of Nash equilibrium for both the graphon game and the $n$-agent game without common noise. Furthermore, we establish a convergence result showing that, with modest assumptions on the sensitivity matrix, as the number of agents increases, the Nash equilibrium and associated equilibrium value of the finite-agent game converge to those of the graphon game. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constrained portfolio game with heterogeneous agents Liang, Zongxia Zhang, Keyu Zhuang, Yaqi Optimization and Control We investigate stochastic utility maximization games under relative performance concerns in both finite-agent and infinite-agent (graphon) settings. An incomplete market model is considered where agents with power (CRRA) utility functions trade in a common risk-free bond and individual stocks driven by both common and idiosyncratic noise. The Nash equilibrium for both settings is characterized by forward-backward stochastic differential equations (FBSDEs) with a quadratic growth generator, where the solution of the graphon game leads to a novel form of infinite-dimensional McKean-Vlasov FBSDEs. Under mild conditions, we prove the existence of Nash equilibrium for both the graphon game and the $n$-agent game without common noise. Furthermore, we establish a convergence result showing that, with modest assumptions on the sensitivity matrix, as the number of agents increases, the Nash equilibrium and associated equilibrium value of the finite-agent game converge to those of the graphon game. |
| title | Constrained portfolio game with heterogeneous agents |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.03070 |