A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910392073060352 |
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| author | Laurière, Mathieu Tangpi, Ludovic Zhou, Xuchen |
| author_facet | Laurière, Mathieu Tangpi, Ludovic Zhou, Xuchen |
| contents | Graphon games have been introduced to study games with many players who interact through a weighted graph of interaction. By passing to the limit, a game with a continuum of players is obtained, in which the interactions are through a graphon. In this paper, we focus on a graphon game for optimal investment under relative performance criteria, and we propose a deep learning method. The method builds upon two key ingredients: first, a characterization of Nash equilibria by forward-backward stochastic differential equations and, second, recent advances of machine learning algorithms for stochastic differential games. We provide numerical experiments on two different financial models. In each model, we compare the effect of several graphons, which correspond to different structures of interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07365 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents Laurière, Mathieu Tangpi, Ludovic Zhou, Xuchen Optimization and Control Computer Science and Game Theory Machine Learning Graphon games have been introduced to study games with many players who interact through a weighted graph of interaction. By passing to the limit, a game with a continuum of players is obtained, in which the interactions are through a graphon. In this paper, we focus on a graphon game for optimal investment under relative performance criteria, and we propose a deep learning method. The method builds upon two key ingredients: first, a characterization of Nash equilibria by forward-backward stochastic differential equations and, second, recent advances of machine learning algorithms for stochastic differential games. We provide numerical experiments on two different financial models. In each model, we compare the effect of several graphons, which correspond to different structures of interactions. |
| title | A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents |
| topic | Optimization and Control Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2402.07365 |