A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929334483156992 |
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| author | Liang, Zongxia Zhang, Keyu |
| author_facet | Liang, Zongxia Zhang, Keyu |
| contents | This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the n-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation Liang, Zongxia Zhang, Keyu Optimization and Control Mathematical Finance This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the n-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results. |
| title | A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation |
| topic | Optimization and Control Mathematical Finance |
| url | https://arxiv.org/abs/2401.15659 |