Time-inconsistent mean field and n-agent games under relative performance criteria
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929329364008960 |
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| author | Liang, Zongxia Zhang, Keyu |
| author_facet | Liang, Zongxia Zhang, Keyu |
| contents | In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the relative wealth and consumption to her competitors. Due to the presence of a non-exponential discount factor, each agent's optimal strategy becomes time-inconsistent. In order to resolve time-inconsistency, each agent makes a decision in a sophisticated way, choosing open-loop equilibrium strategy in response to the strategies of all the other agents. We construct explicit solutions for the $n$-agent games and the corresponding mean field games (MFGs) where the limit of former yields the latter. This solution is unique in a special class of equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14437 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Time-inconsistent mean field and n-agent games under relative performance criteria Liang, Zongxia Zhang, Keyu Mathematical Finance In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the relative wealth and consumption to her competitors. Due to the presence of a non-exponential discount factor, each agent's optimal strategy becomes time-inconsistent. In order to resolve time-inconsistency, each agent makes a decision in a sophisticated way, choosing open-loop equilibrium strategy in response to the strategies of all the other agents. We construct explicit solutions for the $n$-agent games and the corresponding mean field games (MFGs) where the limit of former yields the latter. This solution is unique in a special class of equilibria. |
| title | Time-inconsistent mean field and n-agent games under relative performance criteria |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2312.14437 |