Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917038009614336 |
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| author | Feng, Zixin Tian, Dejian Zheng, Harry |
| author_facet | Feng, Zixin Tian, Dejian Zheng, Harry |
| contents | The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial scenarios compared to the Markovian setting. The optimal consumption and investment strategies are derived using the martingale optimal principle and quadratic backward stochastic differential equations (BSDEs) whose solutions admit some exponential moment. This integrability property plays a crucial role in establishing a key martingale argument. In addition, the paper also examines the associated dual problem and several models within the specified parameter framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets Feng, Zixin Tian, Dejian Zheng, Harry Mathematical Finance 91G10, 60H30 The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial scenarios compared to the Markovian setting. The optimal consumption and investment strategies are derived using the martingale optimal principle and quadratic backward stochastic differential equations (BSDEs) whose solutions admit some exponential moment. This integrability property plays a crucial role in establishing a key martingale argument. In addition, the paper also examines the associated dual problem and several models within the specified parameter framework. |
| title | Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets |
| topic | Mathematical Finance 91G10, 60H30 |
| url | https://arxiv.org/abs/2407.19995 |