Optimal Comfortable Consumption under Epstein-Zin utility
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913701462802432 |
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| author | Tian, Dejian Tian, Weidong Zhu, Zimu |
| author_facet | Tian, Dejian Tian, Weidong Zhu, Zimu |
| contents | We introduce a novel approach to solving the optimal portfolio choice problem under Epstein-Zin utility with a time-varying consumption constraint, where analytical expressions for the value function and the dual value function are not obtainable. We first establish several key properties of the value function, with a particular focus on the $C^2$ smoothness property. We then characterize the value function and prove the verification theorem by using the linearization method to the highly nonlinear HJB equation, despite the candidate value function being unknown a priori. Additionally, we present the sufficient and necessary conditions for the value function and explicitly characterize the constrained region. Our approach is versatile and can be applied to other portfolio choice problems with constraints where explicit solutions for both the primal and dual problems are unavailable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Comfortable Consumption under Epstein-Zin utility Tian, Dejian Tian, Weidong Zhu, Zimu Optimization and Control 93E20, 91G10 We introduce a novel approach to solving the optimal portfolio choice problem under Epstein-Zin utility with a time-varying consumption constraint, where analytical expressions for the value function and the dual value function are not obtainable. We first establish several key properties of the value function, with a particular focus on the $C^2$ smoothness property. We then characterize the value function and prove the verification theorem by using the linearization method to the highly nonlinear HJB equation, despite the candidate value function being unknown a priori. Additionally, we present the sufficient and necessary conditions for the value function and explicitly characterize the constrained region. Our approach is versatile and can be applied to other portfolio choice problems with constraints where explicit solutions for both the primal and dual problems are unavailable. |
| title | Optimal Comfortable Consumption under Epstein-Zin utility |
| topic | Optimization and Control 93E20, 91G10 |
| url | https://arxiv.org/abs/2502.15138 |