Optimal consumption under loss-averse multiplicative habit-formation preferences
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912974630813696 |
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| author | Angoshtari, Bahman Yu, Xiang Yuan, Fengyi |
| author_facet | Angoshtari, Bahman Yu, Xiang Yuan, Fengyi |
| contents | This paper studies a loss-averse version of the multiplicative habit formation preference and the corresponding optimal investment and consumption strategies over an infinite horizon. The agent's consumption preference is depicted by a general S-shaped utility function of her consumption-to-habit ratio. By considering the concave envelope of the S-shaped utility and the associated dual value function, we provide a thorough analysis of the HJB equation for the concavified problem via studying a related nonlinear free boundary problem. Based on established properties of the solution to this free boundary problem, we obtain the optimal consumption and investment policies in feedback form. Some new and technical verification arguments are developed to cope with generality of the utility function. The equivalence between the original problem and the concavified problem readily follows from the structure of the feedback controls. We also discuss some quantitative properties of the optimal policies, complemented by illustrative numerical examples and their financial implications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal consumption under loss-averse multiplicative habit-formation preferences Angoshtari, Bahman Yu, Xiang Yuan, Fengyi Mathematical Finance Portfolio Management 93E20, 91G10, 9101 This paper studies a loss-averse version of the multiplicative habit formation preference and the corresponding optimal investment and consumption strategies over an infinite horizon. The agent's consumption preference is depicted by a general S-shaped utility function of her consumption-to-habit ratio. By considering the concave envelope of the S-shaped utility and the associated dual value function, we provide a thorough analysis of the HJB equation for the concavified problem via studying a related nonlinear free boundary problem. Based on established properties of the solution to this free boundary problem, we obtain the optimal consumption and investment policies in feedback form. Some new and technical verification arguments are developed to cope with generality of the utility function. The equivalence between the original problem and the concavified problem readily follows from the structure of the feedback controls. We also discuss some quantitative properties of the optimal policies, complemented by illustrative numerical examples and their financial implications. |
| title | Optimal consumption under loss-averse multiplicative habit-formation preferences |
| topic | Mathematical Finance Portfolio Management 93E20, 91G10, 9101 |
| url | https://arxiv.org/abs/2406.20063 |