Impact Of Income And Leisure On Optimal Portfolio, Consumption, Retirement Decisions Under Exponential Utility
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916507077836800 |
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| author | Gang, Tae Ung Shin, Yong Hyun |
| author_facet | Gang, Tae Ung Shin, Yong Hyun |
| contents | We study an optimal control problem encompassing investment, consumption, and retirement decisions under exponential (CARA-type) utility. The financial market comprises a bond with constant drift and a stock following geometric Brownian motion. The agent receives continuous income, consumes over time, and has the option to retire irreversibly, gaining increased leisure post-retirement compared to pre-retirement. The objective is to maximize the expected exponential utility of weighted consumption and leisure over an infinite horizon. Using a martingale approach and dual value function, we derive implicit solutions for the optimal portfolio, consumption, and retirement time. The analysis highlights key contributions: first, the equivalent condition for no retirement is characterized by a specific income threshold; second, the influence of income and leisure levels on optimal portfolio, consumption, and retirement decisions is thoroughly examined. These results provide valuable insights into the interplay between financial and lifestyle choices in retirement planning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Impact Of Income And Leisure On Optimal Portfolio, Consumption, Retirement Decisions Under Exponential Utility Gang, Tae Ung Shin, Yong Hyun Optimization and Control 91G10, 93E20 We study an optimal control problem encompassing investment, consumption, and retirement decisions under exponential (CARA-type) utility. The financial market comprises a bond with constant drift and a stock following geometric Brownian motion. The agent receives continuous income, consumes over time, and has the option to retire irreversibly, gaining increased leisure post-retirement compared to pre-retirement. The objective is to maximize the expected exponential utility of weighted consumption and leisure over an infinite horizon. Using a martingale approach and dual value function, we derive implicit solutions for the optimal portfolio, consumption, and retirement time. The analysis highlights key contributions: first, the equivalent condition for no retirement is characterized by a specific income threshold; second, the influence of income and leisure levels on optimal portfolio, consumption, and retirement decisions is thoroughly examined. These results provide valuable insights into the interplay between financial and lifestyle choices in retirement planning. |
| title | Impact Of Income And Leisure On Optimal Portfolio, Consumption, Retirement Decisions Under Exponential Utility |
| topic | Optimization and Control 91G10, 93E20 |
| url | https://arxiv.org/abs/2412.03001 |