Optimal annuitization with labor income under age-dependent force of mortality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915548495872000 |
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| author | Birungi, Criscent Hyndman, Cody |
| author_facet | Birungi, Criscent Hyndman, Cody |
| contents | We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consumption, portfolio, and labor supply strategies. Our results show that before retirement, investment behavior increases with wealth until a threshold set by labor supply. After retirement, agents tend to consume a larger portion of their wealth. Two main factors influence optimal annuitization decisions as people get older. First, the agent's perspective (demand side); the agent's personal discount rate rises with age, reducing their desire to annuitize. Second, the insurer's perspective (supply side); insurers offer higher payout rates (mortality credits). Our model demonstrates that beyond a certain age, sharply declining survival probabilities make annuitization substantially optimal, as the powerful incentive of mortality credits outweighs the agent's high personal discount rate. Finally, post-retirement labor income serves as a direct substitute for annuitization by providing an alternative stable income source. It enhances the financial security of retirees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal annuitization with labor income under age-dependent force of mortality Birungi, Criscent Hyndman, Cody Portfolio Management Optimization and Control 91G10 (Primary) 91G05, 60G40, 91B16, 93E20 (Secondary) We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consumption, portfolio, and labor supply strategies. Our results show that before retirement, investment behavior increases with wealth until a threshold set by labor supply. After retirement, agents tend to consume a larger portion of their wealth. Two main factors influence optimal annuitization decisions as people get older. First, the agent's perspective (demand side); the agent's personal discount rate rises with age, reducing their desire to annuitize. Second, the insurer's perspective (supply side); insurers offer higher payout rates (mortality credits). Our model demonstrates that beyond a certain age, sharply declining survival probabilities make annuitization substantially optimal, as the powerful incentive of mortality credits outweighs the agent's high personal discount rate. Finally, post-retirement labor income serves as a direct substitute for annuitization by providing an alternative stable income source. It enhances the financial security of retirees. |
| title | Optimal annuitization with labor income under age-dependent force of mortality |
| topic | Portfolio Management Optimization and Control 91G10 (Primary) 91G05, 60G40, 91B16, 93E20 (Secondary) |
| url | https://arxiv.org/abs/2510.10371 |