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Optimal Consumption and Portfolio Selection with Early Retirement Option

Author

Listed:
  • Zhou Yang

    (School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China)

  • Hyeng Keun Koo

    (Department of Financial Engineering, Ajou University, Yeongtong-gu, Suwon, 16499, Korea)

Abstract

In this paper we propose an approach to investigate a model of consumption and investment with a mandatory retirement date and early retirement option; we analyze properties of the optimal strategy and thereby contribute to understanding the interaction between retirement, consumption, and portfolio decisions in the presence of both the important features of retirement. In particular, we provide a characterization of the threshold of wealth as a function of time, and we show that it is strictly decreasing near the mandatory retirement date. The threshold is similar to the early exercise boundary of an American option in the sense that if the agent’s wealth is above or equal to the threshold level, then the agent immediately retires. We also provide comparative static analysis.

Suggested Citation

  • Zhou Yang & Hyeng Keun Koo, 2018. "Optimal Consumption and Portfolio Selection with Early Retirement Option," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1378-1404, November.
    • Handle: RePEc:inm:ormoor:v:43:y:2018:i:4:p:1378-1404
    DOI: 10.1287/moor.2017.0909
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    References listed on IDEAS

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    Cited by:

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    2. He, Lin & Liang, Zongxia & Song, Yilun & Ye, Qi, 2022. "Optimal asset allocation, consumption and retirement time with the variation in habitual persistence," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 188-202.
    3. Giorgio Ferrari & Shihao Zhu, 2022. "On a Merton Problem with Irreversible Healthcare Investment," Papers 2212.05317, arXiv.org, revised Dec 2023.
    4. Hyun Jin Jang & Zuo Quan Xu & Harry Zheng, 2020. "Optimal Investment, Heterogeneous Consumption and Best Time for Retirement," Papers 2008.00392, arXiv.org, revised Jun 2022.
    5. Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    6. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    7. Guohui Guan & Qitao Huang & Zongxia Liang & Fengyi Yuan, 2020. "Retirement decision with addictive habit persistence in a jump diffusion market," Papers 2011.10166, arXiv.org, revised Feb 2024.
    8. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    9. Jeon, Junkee & Koo, Hyeng Keun & Park, Kyunghyun, 2021. "Finite horizon portfolio selection with durable goods," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 55-67.
    10. Junkee Jeon & Hyeng Keun Koo & Kyunghyun Park, 2018. "Optimal Insurance with Limited Commitment in a Finite Horizon," Papers 1812.11669, arXiv.org, revised Jan 2019.
    11. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2021. "Optimal Investment and Consumption under a Habit-Formation Constraint," Papers 2102.03414, arXiv.org, revised Nov 2021.
    12. Ling Wang & Kexin Chen & Mei Choi Chiu & Hoi Ying Wong, 2021. "Optimal Expansion of Business Opportunity," Papers 2112.06706, arXiv.org.
    13. Bae, Se Yung & Jeon, Junkee & Koo, Hyeng Keun & Park, Kyunghyun, 2020. "Social insurance for the elderly," Economic Modelling, Elsevier, vol. 91(C), pages 274-299.
    14. Wang, Ling & Chen, Kexin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Optimal expansion of business opportunity," European Journal of Operational Research, Elsevier, vol. 309(1), pages 432-445.
    15. Lin He & Zongxia Liang & Yilun Song & Qi Ye, 2021. "Optimal Retirement Time and Consumption with the Variation in Habitual Persistence," Papers 2103.16800, arXiv.org.
    16. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    17. Zhou Yang & Junkee Jeon, 2023. "A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization," Papers 2309.12588, arXiv.org.
    18. Junkee Jeon & Hyeng Keun Koo & Yong Hyun Shin & Zhou Yang, 2021. "An Integral Equation Representation for Optimal Retirement Strategies in Portfolio Selection Problem," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 885-914, October.
    19. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    20. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    21. Junkee Jeon & Kyunghyun Park, 2021. "Portfolio selection with drawdown constraint on consumption: a generalization model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 243-289, April.
    22. Hyeng Keun Koo & Kum-Hwan Roh & Yong Hyun Shin, 2021. "Optimal consumption/investment and retirement with necessities and luxuries," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 281-317, October.
    23. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    24. Ferrari, Giorgio & Zhu, Shihao, 2022. "Consumption Descision, Portfolio Choice and Healthcare Irreversible Investment," Center for Mathematical Economics Working Papers 671, Center for Mathematical Economics, Bielefeld University.
    25. Luo, Shangzhen & Wang, Mingming & Zhu, Wei, 2022. "Time-inconsistent life-cycle consumption and retirement choice with mortality risk," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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