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Portfolio selection with drawdown constraint on consumption: a generalization model

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  • Junkee Jeon

    (Kyung Hee University)

  • Kyunghyun Park

    (Seoul National University)

Abstract

In this study, we generalize the results of Arun (The Merton problem with a drawdown constraint on consumption. Working paper, 2013) on the optimal consumption and investment problem of an infinitely lived agent who does not accept her consumption falling below a fixed proportion of her historically highest level, the so-called drawdown constraint on consumption. We extend the results to a general class of utility functions. We use the martingale method to study the dual problem, which involves the choice of a maximum consumption process. The dual problem can be formulated as a two-dimensional singular control problem, with the free boundary depending on a state variable of the maximum process. We establish the duality theorem and provide semi-closed form solutions regarding the optimal strategies. To highlight our methodology, we present some special cases of utility functions that do not allow for the dimension reduction considered in Arun (2013).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:2:d:10.1007_s00186-020-00734-6
    DOI: 10.1007/s00186-020-00734-6
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    1. Mork, Knut Anton & Harang, Fabian Andsem & Trønnes, Haakon Andreas & Bjerketvedt, Vegard Skonseng, 2023. "Dynamic spending and portfolio decisions with a soft social norm," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    2. Xiaoshan Chen & Xun Li & Fahuai Yi & Xiang Yu, 2022. "Optimal consumption under a drawdown constraint over a finite horizon," Papers 2207.07848, arXiv.org, revised Nov 2024.
    3. Li, Xun & Yu, Xiang & Zhang, Qinyi, 2023. "Optimal consumption and life insurance under shortfall aversion and a drawdown constraint," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 25-45.
    4. Lijun Bo & Yijie Huang & Kaixin Yan & Xiang Yu, 2024. "Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint," Papers 2410.16611, arXiv.org.
    5. Knut Anton Mork & Fabian Andsem Harang & Haakon Andreas Tr{o}nnes & Vegard Skonseng Bjerketvedt, 2022. "Dynamic spending and portfolio decisions with a soft social norm," Papers 2212.10053, arXiv.org.

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