IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v93y2021i2d10.1007_s00186-020-00734-6.html
   My bibliography  Save this article

Portfolio selection with drawdown constraint on consumption: a generalization model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-020-00734-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-020-00734-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    2. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    3. 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.
    4. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    5. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    6. Avinash K. Dixit & Robert S. Pindyck, 1998. "Expandability, Reversibility, and Optimal Capacity Choice," NBER Working Papers 6373, National Bureau of Economic Research, Inc.
    7. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    8. Riedel, Frank, 2009. "Optimal consumption choice with intolerance for declining standard of living," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 449-464, July.
    9. Philip H. Dybvig, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 287-313.
    10. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2012. "An Empirical Evaluation of the Long-Run Risks Model for Asset Prices," Critical Finance Review, now publishers, vol. 1(1), pages 183-221, January.
    11. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    12. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    13. Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    14. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2018. "Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates," Papers 1806.07499, arXiv.org, revised Mar 2019.
    15. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    3. Kyoung Jin Choi & Junkee Jeon & Hyeng Keun Koo, 2018. "Duesenberry's Theory of Consumption: Habit, Learning, and Ratcheting," Papers 1812.10038, arXiv.org.
    4. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    5. Adrien Verdelhan, 2010. "A Habit‐Based Explanation of the Exchange Rate Risk Premium," Journal of Finance, American Finance Association, vol. 65(1), pages 123-146, February.
    6. 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.
    7. Zhou, Y., 2014. "Essays on habit formation and inflation hedging," Other publications TiSEM 4886da12-1b84-4fd9-aa07-3, Tilburg University, School of Economics and Management.
    8. 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.
    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. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    11. Tobias Adrian & Richard K. Crump & Erik Vogt, 2019. "Nonlinearity and Flight‐to‐Safety in the Risk‐Return Trade‐Off for Stocks and Bonds," Journal of Finance, American Finance Association, vol. 74(4), pages 1931-1973, August.
    12. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    13. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    14. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    15. Francisco Gomes & Alexander Michaelides, 2003. "Portfolio Choice With Internal Habit Formation: A Life-Cycle Model With Uninsurable Labor Income Risk," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 729-766, October.
    16. 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.
    17. Bernard Dumas & Alexander Kurshev & Raman Uppal, 2009. "Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility," Journal of Finance, American Finance Association, vol. 64(2), pages 579-629, April.
    18. Xianzhe Chen & Weidong Tian, 2014. "Optimal portfolio choice and consistent performance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 453-474, October.
    19. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    20. Yeung Lewis Chan & Leonid Kogan, 2002. "Catching Up with the Joneses: Heterogeneous Preferences and the Dynamics of Asset Prices," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1255-1285, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:93:y:2021:i:2:d:10.1007_s00186-020-00734-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.