IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v58y2021i3d10.1007_s10614-020-10056-8.html
   My bibliography  Save this article

An Integral Equation Representation for Optimal Retirement Strategies in Portfolio Selection Problem

Author

Listed:
  • Junkee Jeon

    (Kyung Hee University)

  • Hyeng Keun Koo

    (Ajou University)

  • Yong Hyun Shin

    (Sookmyung Women’s University)

  • Zhou Yang

    (South China Normal University)

Abstract

In this paper we study the consumption and portfolio selection problem of a finitely-lived economic agent with an early retirement option, that is, the agent can choose her/his early retirement time before a mandatory retirement time. Based on the theoretical results in Yang and Koo (Math Oper Res, 43(4):1378–1404, 2018), we derive an integral equation satisfied by the optimal retirement boundary or free boundary using the Mellin transform technique. We also derive integral equation representations for the optimal consumption-portfolio strategies and the optimal wealth process. By using the recursive integration method, we obtain the numerical solutions for the integral equations and discuss economic implications for the optimal retirement strategies by using numerical solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:58:y:2021:i:3:d:10.1007_s10614-020-10056-8
    DOI: 10.1007/s10614-020-10056-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-020-10056-8
    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/s10614-020-10056-8?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. Byung Hwa Lim & Yong Shin, 2011. "Optimal investment, consumption and retirement decision with disutility and borrowing constraints," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1581-1592.
    2. Klaus Prettner & David Canning, 2014. "Increasing life expectancy and optimal retirement in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 191-217, May.
    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. Gruber, Jonathan & Wise, David, 1998. "Social Security and Retirement: An International Comparison," American Economic Review, American Economic Association, vol. 88(2), pages 158-163, May.
    5. Hurd, Michael D, 1990. "Research on the Elderly: Economic Status, Retirement, and Consumption and Saving," Journal of Economic Literature, American Economic Association, vol. 28(2), pages 565-637, June.
    6. Kyoung Jin Choi & Gyoocheol Shim, 2006. "Disutility, Optimal Retirement, And Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 443-467, April.
    7. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    8. Bloom, David E. & Canning, David & Mansfield, Richard K. & Moore, Michael, 2007. "Demographic change, social security systems, and savings," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 92-114, January.
    9. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    10. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
    11. Kyoung Jin Choi & Gyoocheol Shim & Yong Hyun Shin, 2008. "Optimal Portfolio, Consumption‐Leisure And Retirement Choice Problem With Ces Utility," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 445-472, July.
    12. David E. Bloom & David Canning & Michael Moore, 2007. "A Theory of Retirement," NBER Working Papers 13630, National Bureau of Economic Research, Inc.
    13. 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.
    14. Hurd, Michael D, 1989. "Mortality Risk and Bequests," Econometrica, Econometric Society, vol. 57(4), pages 779-813, July.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. 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.
    17. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    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. Martire, Antonio Luciano, 2022. "Volterra integral equations: An approach based on Lipschitz-continuity," Applied Mathematics and Computation, Elsevier, vol. 435(C).

    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. 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.
    2. 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).
    3. 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.
    4. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    5. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    6. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    7. 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.
    8. Lee, Ho-Seok & Lim, Byung Hwa, 2023. "Personal bankruptcy and post-bankruptcy liquidity constraint," Journal of Banking & Finance, Elsevier, vol. 152(C).
    9. 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.
    10. Park, Seyoung, 2015. "A generalization of Yaari’s result on annuitization with optimal retirement," Economics Letters, Elsevier, vol. 137(C), pages 17-20.
    11. Bong-Gyu Jang & Hyeng Keun Koo & Yuna Rhee, 2016. "Asset demands and consumption with longevity risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 587-633, August.
    12. Bäuerle Nicole & Chen An, 2019. "Optimal retirement planning under partial information," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 37-55, December.
    13. Park, Seyoung, 2020. "Verification theorems for models of optimal consumption and investment with annuitization," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 36-44.
    14. Chae, Jiwon & Jang, Bong-Gyu & Park, Seyoung, 2023. "Analytic approach for models of optimal retirement with disability risk," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 68-75.
    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. 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.
    17. 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.
    18. Chen, An & Hentschel, Felix & Steffensen, Mogens, 2021. "On retirement time decision making," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 107-129.
    19. 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.
    20. An Chen & Giorgio Ferrari & Shihao Zhu, 2023. "Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning," Papers 2312.02943, arXiv.org.

    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:kap:compec:v:58:y:2021:i:3:d:10.1007_s10614-020-10056-8. 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.