IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v101y2025i3d10.1007_s00186-025-00899-y.html
   My bibliography  Save this article

Optimal consumption and investment with a costly reversible job-switching option

Author

Listed:
  • Gyoocheol Shim

    (Ajou University)

  • Junkee Jeon

    (Kyung Hee University)

Abstract

In this paper, we investigate an optimal consumption and investment problem for an economic agent who possesses the option to switch jobs. We assume that two types of jobs are available. One type offers higher income but also entails a greater level of disutility from labor compared to the other type. The option to switch jobs is reversible, enabling the agent to transition between them at any time, albeit incurring a cost. Our utility maximization problem involves aspects of both optimal switching and stochastic control. By employing the martingale-duality approach, we reduce the maximization problem to a pure optimal switching problem. This problem encompasses a system of two variational inequalities, which admits a continuously differentiable and closed-form solution. We fully characterize the optimal job-switching strategy based on two free boundaries. Furthermore, we derive a closed-form solution for the optimal consumption and portfolio strategy through the duality relationship.

Suggested Citation

  • Gyoocheol Shim & Junkee Jeon, 2025. "Optimal consumption and investment with a costly reversible job-switching option," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(3), pages 459-506, June.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00899-y
    DOI: 10.1007/s00186-025-00899-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-025-00899-y
    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/s00186-025-00899-y?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    4. Kyoung Jin Choi & Gyoocheol Shim, 2006. "Disutility, Optimal Retirement, And Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 443-467, April.
    5. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    6. 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.
    7. 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.
    8. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    9. Randall Martyr, 2016. "Finite-Horizon Optimal Multiple Switching with Signed Switching Costs," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1432-1447, November.
    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. Geonwoo Kim & Junkee Jeon, 2025. "Optimal Job-Switching and Portfolio Decisions with a Mandatory Retirement Date," Mathematics, MDPI, vol. 13(17), pages 1-16, September.

    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. An, Jongbong & Jeon, Junkee & Kim, Takwon, 2025. "Optimal portfolio and retirement decisions with costly job switching options," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    2. Zhou Yang & Junkee Jeon, 2023. "A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization," Papers 2309.12588, arXiv.org.
    3. 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).
    4. 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.
    5. 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.
    6. Geonwoo Kim & Junkee Jeon, 2025. "Optimal Job-Switching and Portfolio Decisions with a Mandatory Retirement Date," Mathematics, MDPI, vol. 13(17), pages 1-16, September.
    7. Geonwoo Kim & Junkee Jeon, 2025. "Optimal Consumption, Portfolio, and Retirement Under Implementation Delay," Mathematics, MDPI, vol. 13(17), pages 1-12, August.
    8. Junkee Jeon & Hyeng Keun Koo & Minsuk Kwak, 2024. "Human capital and portfolio choice: borrowing constraint and reversible retirement," Mathematics and Financial Economics, Springer, volume 18, number 5.
    9. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    10. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    11. Park, Seyoung, 2015. "A generalization of Yaari’s result on annuitization with optimal retirement," Economics Letters, Elsevier, vol. 137(C), pages 17-20.
    12. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.
    13. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    14. Francisco Gomes & Michael Haliassos & Tarun Ramadorai, 2021. "Household Finance," Journal of Economic Literature, American Economic Association, vol. 59(3), pages 919-1000, September.
    15. Zuo Quan Xu & Fahuai Yi, 2014. "An Optimal Consumption-Investment Model with Constraint on Consumption," Papers 1404.7698, arXiv.org.
    16. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    17. Chellathurai, Thamayanthi & Draviam, Thangaraj, 2007. "Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2168-2195, July.
    18. Tae Ung Gang & Seyoung Park & Yong Hyun Shin, 2025. "Income Disaster, Role of Income Support, and Optimal Retirement," Papers 2509.12874, arXiv.org, revised Sep 2025.
    19. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    20. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:101:y:2025:i:3:d:10.1007_s00186-025-00899-y. 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.