IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i6p989-d1614552.html
   My bibliography  Save this article

Optimal Consumption, Leisure, and Investment with Partial Borrowing Constraints over a Finite Horizon

Author

Listed:
  • Geonwoo Kim

    (School of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
    These authors contributed equally to this work.)

  • Junkee Jeon

    (Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of Korea
    These authors contributed equally to this work.)

Abstract

We study an optimal consumption, leisure, and investment problem over a finite horizon in a continuous-time financial market with partial borrowing constraints. The agent derives utility from consumption and leisure, with preferences represented by a Cobb–Douglas utility function. The agent allocates time between work and leisure, earning wage income based on working hours. A key feature of our model is a partial borrowing constraint that limits the agent’s debt capacity to a fraction of the present value of their maximum future labor income. We employ the dual-martingale approach to derive the optimal consumption, leisure, and investment strategies. The problem reduces to solving a variational inequality with a free boundary, which we analyze using analytical and numerical methods. We provide an integral equation representation of the free boundary and solve it numerically via a recursive integration method. Our results highlight the impact of the borrowing constraint on the agent’s optimal decisions and the interplay between labor supply, consumption, and portfolio choice.

Suggested Citation

  • Geonwoo Kim & Junkee Jeon, 2025. "Optimal Consumption, Leisure, and Investment with Partial Borrowing Constraints over a Finite Horizon," Mathematics, MDPI, vol. 13(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:989-:d:1614552
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/6/989/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/6/989/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:6:p:989-:d:1614552. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.