IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v111y2024ics0304406824000028.html
   My bibliography  Save this article

On the fragility of the basis on the Hamilton–Jacobi–Bellman equation in economic dynamics

Author

Listed:
  • Hosoya, Yuhki

Abstract

In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton–Jacobi–Bellman equation but the value function does not satisfy this equation. We consider the cause of this phenomenon, and find that the lack of a solution to the original problem is crucial. We show that under several conditions, there exists a solution to the original problem if and only if the value function solves the Hamilton–Jacobi–Bellman equation. Moreover, in this case, the value function is the unique nondecreasing concave solution to the Hamilton–Jacobi–Bellman equation. We also show that without our conditions, this uniqueness result does not hold.

Suggested Citation

  • Hosoya, Yuhki, 2024. "On the fragility of the basis on the Hamilton–Jacobi–Bellman equation in economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    • Handle: RePEc:eee:mateco:v:111:y:2024:i:c:s0304406824000028
    DOI: 10.1016/j.jmateco.2024.102940
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406824000028
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2024.102940?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.

    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:eee:mateco:v:111:y:2024:i:c:s0304406824000028. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.