IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2502.17012.html
   My bibliography  Save this paper

A Deterministic and Linear Model of Dynamic Optimization

Author

Listed:
  • Somdeb Lahiri

Abstract

We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the Euler condition and transversality condition being unconditionally sufficient for optimality of a trajectory. We show that the optimal value function is concave and continuous and the optimal trajectory satisfies the functional equation of dynamic programming. Linearity bites when it comes to the definition of optimal decision rules which can no longer be guaranteed to be single-valued. We show that the optimal decision rule is an upper semi-continuous correspondence. For linear cake-eating problems, we obtain monotonicity results for the optimal value function and a conditional monotonicity result for optimal decision rules. We also introduce the concept of a two-phase linear cake eating problem and obtain a necessary condition that must be satisfied by all solutions of such problems.

Suggested Citation

  • Somdeb Lahiri, 2025. "A Deterministic and Linear Model of Dynamic Optimization," Papers 2502.17012, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2502.17012
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2502.17012
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    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:arx:papers:2502.17012. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.