IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03252606.html
   My bibliography  Save this paper

Optimal control on graphs: existence, uniqueness, and long-term behavior

Author

Listed:
  • Olivier Guéant

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Iuliia Manziuk

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with results on the associated ergodic Hamilton-Jacobi equation.

Suggested Citation

  • Olivier Guéant & Iuliia Manziuk, 2020. "Optimal control on graphs: existence, uniqueness, and long-term behavior," Post-Print hal-03252606, HAL.
    • Handle: RePEc:hal:journl:hal-03252606
    DOI: 10.1051/cocv/2019071
    Note: View the original document on HAL open archive server: https://hal.science/hal-03252606
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03252606/document
    Download Restriction: no
    File URL: https://libkey.io/10.1051/cocv/2019071?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
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2023. "Algorithmic market making in dealer markets with hedging and market impact," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 41-79, January.
    2. Philippe Bergault & Olivier Gu'eant, 2023. "Liquidity Dynamics in RFQ Markets and Impact on Pricing," Papers 2309.04216, arXiv.org, revised Jun 2024.
    3. Jialun Cao & David v{S}iv{s}ka & Lukasz Szpruch & Tanut Treetanthiploet, 2024. "Logarithmic regret in the ergodic Avellaneda-Stoikov market making model," Papers 2409.02025, arXiv.org.

    More about this item

    Keywords

    Optimal control; graphs; asymptotic analysis; Ergodic Hamilton-Jacobi equation;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:hal-03252606. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.