IDEAS home Printed from https://ideas.repec.org/h/spr/isochp/978-0-306-48102-4_22.html
   My bibliography  Save this book chapter

Risk-Sensitive Optimal Control in Communicating Average Markov Decision Chains

In: Modeling Uncertainty

Author

Listed:
  • Rolando Cavazos-Cadena

    (UniversidadAutónoma Agraria Antonio Narro)

  • Emmanuel Fernández-Gaucherand

    (University of Cincinnati)

Abstract

This work concerns discrete-time Markov decision processes with denumerable state space and bounded costs per stage. The performance of a control policy is measured by a (long-run) risk-sensitive average cost criterion associated to a utility function with constant risk sensitivity coefficient λ, and the main objective of the paper is to study the existence of bounded solutions to the risk-sensitive average cost optimality equation for arbitrary values of λ. The main results are as follows: When the state space is finite, if the transition law is communicating, in the sense that under an arbitrary stationary policy transitions are possible between every pair of states, the optimality equation has a bounded solution for arbitrary non-null λ. However, when the state space is infinite and denumerable, the communication requirement and a strong form of the simultaneous Doeblin condition do not yield a bounded solution to the optimality equation if the risk sensitivity coefficie nt has a sufficiently large absolute value, in general.

Suggested Citation

  • Rolando Cavazos-Cadena & Emmanuel Fernández-Gaucherand, 2002. "Risk-Sensitive Optimal Control in Communicating Average Markov Decision Chains," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 515-553, Springer.
    • Handle: RePEc:spr:isochp:978-0-306-48102-4_22
    DOI: 10.1007/0-306-48102-2_22
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:isochp:978-0-306-48102-4_22. 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: 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.