IDEAS home Printed from
   My bibliography  Save this article

Constrained Markov decision processes with first passage criteria


  • Yonghui Huang


  • Qingda Wei


  • Xianping Guo



This paper deals with constrained Markov decision processes (MDPs) with first passage criteria. The objective is to maximize the expected reward obtained during a first passage time to some target set, and a constraint is imposed on the associated expected cost over this first passage time. The state space is denumerable, and the rewards/costs are possibly unbounded. In addition, the discount factor is state-action dependent and is allowed to be equal to one. We develop suitable conditions for the existence of a constrained optimal policy, which are generalizations of those for constrained MDPs with the standard discount criteria. Moreover, it is revealed that the constrained optimal policy randomizes between two stationary policies differing in at most one state. Finally, we use a controlled queueing system to illustrate our results, which exhibits some advantage of our optimality conditions. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Yonghui Huang & Qingda Wei & Xianping Guo, 2013. "Constrained Markov decision processes with first passage criteria," Annals of Operations Research, Springer, vol. 206(1), pages 197-219, July.
  • Handle: RePEc:spr:annopr:v:206:y:2013:i:1:p:197-219:10.1007/s10479-012-1292-1
    DOI: 10.1007/s10479-012-1292-1

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Sack, Brian & Wieland, Volker, 2000. "Interest-rate smoothing and optimal monetary policy: a review of recent empirical evidence," Journal of Economics and Business, Elsevier, vol. 52(1-2), pages 205-228.
    2. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 461-484, June.
    3. Newell, Richard G. & Pizer, William A., 2003. "Discounting the distant future: how much do uncertain rates increase valuations?," Journal of Environmental Economics and Management, Elsevier, vol. 46(1), pages 52-71, July.
    4. Berument, Hakan & Kilinc, Zubeyir & Ozlale, Umit, 2004. "The effects of different inflation risk premiums on interest rate spreads," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 317-324.
    5. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 461-484, June.
    6. Haberman, Steven & Sung, Joo-Ho, 2005. "Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 103-116, February.
    7. Lee, Pei-Ting & Rosenfield, Donald B., 2005. "When to refinance a mortgage: A dynamic programming approach," European Journal of Operational Research, Elsevier, vol. 166(1), pages 266-277, October.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. David González-Sánchez & Fernando Luque-Vásquez & J. Adolfo Minjárez-Sosa, 2019. "Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies," Dynamic Games and Applications, Springer, vol. 9(1), pages 103-121, March.


    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:annopr:v:206:y:2013:i:1:p:197-219:10.1007/s10479-012-1292-1. See general information about how to correct material in RePEc.

    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). General contact details of provider: .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.