IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v206y2013i1p197-21910.1007-s10479-012-1292-1.html
   My bibliography  Save this article

Constrained Markov decision processes with first passage criteria

Author

Listed:
  • Yonghui Huang
  • Qingda Wei
  • Xianping Guo

Abstract

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1292-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1292-1?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.

    References listed on IDEAS

    as
    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. Lanlan Zhang & Xianping Guo, 2008. "Constrained continuous-time Markov decision processes with average criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 323-340, April.
    6. 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.
    7. 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.
    8. 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

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


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juan González-Hernández & Raquiel López-Martínez & J. Pérez-Hernández, 2007. "Markov control processes with randomized discounted cost," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 27-44, February.
    2. Guo, Xianping & Zhang, Wenzhao, 2014. "Convergence of controlled models and finite-state approximation for discounted continuous-time Markov decision processes with constraints," European Journal of Operational Research, Elsevier, vol. 238(2), pages 486-496.
    3. Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    4. Héctor Jasso-Fuentes & Tomás Prieto-Rumeau, 2024. "Constrained Markov Decision Processes with Non-constant Discount Factor," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 897-931, August.
    5. Adolfson, Malin, 2001. "Monetary Policy with Incomplete Exchange Rate Pass-Through," SSE/EFI Working Paper Series in Economics and Finance 476, Stockholm School of Economics.
    6. Ellison, Martin, 2006. "The learning cost of interest rate reversals," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1895-1907, November.
    7. Steve Newbold & Charles Griffiths & Christopher C. Moore & Ann Wolverton & Elizabeth Kopits, 2010. "The "Social Cost of Carbon" Made Simple," NCEE Working Paper Series 201007, National Center for Environmental Economics, U.S. Environmental Protection Agency, revised Aug 2010.
    8. Luboš Komárek & Filip Rozsypal, 2009. "Vymezení a vyhodnocení agresivity centrálních bank [Definition and Evaluation of the Central Bank agresivity]," Politická ekonomie, Prague University of Economics and Business, vol. 2009(3), pages 383-404.
    9. Frederick H. Wallace & Gary L. Shelley & Luis F. Cabrera Castellanos, 2004. "Pruebas de la neutralidad monetaria a largo plazo: el caso de Nicaragua," Monetaria, CEMLA, vol. 0(4), pages 407-418, octubre-d.
    10. Mala Raghavan & Mardi Dungey, 2015. "Should ASEAN-5 monetary policy-makers act pre-emptively against stock market bubbles?," Applied Economics, Taylor & Francis Journals, vol. 47(11), pages 1086-1105, March.
    11. Minford, Patrick & Ou, Zhirong, 2013. "Taylor Rule or optimal timeless policy? Reconsidering the Fed's behavior since 1982," Economic Modelling, Elsevier, vol. 32(C), pages 113-123.
    12. Hannes Draack, 2018. "Monetary Policy with Imperfect Signals: The Target Problem in a New Monetarist Approach," ECON - Working Papers 296, Department of Economics - University of Zurich.
    13. Jinho Bae & Chang-Jin Kim & Dong Kim, 2012. "The evolution of the monetary policy regimes in the U.S," Empirical Economics, Springer, vol. 43(2), pages 617-649, October.
    14. Michael D. Bauer & Eric T. Swanson, 2023. "An Alternative Explanation for the "Fed Information Effect"," American Economic Review, American Economic Association, vol. 113(3), pages 664-700, March.
    15. Benigno, Gianluca, 2004. "Real exchange rate persistence and monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 51(3), pages 473-502, April.
    16. Defrancesco, Edi & Gatto, Paola & Rosato, Paolo, 2014. "A ‘component-based’ approach to discounting for natural resource damage assessment," Ecological Economics, Elsevier, vol. 99(C), pages 1-9.
    17. Ayşegül Ladin SÜMER, 2020. "Optimal Taylor rule in the new era central banking perspective," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(1(622), S), pages 159-170, Spring.
    18. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    19. Hansen, Anders Chr., 2006. "Do declining discount rates lead to time inconsistent economic advice?," Ecological Economics, Elsevier, vol. 60(1), pages 138-144, November.
    20. Silvia Sgherri & Tamim Bayoumi, 2004. "Monetary Magic? How the Fed Improved the Supply Side of the Economy," Econometric Society 2004 Australasian Meetings 20, Econometric Society.

    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: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.

    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 bibliographic 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.

    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.