IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v73y1998i1p101-118.html
   My bibliography  Save this article

Markov-achievable payoffs for finite-horizon decision models

Author

Listed:
  • Pestien, Victor
  • Wang, Xiaobo

Abstract

Consider the class of n-stage decision models with state space S, action space A, and payoff function g : (S x A)n x S --> R. The function g is Markov-achievable if for any possible set of available randomized actions and all transition laws, each plan has a corresponding Markov plan whose value is at least as good. A condition on g, called the "non-forking linear sections property", is necessary and sufficient for g to be Markov achievable. If g satisfies the slightly stronger "general linear sections property", then g can be written as a sum of products of certain simple neighboring-stage payoffs.

Suggested Citation

  • Pestien, Victor & Wang, Xiaobo, 1998. "Markov-achievable payoffs for finite-horizon decision models," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 101-118, January.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:1:p:101-118
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00095-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Uriel G. Rothblum, 1984. "Multiplicative Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 6-24, February.
    2. Hill, Theodore P. & Pestien, Victor C., 1987. "The existence of good Markov strategies for decision processes with general payoffs," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 61-76, February.
    3. Eugene A. Feinberg & Adam Shwartz, 1995. "Constrained Markov Decision Models with Weighted Discounted Rewards," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 302-320, May.
    4. Pestien, Victor & Wang, Xiaobo, 1993. "Finite-stage reward functions having the Markov adequacy property," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 129-151, May.
    5. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
    Full references (including those not matched with items on IDEAS)

    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. Basu, Arnab & Ghosh, Mrinal Kanti, 2014. "Zero-sum risk-sensitive stochastic games on a countable state space," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 961-983.
    2. V. S. Borkar & S. P. Meyn, 2002. "Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 192-209, February.
    3. Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, November.
    4. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    5. Arnab Basu & Mrinal K. Ghosh, 2018. "Nonzero-Sum Risk-Sensitive Stochastic Games on a Countable State Space," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 516-532, May.
    6. Krishnamurthy Iyer & Nandyala Hemachandra, 2010. "Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 401-425, June.
    7. Zeynep Erkin & Matthew D. Bailey & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2010. "Eliciting Patients' Revealed Preferences: An Inverse Markov Decision Process Approach," Decision Analysis, INFORMS, vol. 7(4), pages 358-365, December.
    8. Monahan, George E. & Sobel, Matthew J., 1997. "Risk-Sensitive Dynamic Market Share Attraction Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 149-160, August.
    9. Erick Delage & Shie Mannor, 2010. "Percentile Optimization for Markov Decision Processes with Parameter Uncertainty," Operations Research, INFORMS, vol. 58(1), pages 203-213, February.
    10. Naci Saldi & Tamer Bas¸ ar & Maxim Raginsky, 2020. "Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1596-1620, November.
    11. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2015. "Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 83-112, February.
    12. Dellaert, N.P. & Frenk, J.B.G. & van Rijsoort, L.P., 1993. "Optimal claim behaviour for vehicle damage insurances," Econometric Institute Research Papers 11669, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Rolando Cavazos-Cadena, 2009. "Solutions of the average cost optimality equation for finite Markov decision chains: risk-sensitive and risk-neutral criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 541-566, December.
    14. Rolando Cavazos-Cadena, 2018. "Characterization of the Optimal Risk-Sensitive Average Cost in Denumerable Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 1025-1050, August.
    15. Grzegorz Hałaj, 2016. "Dynamic Balance Sheet Model With Liquidity Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-37, November.
    16. Ohlmann, Jeffrey W. & Bean, James C., 2009. "Resource-constrained management of heterogeneous assets with stochastic deterioration," European Journal of Operational Research, Elsevier, vol. 199(1), pages 198-208, November.
    17. Xianggang Lu & Lin Sun, 2023. "Discounted Risk-Sensitive Optimal Control of Switching Diffusions: Viscosity Solution and Numerical Approximation," Mathematics, MDPI, vol. 12(1), pages 1-24, December.
    18. Kumar, Uday M & Bhat, Sanjay P. & Kavitha, Veeraruna & Hemachandra, Nandyala, 2023. "Approximate solutions to constrained risk-sensitive Markov decision processes," European Journal of Operational Research, Elsevier, vol. 310(1), pages 249-267.
    19. Daniel Hernández Hernández & Diego Hernández Bustos, 2017. "Local Poisson Equations Associated with Discrete-Time Markov Control Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 1-29, April.
    20. Nicole Bäuerle & Alexander Glauner, 2021. "Minimizing spectral risk measures applied to Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 35-69, August.

    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:eee:spapps:v:73:y:1998:i:1:p:101-118. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.