IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v62y2005i2p297-318.html
   My bibliography  Save this article

Ergodic and adaptive control of hidden Markov models

Author

Listed:
  • T. Duncan
  • B. Pasik-Duncan
  • L. Stettner

Abstract

A partially observed stochastic system is described by a discrete time pair of Markov processes. The observed state process has a transition probability that is controlled and depends on a hidden Markov process that also can be controlled. The hidden Markov process is completely observed in a closed set, which in particular can be the empty set and only observed through the other process in the complement of this closed set. An ergodic control problem is solved by a vanishing discount approach. In the case when the transition operators for the observed state process and the hidden Markov process depend on a parameter and the closed set, where the hidden Markov process is completely observed, is nonempty and recurrent an adaptive control is constructed based on this family of estimates that is almost optimal. Copyright Springer-Verlag Berlin Heidelberg 2005

Suggested Citation

  • T. Duncan & B. Pasik-Duncan & L. Stettner, 2005. "Ergodic and adaptive control of hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 297-318, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:297-318
    DOI: 10.1007/s00186-005-0010-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-005-0010-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-005-0010-z?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. Borkar, V.S.Vivek S. & Budhiraja, Amarjit, 2004. "A further remark on dynamic programming for partially observed Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 79-93, July.
    2. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, January.
    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. Zhiqiang Li & Jie Xiong, 2015. "Stability of the filter with Poisson observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 293-313, October.
    2. Stéphane Chrétien & Juan-Pablo Ortega, 2018. "A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone," Mathematics, MDPI, vol. 6(3), pages 1-5, 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. Bank, Peter & Riedel, Frank, 1999. "Optimal consumption choice under uncertainty with intertemporal substitution," SFB 373 Discussion Papers 1999,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Guo, Fenglong, 2022. "Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    3. M. C. Chiu & D. Li, 2009. "Asset-Liability Management Under the Safety-First Principle," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 455-478, December.
    4. Jan Kallsen & Johannes Muhle-Karbe, 2010. "Utility Maximization In Affine Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 459-477.
    5. Jacobovic, Royi & Kella, Offer, 2020. "Minimizing a stochastic convex function subject to stochastic constraints and some applications," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 7004-7018.
    6. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    7. Jan Kallsen & Johannes Muhle-Karbe, 2009. "Utility maximization in models with conditionally independent increments," Papers 0911.3608, arXiv.org.
    8. Benjamin Avanzi & Hayden Lau & Mogens Steffensen, 2022. "Optimal reinsurance design under solvency constraints," Papers 2203.16108, arXiv.org, revised Jun 2023.
    9. Mayank Goel & K. Suresh Kumar, 2007. "A Risk-Sensitive Portfolio Optimization Problem with Fixed Incomes Securities," Papers 0711.2718, arXiv.org.
    10. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Working Papers hal-01058657, HAL.
    11. Lihua Chen & Ralf Korn, 2019. "Worst-case portfolio optimization in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 197-227, October.
    12. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    13. Marcel Prokopczuk, 2011. "Optimal portfolio choice in the presence of domestic systemic risk: empirical evidence from stock markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 141-168, November.
    14. Nicole Bäuerle & Stefanie Grether, 2015. "Complete markets do not allow free cash flow streams," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 137-146, April.
    15. M. Goel & K. S. Kumar, 2009. "Risk-Sensitive Portfolio Optimization Problems with Fixed Income Securities," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 67-84, July.
    16. Riedel, Frank, 2009. "Optimal consumption choice with intolerance for declining standard of living," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 449-464, July.
    17. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Papers 1408.6455, arXiv.org.
    18. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    19. Anne MacKay & Adriana Ocejo, 2022. "Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1021-1049, June.
    20. Cheung, Ka Chun & Yang, Hailiang, 2005. "Optimal stopping behavior of equity-linked investment products with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 599-614, December.

    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:mathme:v:62:y:2005:i:2:p:297-318. 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.