IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v49y2001i4p516-530.html
   My bibliography  Save this article

Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming

Author

Listed:
  • Kurt Helmes

    (Institute of Operations Research, Humboldt University of Berlin, Berlin, Germany)

  • Stefan Röhl

    (Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany)

  • Richard H. Stockbridge

    (Department of Statistics, University of Kentucky, Lexington, Kentucky)

Abstract

We provide a new approach to the numerical computation of moments of the exit time distribution of Markov processes. The method relies on a linear programming formulation of a process exiting from a bounded domain. The LP formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments. The conditions the moments have to satisfy are derived directly from the generator of the Markov process and are not based on some approximation of the process. Excellent software is readily available because the computations involve finite dimensional linear programs.

Suggested Citation

  • Kurt Helmes & Stefan Röhl & Richard H. Stockbridge, 2001. "Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming," Operations Research, INFORMS, vol. 49(4), pages 516-530, August.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:4:p:516-530
    DOI: 10.1287/opre.49.4.516.11221
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.49.4.516.11221
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.49.4.516.11221?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
    ---><---

    References listed on IDEAS

    as
    1. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, January.
    2. Dawson, Donald A., 1980. "Qualitative behavior of geostochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 10(1), pages 1-31, June.
    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. Kurt Helmes & Stefan Röhl, 2008. "A Geometrical Characterization of Multidimensional Hausdorff Polytopes with Applications to Exit Time Problems," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 315-326, May.

    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. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    2. Situngkir, Hokky, 2006. "Value at Risk yang memperhatikan sifat statistika distribusi return," MPRA Paper 895, University Library of Munich, Germany.
    3. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    4. Federico Bandi & Peter C. B. Phillips, 2000. "Accelerated Asymptotics for Diffusion Model Estimation," Econometric Society World Congress 2000 Contributed Papers 1656, Econometric Society.
    5. Richmond, Peter & Sabatelli, Lorenzo, 2004. "Peer pressure and Generalised Lotka Volterra models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 344-348.
    6. Hokky Situngkir & Yohanes Surya, 2004. "Stylized Statistical Facts of Indonesian Financial Data: Empirical Study of Several Stock Indexes in Indonesia," Papers cond-mat/0403465, arXiv.org.
    7. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Skewness and Kurtosis Implied by Option Prices: A Second Comment," FMG Discussion Papers dp419, Financial Markets Group.
    8. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    9. José Carlos Ramirez Sánchez, 2004. "Usos y limitaciones de los procesos estocásticos en el tratamiento de distribuciones de rendimientos con colas gordas," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 19(1), pages 51-76, June.
    10. Marcin Magdziarz & Janusz Gajda, 2012. "Anomalous dynamics of Black–Scholes model time-changed by inverse subordinators," HSC Research Reports HSC/12/04, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    11. Shen, Weixi & Xu, Huiping, 2005. "The valuation of unit-linked policies with or without surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 79-92, February.
    12. Rockerbie, Duane W. & Easton, Stephen T., 2009. "Commercial banks, default insurance and IMF reforms," Economics Discussion Papers 2009-39, Kiel Institute for the World Economy (IfW Kiel).
    13. McCauley, Joseph l., 2004. "Thermodynamic analogies in economics and finance: instability of markets," MPRA Paper 2159, University Library of Munich, Germany.
    14. Frehen, Rik G.P. & Hoevenaars, Roy P.M.M. & Palm, Franz C. & Schotman, Peter C., 2008. "Regret aversion and annuity risk in defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1050-1061, June.
    15. Ryle Perera, 2000. "The role of index bonds in universal currency hedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 271-284.
    16. J.L. McCauley & G.h. Gunaratne, 2002. "An empirical model of volatility of returns and option pricing," Computing in Economics and Finance 2002 186, Society for Computational Economics.
    17. Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 87-127, September.
    18. Kwamie Dunbar, . "An Empirical Review of United States Corporate Default Swap Valuation: The Implications of Functional Forms," Fordham Economics Dissertations, Fordham University, Department of Economics, number 2005.2.
    19. Becker, Ralf, 1998. "Die verallgemeinerte Momentenmethode: Darstellung und Anwendung," Arbeitspapiere des Instituts für Statistik und Ökonometrie 16, Johannes Gutenberg-Universität Mainz, Institut für Statistik und Ökonometrie.
    20. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, 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:inm:oropre:v:49:y:2001:i:4:p:516-530. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.