IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v9y2005i4p519-537.html
   My bibliography  Save this article

Anomalous PDEs in Markov chains: Domains of validity and numerical solutions

Author

Listed:
  • Ragnar Norberg

Abstract

Conditional expected values in Markov chains are solutions to a set of backward differential equations, which may be ordinary or partial depending on the number of relevant state variables. This paper investigates the validity of these differential equations by locating the points of non-smoothness of the state-wise conditional expected values, and it presents a numerical method for computation of such expected values with a controlled global error. Two cases leading to first order partial differential equations in two variables are considered, both from finance and insurance: option pricing in a Markov chain driven financial market, and probability distributions of discounted cash flows generated by multi-state life insurance contracts. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Ragnar Norberg, 2005. "Anomalous PDEs in Markov chains: Domains of validity and numerical solutions," Finance and Stochastics, Springer, vol. 9(4), pages 519-537, October.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:4:p:519-537
    DOI: 10.1007/s00780-005-0157-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-005-0157-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-005-0157-8?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.

    Citations

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


    Cited by:

    1. Djehiche, Boualem & Löfdahl, Björn, 2016. "Nonlinear reserving in life insurance: Aggregation and mean-field approximation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 1-13.
    2. Christiansen, Marcus C. & Djehiche, Boualem, 2020. "Nonlinear reserving and multiple contract modifications in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 187-195.
    3. Jacek Jakubowski & Mariusz Niewk{e}g{l}owski, 2013. "Risk-minimization and hedging claims on a jump-diffusion market model, Feynman-Kac Theorem and PIDE," Papers 1305.4132, arXiv.org, revised Jul 2013.

    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:finsto:v:9:y:2005:i:4:p:519-537. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.