IDEAS home Printed from
   My bibliography  Save this article

Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity


  • Ji-Wook Jang

    () (Actuarial Studies, Faculty of Commerce and Economics, University of New South Wales, Sydney, NSW 2052, Australia Manuscript)

  • Angelos Dassios

    () (Department of Statistics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, United Kingdom)


We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov process theory. We apply the model to price stop-loss catastrophe reinsurance contract and catastrophe insurance derivatives. The asymptotic distribution of the claim intensity is used to derive pricing formulae for stop-loss reinsurance contract for catastrophic events and catastrophe insurance derivatives. We assume that there is an absence of arbitrage opportunities in the market to obtain the gross premium for stop-loss reinsurance contract and arbitrage-free prices for insurance derivatives. This can be achieved by using an equivalent martingale probability measure in the pricing models. The Esscher transform is used for this purpose.

Suggested Citation

  • Ji-Wook Jang & Angelos Dassios, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," Finance and Stochastics, Springer, vol. 7(1), pages 73-95.
  • Handle: RePEc:spr:finsto:v:7:y:2003:i:1:p:73-95
    Note: received: February 2001; final version received: April 2002

    Download full text from publisher

    File URL:
    Download Restriction: Access to the full text of the articles in this series is restricted

    As the access to this document is restricted, you may want to search for a different version of it.


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

    Cited by:

    1. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 297-302, October.

    More about this item


    The Cox process; shot noise process; piecewise deterministic Markov process; stop-loss reinsurance contract; catastrophe insurance derivatives; equivalent martingale probability measure; Esscher transform;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies


    Access and download statistics


    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:7:y:2003:i:1:p:73-95. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.