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

Author

Listed:
  • 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)

Abstract

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
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    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

    Keywords

    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

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