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Some applications of the fast Fourier transform algorithm in insurance mathematics This paper is dedicated to Professor W. S. Jewell on the occasion of his 60th birthday

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  • P. Embrechts
  • R. Grübel
  • S. M. Pitts

Abstract

Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre‐Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distributions.

Suggested Citation

  • P. Embrechts & R. Grübel & S. M. Pitts, 1993. "Some applications of the fast Fourier transform algorithm in insurance mathematics This paper is dedicated to Professor W. S. Jewell on the occasion of his 60th birthday," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(1), pages 59-75, March.
    • Handle: RePEc:bla:stanee:v:47:y:1993:i:1:p:59-75
    DOI: 10.1111/j.1467-9574.1993.tb01406.x
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    Cited by:

    1. Jeanne, Olivier & Masson, Paul, 2000. "Currency crises, sunspots and Markov-switching regimes," Journal of International Economics, Elsevier, vol. 50(2), pages 327-350, April.
    2. A. G. Malliaris & Jerome L. Stein, 2005. "Methodological issues in asset pricing: Random walk or chaotic dynamics," World Scientific Book Chapters, in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 8, pages 85-115, World Scientific Publishing Co. Pte. Ltd..
    3. Cao, Liangyue & Soofi, Abdol S., 1999. "Nonlinear deterministic forecasting of daily dollar exchange rates," International Journal of Forecasting, Elsevier, vol. 15(4), pages 421-430, October.

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