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Improved Error Bounds for Bertram's Method

Published online by Cambridge University Press:  29 August 2014

Bjørn Sundt
Bjørn Sundt*
Affiliation:
The Wyatt Company, Oslo
*
The Wyatt Company A.S, P.O. Box 1508 Vika, N-0117 Oslo, Norway
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Abstract

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In an earlier note the present author deduced bounds for the approximation error of stop loss premiums when the aggregate claims distribution is calculated by a method introduced by Bertram. From the error bounds of the stop loss premiums we deduced bounds for the approximation error of the cumulative distribution and the discrete density of the aggregate claims. In the present note we shall improve the bounds for the cumulative distribution and the discrete density.

Keywords

Aggregate claims distributionsapproximationserror bounds
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 2 , November 1993 , pp. 301 - 303
Copyright
Copyright © International Actuarial Association 1993

References

REFERENCES

Bertram, J. (1981) Numerische Berechnung von Gesamtschadenverteilungen. Blätter der deutschen Gesellschaft für Versicherungsmathematik XV, 175–194.Google Scholar
Sundt, B. (1986) Discussion on W. Hürlimann: Error bounds for stop-loss premiums calculated with the Fast Fourier Transform. Scandinavian Actuarial Journal, 114–116.CrossRefGoogle Scholar
Sundt, B. (1991) An introduction to non-life insurance mathematics. (2. ed.) Verlag Versicherungswirtschaft e.V., Karlsruhe.Google Scholar
Willmot, G. E. (1993) On the tails of compound geometric distributions. Research Report 93–02.Google Scholar