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Some Notes on the Statistical Theory of Extreme Values

Published online by Cambridge University Press:  29 August 2014

R. E. Beard
R. E. Beard*
Affiliation:
London, England
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In preparing the notes on the subjects for discussion at the 4th ASTIN Colloquium at Trieste [1] I used some of the material which formed the basis of a talk given to the Scandinavian Actuarial Societies in September 1962. The papers presented in Trieste have established on a firm mathematical footing the formula for the excess loss premium derived in my note but the discussions also showed that some of the other 1962 material would be of interest.

It will be appreciated that the question originally proposed, i.e. to calculate an excess of loss reinsurance premium when the only information available is the largest claim experienced in each of a succession of periods, was deliberately phrased in this form as being the most troublesome case likely to arise in practice. Clearly if other information is available it would not be rejected in arriving at a premium, but this immediately extends the problem to one of finding the best methods of combining information of different kinds. For example if, say, the largest 5 claims in each period are known, what technique will make the maximum use of the data? Such extensions of the problem are not discussed in this note. Furthermore, I am not unmindful of the valuable comment by Jung, “that there is a natural law which states that you can never get more out of a mincing machine than what you have put into it” [2].

Type
Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 3 , Issue 1 , December 1963 , pp. 6 - 12
Copyright
Copyright © International Actuarial Association 1963

References

[1]Beard, R. E.: ASTIN Bulletin, Vol. II, Pt. III, page 313, 1963.Google Scholar
[2]Jung, J.: ASTIN Bulletin, Vol. III, Pt. II. *)Google Scholar
[3]Gumbel, E. J.: Statistics of Extremes, Columbia University Press, New York, 1958.CrossRefGoogle Scholar
[4]D'Hooge, L.: ASTIN Bulletin, Vol. III, Pt. II. *)Google Scholar
[5]Franckx, E.: ASTIN Bulletin, Vol. II, Pt. III, page 415, 1963.CrossRefGoogle Scholar
[6]Benktander, G.: ASTIN Bulletin, Vol. II, Pt. III, page 387, 1963.Google Scholar
[7]Property Insurance Fact Book 1960, Insurance information Institute, New York. * These papers will appear in 1964.Google Scholar