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Estimation of the number of excess claims by means of the credibility theory

Published online by Cambridge University Press:  29 August 2014

E. Straub
E. Straub*
Affiliation:
Zurich
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The purpose of this paper is to describe a possible application on the rating of excess of loss covers of Mr. Bühlmann's work on Experience Rating and Credibility). One of the most important problems in connection with the rating of such treaties consists in estimating the number of excess claims and the average excess claim amount. Especially with cases where claims data are scarce there is a temptation to estimate these two quantities by means of the credibility theory. This approach leads, on the one hand, to a relatively complicated formula when considering the average excess claim amount, and, on the other, to a rather simple one for the credibility factor of the number of excess claims.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 5 , Issue 3 , February 1971 , pp. 388 - 392
Copyright
Copyright © International Actuarial Association 1971

References

page 388 note 1) Optimale Prämienstufensysteme, Mitteilung der Vereinigung schweizerischer Versicherungsmathematiker, 64. Band, Heft 2.

page 388 note 2) Experience Rating and Credibility, The ASTIN-Bulletin, Vol. IV, Part III.

page 389 note 3) Using Philipson's terminology in his article “on the difference between the concepts “compound” and “composed” Poisson processes”, ASTIN-Bulletin Vol. II, Part III.

page 389 note *) For the sake of simplicity the calculations are only made for the simple Poisson-distribution, although it can be proved, without further difficulties that the results of this note hold true for compound Poisson laws as well.