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Experience Rating and Credibility

Published online by Cambridge University Press:  29 August 2014

Hans Bühlmann
Hans Bühlmann*
Affiliation:
Zürich
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Classical statistics deals with the following standard problem of estimation:

Given: random variables X1, X2 … Xn independent, identically distributed, and

observations x1, X2 … xn,

Estimate: parameter (or function thereof) of the distribution function common to all Xi.

It is not surprising that the “classical actuary” has mostly been involved in solving the actuarial equivalent of this problem in insurance, namely

Given: risks R1R2 … Rn no contagion, homogeneous group,

Find: the proper (common) rate for all risks in the given class.

There have, of course, always been actuaries who have questioned the assumptions of independence (no contagion) and/or identical distribution (homogeneity). As long as ratemaking is considered equivalent to the determination of the mean, there seem to be no additional difficulties if the hypothesis of independence is dropped. But is there a way to drop the condition of homogeneity (identical distribution)?

Type
Astin Colloquium 1965 Lucerne Subject two
Information
ASTIN Bulletin: The Journal of the IAA , Volume 4 , Issue 3 , July 1967 , pp. 199 - 207
Copyright
Copyright © International Actuarial Association 1967

References

page 201 note 1) Published in Astin Bulletin vol. IV Part I.

page 202 note *) In the discussion Philipson, Carl has pointed at some earlier researches of Ammeter (“A Generalization of the Collective Theory of Risk in Regard to Fluctuating Basic Probabilities”, Skand. Akt. Tidskrift 1948)Google Scholar and Philipson, (“Einige Bemerkungen zur Bonusfrage in der Kraftversicherung” BDGVM 1963Google Scholar; Eine Bemerkung zu Bichsels Herleitung der bedingten zukünftigen Schadenhäufigkeit einer Polya-Verteilung” MVSVM 1964)Google Scholar.

page 204 note 1) Published in Astin Bulletin Vol. IV Part 1.