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Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation1

Published online by Cambridge University Press:  29 August 2014

Dieter Denneberg
Dieter Denneberg*
Affiliation:
Bremen, FRG
*
FB Mathematik/Informatik, Universität Bremen, D-2800 Bremen 33.
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Abstract

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Average absolute (instead of quadratic) deviation from median (instead of expectation) is better suited to determine the safety loading for insurance premiums than standard deviation: The corresponding premium functionals behave additive under the practically relevant risk sharing schemes between first insurer and reinsurer.

Keywords

Premium principlesaverage absolute deviationcomonotonic additivitydistorted probabilities
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 2 , November 1990 , pp. 181 - 190
Copyright
Copyright © International Actuarial Association 1990

Footnotes

1

Lecture, given under the title “Quantilsabhängige Prämienprinzipien” at 21. Tagung der ASTIN-Gruppe in der DGVM, October 13th, 1989, Stuttgart.

References

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