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A Note on Iterative Premium Calculation Principles

Published online by Cambridge University Press:  29 August 2014

M. J. Goovaerts  and
F. De Vylder
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Abstract

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Gerber (1974) has given a characterization of the exponential utility function by proving the fact that a premium calculation principle of zero utility is iterative iff the underlying utility function is linear or exponential. In the present note we prove the more general result that the premium calculation principle introduced by Bühlmann, Gagliardi, Gerber and Straub (1977) is iterative iff the underlying function v is linear or exponential or when the principle is a mean value principle.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 10 , Issue 3 , December 1979 , pp. 325 - 329
Copyright
Copyright © International Actuarial Association 1979

References

REFERENCES

Bühlmann, H. (1970), Mathematical Methods in Risk Theory, Berlin: Springer-Verlag.Google Scholar
Bühlmann, H., Gagliardi, B., Gerber, H. U., and Straub, F. (1977), Some Inequalities for Stop Loss Premiums, Astin Bulletin 9, 75–83.CrossRefGoogle Scholar
Gerber, H. U. (1974), On Iterative Premium Calculation Principles, Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker 74, 163–172.Google Scholar