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The Esscher Premium Principle: A Criticism. Comment.

Published online by Cambridge University Press:  29 August 2014

Hans U. Gerber
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Zehnwirth (1981) contains some flaws. If

is the Esscher premium for a risk X, the loading is H(X) — E(X) and not h as Zehnwirth states. The first and third formulas on page 78 are wrong, since o(h) is a quantity such that

A correct statement would have been that

or simply that H(X) is a continuous function of the parameter h. However, this continuity is not uniform in all risks, which is illustrated by (3). No matter how small h is, there is always an X such that the difference between H(X) and E(X) is substantial. In view of this what is the meaning of a statement like “… the Esscher premium is a small perturbation of the linearized credibility premium”?

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 12 , Issue 2 , December 1981 , pp. 139 - 140
Copyright
Copyright © International Actuarial Association 1981

References

REFERENCE

Zehnwirth, B. (1981). The Esscher Premium Principle: A Criticism. Astin Bulletin, 12, 77–78.CrossRefGoogle Scholar