The Esscher Premium Principle: A Criticism. Comment

Hans U. Gerber

ASTIN Bulletin, 1981, vol. 12, issue 2, 139-140

Abstract: Zehnwirth (1981) contains some flaws. Ifis 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 thatA correct statement would have been thator 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”?

Date: 1981
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