On the consistency of credibility premiums regarding Esscher principle
In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions.
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- Gerber, Hans U., 1981. "The Esscher Premium Principle: A Criticism. Comment," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(02), pages 139-140, December.
- Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
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