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On the consistency of credibility premiums regarding Esscher principle

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  • Pan, Maolin
  • Wang, Rongming
  • Wu, Xianyi

Abstract

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.

Suggested Citation

  • Pan, Maolin & Wang, Rongming & Wu, Xianyi, 2008. "On the consistency of credibility premiums regarding Esscher principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 119-126, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:119-126
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    References listed on IDEAS

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    1. Virginia Young, 1998. "Credibility Using a Loss Function from Spline Theory," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 101-111.
    2. Gerber, Hans U., 1981. "The Esscher Premium Principle: A Criticism. Comment," ASTIN Bulletin, Cambridge University Press, vol. 12(2), pages 139-140, December.
    3. Virginia Young, 1998. "Author’s Reply: Credibility Using a Loss Function from Spline Theory: Parametric Models with a One-Dimensional Sufficient Statistic - Discussion by F. Etienne De Vylder; Donald A. Jones; Bjørn Sundt; ," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 117-117.
    4. 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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    Cited by:

    1. Kim, Joseph H.T. & Jeon, Yongho, 2013. "Credibility theory based on trimming," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 36-47.
    2. Zhang, Jianjun & Qiu, Chunjuan & Wu, Xianyi, 2018. "Bayesian ratemaking with common effects modeled by mixture of Polya tree processes," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 87-94.
    3. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.

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