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A Note on Iterative Premium Calculation Principles

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  • Goovaerts, M. J.
  • Vylder, F. De

Abstract

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.

Suggested Citation

  • Goovaerts, M. J. & Vylder, F. De, 1979. "A Note on Iterative Premium Calculation Principles," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 325-329, December.
    • Handle: RePEc:cup:astinb:v:10:y:1979:i:03:p:325-329_00
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    Cited by:

    1. A.Hernández-Bastida & M.P. Fernández-Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model; The Variance Premium Principle With Exponential Poisson And Gamma-Gamma Distributions," FEG Working Paper Series 07/02, Faculty of Economics and Business (University of Granada).
    2. Kaluszka, Marek & Krzeszowiec, Michał, 2013. "On iterative premium calculation principles under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 435-440.
    3. Mitja Stadje, 2018. "Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharing," Papers 1811.09615, arXiv.org, revised Dec 2018.
    4. Marek Kałuszka & Michał Krzeszowiec, 2013. "Iteracyjność składek ubezpieczeniowych w ujęciu teorii skumulowanej perspektywy i teorii nieokreśloności," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 45-56.

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