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A Method For Constructing And Interpreting Some Weighted Premium Principles

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  • Castaño-Martínez, Antonia
  • López-Blazquez, Fernando
  • Pigueiras, Gema
  • Sordo, Miguel Á.

Abstract

We present a method for constructing and interpreting weighted premium principles. The method is based on modifying the underlying risk distribution in such a way that the risk-adjusted expected value (or premium) is greater than the expected value of some conveniently chosen function of claims, which defines the insurer’s perception of the risk. Under some assumptions on the function of claims, the method produces distortion premium principles. We provide several examples under different assumptions on the claim arrival process and different functions of claims, including record claims and kth record claims.

Suggested Citation

  • Castaño-Martínez, Antonia & López-Blazquez, Fernando & Pigueiras, Gema & Sordo, Miguel Á., 2020. "A Method For Constructing And Interpreting Some Weighted Premium Principles," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 1037-1064, September.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:3:p:1037-1064_12
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    Cited by:

    1. M. Mercè Claramunt & Maite Mármol & Xavier Varea, 2023. "Facing a Risk: To Insure or Not to Insure—An Analysis with the Constant Relative Risk Aversion Utility Function," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    2. Wei Wang & Huifu Xu, 2023. "Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making," Computational Management Science, Springer, vol. 20(1), pages 1-51, December.
    3. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.

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