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Deriving Robust Bayesian Premiums Under Bands Of Prior Distributions With Applications

Author

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  • Sánchez-Sánchez, M.
  • Sordo, M.A.
  • Suárez-Llorens, A.
  • Gómez-Déniz, E.

Abstract

We study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models.

Suggested Citation

  • Sánchez-Sánchez, M. & Sordo, M.A. & Suárez-Llorens, A. & Gómez-Déniz, E., 2019. "Deriving Robust Bayesian Premiums Under Bands Of Prior Distributions With Applications," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 147-168, January.
    • Handle: RePEc:cup:astinb:v:49:y:2019:i:01:p:147-168_00
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    4. Ángel Berihuete & Marta Sánchez-Sánchez & Alfonso Suárez-Llorens, 2021. "A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve," Mathematics, MDPI, vol. 9(3), pages 1-16, January.

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