Deriving robust bayesian premiums under bands of prior distributions with applications

  1. A. Suarez Llorens
  2. M. Sánchez Sánchez
  3. M. A. Sordo Díaz
  4. E. Gómez Déniz
Actas:
XXXVIII CONGRESO NACIONAL SEIO XII JORNADAS DE ESTADÍSTICA PUBLICA

Editorial: Editado por Eva Vallada y Rubén Ruiz Grupo de Sistemas de Optimización Aplicada http://soa.iti.es/ Universitat Politècnica de València

ISBN: 978-84-09-13580-6

Año de publicación: 2019

Páginas: 165

Tipo: Aportación congreso

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Resumen

We study the propagation of uncertainty from a class of priors introduced by AriasNicolas 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.