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DERIVING ROBUST BAYESIAN PREMIUMS UNDER BANDS OF PRIOR DISTRIBUTIONS WITH APPLICATIONS

Published online by Cambridge University Press:  23 November 2018

M. Sánchez-Sánchez ,
M.A. Sordo ,
A. Suárez-Llorens  and
E. Gómez-Déniz
M. Sánchez-Sánchez
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Avda. Rep. Saharaui s/n, 11510 Puerto Real, Cádiz, Spain E-Mail: marta.sanchez@uca.es
M.A. Sordo
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Avda. Rep. Saharaui s/n, 11510 Puerto Real, Cádiz, Spain E-Mail: mangel.sordo@uca.es
A. Suárez-Llorens*
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Avda. Rep. Saharaui s/n, 11510 Puerto Real, Cádiz, Spain E-Mail: alfonso.suarez@uca.es
E. Gómez-Déniz
Affiliation:
Department of Quantitative MethodsUniversity of Las Palmas de Gran CanariaCampus Universitario de Tafira 35017 las Palmas de Gran Canaria, Spain E-Mail: emilio.gomez-deniz@ulpgc.es
*
E-Mail: alfonso.suarez@uca.es
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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.

Keywords

Credibilityclass of priorsdistortion functionsKolmogorov and Kantorovich metricspremium calculation principlerobust Bayesian analysisstochastic orders
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 147 - 168
Copyright
Copyright © Astin Bulletin 2018 

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