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A METHOD FOR CONSTRUCTING AND INTERPRETING SOME WEIGHTED PREMIUM PRINCIPLES

Published online by Cambridge University Press:  05 June 2020

Antonia Castaño-Martínez ,
Fernando López-Blazquez ,
Gema Pigueiras  and
Miguel Á. Sordo Open the ORCID record for Miguel Á. Sordo [Opens in a new window]
Antonia Castaño-Martínez
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz Cádiz, Spain E-Mail: antonia.castano@uca.es
Fernando López-Blazquez
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla Sevilla, Spain E-Mail: lopez@us.es
Gema Pigueiras
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz Cádiz, Spain E-Mail: gema.pigueiras@uca.es
Miguel Á. Sordo*
Affiliation:
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz Cádiz, Spain E-Mail: mangel.sordo@uca.es
*
E-Mail: mangel.sordo@uca.es
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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.

Keywords

Weighted premium principledistortion premium principleequilibrium distributionorder statisticsrecord valueG220
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 1037 - 1064
Copyright
© 2020 by Astin Bulletin. All rights reserved

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