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On Pareto Conjugate Priors and Their Application to Large Claims Reinsurance Premium Calculation

Published online by Cambridge University Press:  17 April 2015

José L. Vilar-Zanón  and
Cristina Lozano-Colomer
José L. Vilar-Zanón
Affiliation:
Dept. Economía Financiera I., Facultad Ciencias Económicas y Empresariales. Universidad Complutense de Madrid. Campus de Somosaguas. Pozuelo de Alarcón, 28223, España. E-mail: jlvilarz@ccee.ucm.es
Cristina Lozano-Colomer
Affiliation:
Dept. Métodos Cuantitativos, Universidad Pontificia de Comillas (ICADE). Madrid. E-mail: clozano@cee.upcomillas.es
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Abstract

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This paper addresses the Bayesian estimation of the shape parameter of Pareto distributions, and its application to premium calculation of large claims excess of loss (XL) reinsurance contracts. It studies the use of the generalized inverse Gaussian (GIG) as a Pareto prior conjugate, a family that contains as a particular case the gamma distribution. An exact credibility formula is deduced allowing the calculation of individual reinsurance premiums. These are premiums suited to the excesses history of a sole portfolio. A family of predictive distributions for the excesses is derived. We apply our exact credibility model to a sample of excesses arisen in ten Spanish portfolios of liability motor insurance from year 1992 to year 2001.

Keywords

ReinsuranceXL premiumslarge claimsextreme value modelingBayesexact credibilityPareto distributiongeneralized inverse Gaussian familyAMS subject classification62P0560G7062F15
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 405 - 428
Copyright
Copyright © ASTIN Bulletin 2007

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