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RATEMAKING OF DEPENDENT RISKS

Published online by Cambridge University Press:  06 July 2017

J. M. Andrade e Silva  and
M. de Lourdes Centeno
J. M. Andrade e Silva
Affiliation:
CEMAPRE, ISEG, Universidade de Lisboa E-mail: [email protected]
M. de Lourdes Centeno*
Affiliation:
CEMAPRE, ISEG, Universidade de Lisboa
*
E-Mail: [email protected]
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Abstract

We start by describing how, in some cases, we can use variance-related premium principles in ratemaking, when the claim numbers and individual claim amounts are independent. We use quasi-likelihood generalized linear models, under the assumption that the variance function is a power function of the mean of the underlying random variable. We extend this approach to the cases where the claim numbers are correlated. Some alternatives to deal with dependent risks are presented, taking explicitly into account overdispersion. We present regression models covering the bivariate Poisson, the generalized bivariate negative binomial and the bivariate Poisson–Laguerre polynomial, which nest the bivariate negative binomial. We apply these models to a portfolio of the Portuguese insurance company Tranquilidade and compare the results obtained.

Keywords

Ratemakingvariance-related premium principlesgeneralized linear modelsquasi-likelihoodbivariate distributions
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 875 - 894
Copyright
Copyright © Astin Bulletin 2017 

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