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Dependence in Dynamic Claim Frequency Credibility Models

Published online by Cambridge University Press:  17 April 2015

Oana Purcaru  and
Michel Denuit
Oana Purcaru
Affiliation:
Institut de Statistique & Institut des Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays, 20 B-1348 Louvain-la-Neuve, Belgium, E-mail: purcaru@stat.ucl.ac.be & denuit@stat.ucl.ac.be
Michel Denuit
Affiliation:
Institut de Statistique & Institut des Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays, 20 B-1348 Louvain-la-Neuve, Belgium, E-mail: purcaru@stat.ucl.ac.be & denuit@stat.ucl.ac.be
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Abstract

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In nonlife insurance, actuaries usually resort to random effects to take unexplained heterogeneity into account (in the spirit of the Bühlmann-Straub model). This paper aims to study the kind of dependence induced by the introduction of correlated latent variables in the annual numbers of claims reported by policyholders. The effect of reporting claims on the a posteriori distribution of the random effects will be made precise. This will be done by establishing some stochastic monotonicity property of the a posteriori distribution with respect to the claims history.

Keywords

Poisson mixturecredibility theoryexperience ratingrisk classificationcopulastime series for non-gaussian responses
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 1 , May 2003 , pp. 23 - 40
Copyright
Copyright © ASTIN Bulletin 2003

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