Multivariate modelling of multiple guarantees in motor insurance of a household
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Actuarial risk classification is usually performed at a guarantee and policyholder level: for each policyholder, the claim frequencies corresponding to each guarantee are modelled in isolation, without accounting for the correlation between the different guarantees and the different policyholders from the same household. However, sometimes, a common event will trigger both guarantees at the same time. Moreover, the claim frequencies for policyholders from the same household appear to be correlated. This paper aims to supplement the standard actuarial approach by combining two guarantees and the policyholders from the household, which allows to refine the prediction on the claim frequencies and account for the common shocks on multiple guarantees. Some possible cross-selling opportunities can also be identified.
KeywordsMultivariate Poisson mixture model Poisson-lognormal A posteriori risk revaluation Credibility
The financial support of the AXA Research Fund through the JRI project “Actuarial dynamic approach of customer in P&C” is gratefully acknowledged. We thank our colleagues from AXA Belgium, especially Arnaud Deltour, Mathieu Lambert, Alexis Platteau, Stanislas Roth and Louise Tilmant for interesting discussions that greatly contributed to the success of this research project. Also, we thank our colleagues from the SMCS, the UCLouvain platform for statistical computing, for setting us up a comfortable and efficient working environment.
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