Multivariate modelling of multiple guarantees in motor insurance of a household

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