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. In this talk, we aim to supplement the standard actuarial approach by combining multiple guarantees in P&C insurance and multiple policyholders from the same household. This allows to refine the prediction on the claim frequencies and the multivariate model accounts for the common shocks on multiple guarantees.
We will first show using multivariate credibility how the policyholders' claim frequencies are connected to each other by considering only one guarantee, the Motor Third Party Liability Insurance. In the second part of the presentation, we will extend this first model to multiple guarantees from P&C insurance. Some possible cross-selling opportunities will also be identified.