Risk classification of households with multiline P&C insurance claim frequency models

Actuarial risk classification studies are typically confined to univariate, policy-based analyses: Individual claim frequencies are modelled for a single product in isolation, without accounting for the interactions between the different coverages bought by the same policyholder. Moreover, independence between the policyholders is generally assumed. In this thesis, we aim to move from such marginal, policy-based actuarial analyses to joint, household-based risk assessment. Although insurers possess a priori available information about the risks they insure and use this information to discriminate between higher and lower risks, the risk classes constructed with the a priori available variables remain heterogeneous. This heterogeneity originates from the fact that some important but unobserved risk factors still differentiates policyholders from the same a priori constructed risk class. In this thesis, we show that the unobserved risk factors across policyholders from the same household and across different insurance products, namely Motor and Home insurance, are connected to each other. Consequently, we suggest that by proper inclusion of mixed effects in Poisson model for claim frequencies, the unexplained heterogeneity across members of the household and across insurance products is accounted for, allowing for periodic revaluations based on previous claim experience. These latent factors can then be combined using multiline credibility models so that the correlation existing between the different claim frequencies related to members of the same household and related to different insurance products can be exploited for a posteriori corrections.