Home and Motor insurance joined at a household level using multivariate credibility

Actuarial ratemaking is usually performed at product and guarantee level, meaning that each product and guarantee is considered in isolation. Moreover, independence between policyholders is generally assumed. In this paper, we propose a multivariate Poisson mixture, with random effects correlated using a hierarchical structure, to accommodate for the dependence that may exist between unobserved risk factors across Home and Motor insurance and between policyholders from the same household. The hierarchical structure accounts for the fact that Home insurance covers the whole household, whereas Motor insurance policies are subscribed by specific policyholders within the household. The model allows to periodically correct the a priori expected claim frequencies using the reported number of claims in any of the considered products. Applications show that the impact of the number of claims reported in Motor insurance on the number of claims expected in Home insurance is larger than the other way around. Moreover, an out-of-sample analysis validates an improved predictive power. Also, the model allows to identify more rapidly the riskiest households.