Telematicsdevices installed in insured vehicles provide actuaries with new risk factors, such as the time of the day, average speeds, and other driving habits. This paper extends the multivariate mixed model describing the joint dynamics of telematics data and claim frequencies proposed by Denuit et al. (2019a) by allowing for signals with various formats, not necessarily integer-valued, and by replacing the estimation procedure with the Expected Conditional Maximization algorithm. A numerical study performed on a database related to Pay-How-You-Drive, or PHYD motor insurance illustrates the relevance of the proposed approach for practice.

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.

A method is presented for identifying an expected profitable set of customers, to offer them an additional insurance product, by estimating a customer specific latent risk profile, for the additional product, by using the customer specific available data for an existing insurance product of the specific customer. For the purpose, a multivariate credibility estimator is considered and we investigate the effect of assuming that one (of two) insurance products is inactive (without available claims information) when estimating the latent risk profile. Instead, available customer specific claims information from the active existing insurance product is used to estimate the risk profile and thereafter assess whether or not to include a specific customer in an expected profitable set of customers. The method is tested using a large real data set from a Danish insurance company and it is shown that sets of customers, with up to 36% less claims than a priori expected, are produced as a result of the method. It is therefore argued that the proposed method could be considered, by an insurance company, when cross-selling insurance products to existing customers.

We investigate a concept of multivariate pricing, which includes claim history for more than one line of business and is a generalization of the Bühlmann-Straub model. The multivariate credibility model is extended to allow for the age of claims to influence the estimation of future claims. The model is applied to data from a portfolio of commercial lines of business.