Analyzing relationships between risk factors

The 2020 article in Annals of Actuarial Science ‘Home and Motor insurance joined at a household level using multivariate credibility’ shows how realtionships between factors are not revealed by the usual analyses.

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The article "Home and Motor insurance joined at a household level using multivariate credibility" by Florian Pechon, Michel Denuit, and Julien Trufin presents a novel approach to actuarial ratemaking by integrating Home and Motor insurance at a household level. Traditionally, actuarial ratemaking is performed at the product and guarantee level, treating each product and guarantee in isolation and assuming independence between policyholders. However, this paper proposes a multivariate Poisson mixture model with correlated random effects to account for the dependence that may exist between unobserved risk factors across Home and Motor insurance and between policyholders from the same household.

Home insurance covers the entire household, while Motor insurance policies are subscribed by specific policyholders within the household. The model allows for the periodic correction of expected claim frequencies using the reported number of claims in any of the Home or Motor products. The study demonstrates that the impact of the number of claims reported in Motor insurance on the expected number of claims in Home insurance is larger than the other way around. Additionally, the model allows for the identification of the riskiest households and shows improved predictive power in out-of-sample analysis.

The paper builds on previous work and provides a methodology to model the number of claims reported in both Home and Motor insurance at the household level. The study demonstrates that latent risk factors are positively correlated across both Motor and Home insurance products, guarantees, and policyholders from the same household, indicating that unobserved risk factors may be correlated or shared within the household.

The proposed model has implications for insurance companies, as it allows for a more accurate estimation of expected claim frequencies in a household, identifies the riskiest households, and improves the understanding of customer risk profiles. The study also highlights the positive correlation between latent risk factors across different insurance products and policyholders from the same household.

The article presents a novel multivariate credibility model that integrates Home and Motor insurance at a household level, providing insights into the dependencies between claim frequencies and the identification of risk factors. The methodology has implications for improving predictive power and understanding customer risk profiles in the insurance industry.

This sheds light on how many complex risk factors we miss by habitually analysing risk and development at a single level.

Pechon, F., Denuit, M., & Trufin, J. (2020). Home and Motor insurance joined at a household level using multivariate credibility. Annals of Actuarial Science, 1–33. https://doi.org/10.1017/S1748499520000160