arXiv subjects

Robert Matthijs Verschuren

Publications and source records attributed to Robert Matthijs Verschuren.

3 recordsLinked to original sources

arXiv2022

Frequency-Severity Experience Rating based on Latent Markovian Risk Profiles

Bonus-Malus Systems traditionally consider a customer's number of claims irrespective of their sizes, even though these components are dependent in practice. We propose a novel joint experience rating approach based on latent Markovian risk profiles to allow for a positive or negative individual frequency-severity dependence. The latent profiles evolve over time in a Hidden Markov Model to capture updates in a customer's claims experience, making claim counts and sizes conditionally independent. We show that the resulting risk premia lead to a dynamic, claims experience-weighted mixture of standard credibility premia. The proposed approach is applied to a Dutch automobile insurance portfolio and identifies customer risk profiles with distinctive claiming behavior. These profiles, in turn, enable us to better distinguish between customer risks.

stat.AP↗

arXiv2022

Customer Price Sensitivities in Competitive Automobile Insurance Markets

Insurers are increasingly adopting more demand-based strategies to incorporate the indirect effect of premium changes on their policyholders' willingness to stay. However, since in practice both insurers' renewal premia and customers' responses to these premia typically depend on the customer's level of risk, it remains challenging in these strategies to determine how to properly control for this confounding. We therefore consider a causal inference approach in this paper to account for customers' price sensitivity and to deduce optimal, multi-period profit maximizing premium renewal offers. More specifically, we extend the discrete treatment framework of Guelman and Guillén (2014) by Extreme Gradient Boosting, or XGBoost, and by multiple imputation to better account for the uncertainty in the counterfactual responses. We additionally introduce the continuous treatment framework with XGBoost to the insurance literature to allow identification of the exact optimal renewal offers and account for any competition in the market by including competitor offers. The application of the two treatment frameworks to a Dutch automobile insurance portfolio suggests that a policy's competitiveness in the market is crucial for a customer's price sensitivity and that XGBoost is more appropriate to describe this than the traditional logistic regression. Moreover, an efficient frontier of both frameworks indicates that substantially more profit can be gained on the portfolio than realized, also already with less churn and in particular if we allow for continuous rate changes. A multi-period renewal optimization confirms these findings and demonstrates that the competitiveness enables temporal feedback of previous rate changes on future demand.

stat.AP↗

arXiv2020

Predictive Claim Scores for Dynamic Multi-Product Risk Classification in Insurance

It has become standard practice in the non-life insurance industry to employ Generalized Linear Models (GLMs) for insurance pricing. However, these GLMs traditionally work only with a priori characteristics of policyholders, while nowadays we increasingly have a posteriori information of individual customers available, sometimes even across multiple product categories. In this paper, we therefore consider a dynamic claim score to capture this a posteriori information over several product lines. More specifically, we extend the Bonus-Malus-panel model of Boucher and Inoussa (2014) and Boucher and Pigeon (2018) to include claim scores from other product categories and to allow for non-linear effects of these scores. The application of the resulting multi-product framework to a Dutch property and casualty insurance portfolio shows that the claims experience of individual customers can have a significant impact on the risk classification and that it can be very profitable to account for it.

stat.AP↗