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 customer price sensitivities and to deduce optimal, multi-period profit maximizing premium renewal offers. More specifically, we extend the discrete treatment framework of Guelman and Guill\'en (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.