  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.
