Using Gradient Boosting to Identify Pricing Errors in GLM-Based Tariffs for Non-life Insurance

Sammanfattning

Most non-life insurers and many creditors use regressions, more specifically Generalized Linear Models (GLM), to price their liabilities. One limitation with GLMs is that interactions between predictors are handled manually, which makes finding interactions a tedious and time-consuming task. This increases the cost of rate making and, more importantly, actuaries can miss important interactions resulting in sub-optimal customer prices. Several papers have shown that Gradient Tree Boosting can outperform GLMs in insurance pricing since it handles interactions automatically. Insurers and creditors are however reluctant to use so-called ”Black-Box” solutions for both regulatory and technical reasons. Tree-based methods have been used to identify pricing errors in regressions, albeit only as ad-hoc solutions. The authors instead propose a systematic approach to automatically identify and evaluate interactions between predictors before adding them to a traditional GLM. The model can be used in three different ways: Firstly, it can create a table of statistically significant candidate interactions to add to a GLM. Secondly, it can automatically and iteratively add new interactions to an old GLM until no more statistically significant interactions can be found. Lastly, it can automatically create a new GLM without an existing pricing model. All approaches are tested on two motor insurance data sets from a Nordic P&C insurer and the results show that all methods outperform the original GLMs. Although the two iterative modes perform better than the first, insurers are recommended to mainly use the first mode since this results in a reasonable trade-off between automating processes and leveraging actuaries’ professional judgment.