Measuring stability in transparent insurance pricing models after updates
Quantifying structural stability of transparent models for general insurance pricing
Machine Learning
Summary
Insurance companies often need to update their pricing models because the data they use changes quickly. The authors introduce a way to measure how much the structure of these updated models changes, especially for models that are easy to understand. They define a new metric that compares parts of the model before and after updates, helping identify models that remain stable yet accurate. Their tests with real car insurance data show that simpler models change less, and some techniques can make more complex models more stable without hurting their accuracy.
What this means in practice
- •For insurance pricing teams: Evaluate and monitor how updated insurance pricing models change in structure to maintain transparency and reliability.
- •For financial risk analysts: Use the new stability metric to choose models that balance explainability and performance in dynamic financial environments.
Authors
Félix Côté, Marie-Pier Côté
Abstract
The short duration of general insurance contracts leads to rapid distributional shifts in the data, warranting regular model updates. This process may yield a post-update model that differs considerably from the pre-update model in both predictions and structure. Structural stability is upstream of predictive stability, yet existing structural stability metrics are mostly restricted to simple decision trees. Thus, we first introduce the notion of functional transparency, characterising models with a prediction function that can be expressed as a sum of univariate functions for main effects and bivariate functions for pairwise interactions. Then, we propose the Mean Squared Shape function distance, a metric to quantify the structural stability of functionally transparent models, which are particularly relevant in actuarial science. Using three public auto insurance datasets, we present a benchmark study to demonstrate the usefulness of our metric in identifying a stable and accurate transparent model. Generalised linear models with centred numerical covariates are stable, and explainable boosting machines (EBMs) offer a compromise between stability and performance. We also find that stabilisation strategies, such as sequential modelling and fixed hyperparameters, can substantially improve stability for both EBM and XGBoost models, with negligible impact on performance.