1.- Calibrated ML Risk Segmentation for Divorce Insurance: Evidence from 10,000 Synthetic Couples

We benchmark machine-learning (ML) models against a transparent multiplicative score for pricing divorce insurance on a synthetic sample of 10,000 couples (rare event). To make comparisons actuarially meaningful, all models are calibrated to the same mean risk as the traditional score (≈ 1.67%), so any gains reflect segmentation, not prudence shifts. In the current results, smooth, well-regularised models outperform tree/boosting approaches under class imbalance: a GAM with splines achieves ROC-AUC = 0.668 (vs. 0.619 for the traditional score; +0.049), Lift@10% = 3.08 (vs. 1.92), and Lift@20% = 2.12 (vs. 1.54), with Brier = 0.0128 (unchanged) and a small PR-AUC gain (0.0253 vs. 0.0235). A Bayesian logistic model performs similarly (ROC-AUC = 0.664). In contrast, random forests and XGBoost underperform, and stacking collapses, consistent with rare-event/overfitting and probability-calibration issues. These findings indicate that calibrated, shape-constrained generalised models can deliver meaningful lift in the top deciles—reducing cross-subsidies in pricing—while preserving average risk. Ongoing work finalises nested cross-validation, refines class-imbalance treatment, and extends explainability (e.g., partial effects/SHAP) ahead of validation on administrative data and robustness checks across jurisdictions.