A A Segmentation-Based Hybrid Chain Ladder–XGBoost Framework for Incurred But Not Reported Claims Estimation

Abstract

Accurate estimation of Incurred But Not Reported (IBNR) claims is critical in non-life insurance, particularly for portfolios characterized by heterogeneous claim sizes and nonlinear development patterns. Existing hybrid reserving models improve predictive accuracy but typically apply multiple models uniformly to the same claim population, implicitly assuming homogeneous claim behavior. Under heterogeneous portfolios, large and volatile claims can simultaneously distort Chain Ladder development factors and destabilize machine-learning training. This study addresses this limitation by proposing a segmentation-based hybrid Chain Ladder (CL)–XGBoost framework that models claim according to their volatility characteristics rather than treating all claims identically. Claims are partitioned into small and large segments using a data-driven 65th percentile threshold (claim amount €32.49). The threshold is selected through sensitivity analysis by minimizing validation-set Mean Absolute Error (MAE) prior to test evaluation, ensuring that it is not arbitrary or tuned to the test data. Small claims, which exhibit stable development patterns, are modeled using the classical CL method, whereas large high-variance claims are modeled using XGBoost, and segment-level predictions are aggregated to obtain cumulative IBNR estimates. Using motor insurance claims data from 2015–2019, the proposed framework demonstrates substantial improvements over benchmark models. Compared with the classical CL baseline (MAE €1,774.51), the hybrid model reduces MAE to €819.28 (54% reduction), RMSE from €2,026.08 to €819.39 (60% reduction), and MAPE from 0.92% to 0.60%, relative to an average claim size of approximately €387. Bootstrap resampling confirms that the reductions are statistically significant at the 5% level. The proposed model also outperforms standalone XGBoost, Uniform Hybrid and Neural-Network–CL hybrid across all evaluation metrics. The results show that performance gains arise primarily from heterogeneity-aware segmentation rather than hybridization alone. The framework therefore, provides a robust and interpretable reserving approach that stabilizes development estimation for small claims while allowing flexible nonlinear learning for large claims