A Hybrid Framework to Model Insurance Mortality Rates: Graduation and Ensemble Models

Accurate modeling of mortality rates is crucial for effective risk management. It affects product pricing, reserving, and capital estimation. Modeling mortality experience for insurance portfolios is particularly challenging in emerging markets, where data is often limited and inconsistent.

This research introduces a hybrid modeling framework that integrates actuarial graduation with tree-based machine learning models to enhance the modeling and forecasting of insurance mortality rates.

The proposed framework first applies graduation models, including the Makeham law and P-splines, to smooth crude mortality rates and capture underlying patterns. Tree-based machine learning models, including decision trees, random forests, and gradient boosting, are then utilized with two splitting approaches, random splitting and year-based splitting, to estimate and forecast graduated mortality rates, capturing nonlinear dependencies across age, year, and gender.

The methodology is applied to Egyptian life insurance data covering ages 16 to 60 for the period 2013 to 2019. The empirical results showed that the Makeham model provides a better fit and higher predictive accuracy for graduating mortality rates. Among machine learning models, gradient boosting with both random and year-based splitting achieves the highest predictive accuracy and supports reliable prediction of future mortality rates.

By combining the interpretability of actuarial graduation methods with the predictive capability of machine learning, the proposed framework provides a robust approach for modeling and forecasting insurance mortality rates in life insurance applications.