Hybrid Modelling for Accurate Insurance Reserve Prediction: Integrating Machine Learning and Vine Copulas

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In the Insurance industry, accurate reserve forecasts are fundamental for financial stability and regulatory compliance. Traditional methods may be restrictive when claims payments exhibit nonlinear behavior and cross-line dependencies. In this study, we aim to improve the accuracy of insurance reserve forecasting. Therefore, we propose a novel hybrid framework that combines a tuned XGBoost model with vine copula models. We use runoff triangle data (Fire, Breakage Glass and Physical Damage lines of business) from an insurance company to forecast future claim payments. The tuned XGBoost algorithm was employed as the machine learning component to estimate the marginal predictive distributions with bootstrap-based prediction intervals, and regular vine copulas (C-vine and D-vine) to model cross-line dependence. This yields a joint predictive distribution of incremental claims and enables portfolio-level risk assessment using Value-at-Risk and Conditional Value-at-Risk. The tuned XGBoost model outperforms an independence-based Tweedie GLM benchmark, reducing the RMSE by 25.5% for the Glass Breakage line and by 78.2% for the Business Interruption line. The model exhibits significant performance over various development periods, highlighting its potential for practical applications in reserve estimation. This hybrid approach provides a practical method for insurers to accurately forecast reserves, improve risk management, and meet regulatory requirements such as Solvency II.