Abstract
Insurance reserve estimation is a fundamental actuarial task supporting premium pricing, solvency assessment, financial reporting, capital planning, and risk management. Classical reserve methods based on Thiele's differential equation provide a rigorous and interpretable foundation for life insurance valuation, but repeated reserve calculations become computationally expensive in sensitivity analysis, optimization, and large-scale scenario evaluation. This paper presents an Insurance Reserve Intelligence Platform for term-life reserve modelling that combines a classical Thiele-equation solver with a Physics-Informed Neural Network (PINN) enhanced by Knowledge-Informed Neural Network (KINN) losses. The framework includes synthetic policy generation, risk-adjusted premium calculation, classical reserve trajectory generation, reserve-ratio dataset construction, configurable neural training, validation diagnostics, sensitivity and elasticity analysis, prototype optimization workflows, and interest-rate scenario testing. A key refinement is the use of premium ratio and the explicit separation of pricing-time and scenario-time interest-rate semantics. The final model uses seven features: elapsed time, issue age, pricing interest rate, scenario interest rate, premium ratio, sum assured, and mortality intensity. It predicts a standardized reserve ratio instead of raw reserve values, improving numerical stability across policies with different sums assured. The model achieved an R2 of 0.9887, MAE of 785.48, and RMSE of 1212.76 on the test set. On 200 policies, PINN/KINN inference was approximately 119.53 times faster than the classical solver. Results show strong predictive accuracy, physics consistency, and boundary performance, while highlighting remaining limitations in monotonicity and out-of-distribution generalization.
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URL
https://arxiv.org/abs/2609.30765
