保险准备金智能平台
Insurance Reserve Intelligence Platform
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中文总结 AI 辅助
本文提出一个结合Thiele方程与PINN/KINN的保险准备金智能平台，通过预测标准化准备金比率，在测试集上实现R²=0.9887，推理速度比经典求解器快约119倍。
中文摘要 AI 辅助
保险准备金估计是一项基础的精算任务，支持保费定价、偿付能力评估、财务报告、资本规划和风险管理。基于Thiele微分方程的传统准备金方法为寿险估值提供了严谨且可解释的基础，但在敏感性分析、优化和大规模情景评估中，重复的准备金计算变得计算成本高昂。本文提出了一个用于定期寿险准备金建模的保险准备金智能平台，该平台将经典Thiele方程求解器与由知识信息神经网络（KINN）损失增强的物理信息神经网络（PINN）相结合。该框架包括合成保单生成、风险调整保费计算、经典准备金轨迹生成、准备金比率数据集构建、可配置的神经训练、验证诊断、敏感性和弹性分析、原型优化工作流以及利率情景测试。一个关键的改进是使用保费比率，并明确区分定价时间和情景时间的利率语义。最终模型使用七个特征：已用时间、签发年龄、定价利率、情景利率、保费比率、保额和死亡率强度。它预测标准化准备金比率而非原始准备金值，从而提高了不同保额保单间的数值稳定性。该模型在测试集上取得了R²为0.9887、MAE为785.48、RMSE为1212.76的成绩。在200份保单上，PINN/KINN推理比经典求解器快约119.53倍。结果表明，该模型具有较高的预测准确性、物理一致性和边界性能，同时也凸显了在单调性和分布外泛化方面仍存在的局限性。
英文摘要
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.
