AI 中文总结
研究针对保险业ALM模型计算成本高的问题，基于路径签名理论提出近似框架，通过签名项线性组合近似ALM输出，该方法易校准、预测性强且能降低成本，适用于精算应用中的大规模分析和评估。
AI 中文摘要
在保险业中，资产负债管理（ALM）模型是众多应用的关键工具，包括偿付能力资本要求（SCR）计算和资产配置优化。然而，其使用通常需要巨大的计算成本，特别是在必须进行大量敏感性分析或压力资产负债表评估时。在这项工作中，我们基于路径签名理论，为ALM模型的输出（如有效价值或最佳估计）提出了一个近似框架。具体而言，所提出的方法包括通过从输入经济情景导出的签名项的线性组合来近似ALM输出。我们表明，所得的替代模型易于校准，主要通过正则化线性回归实现，并且在大幅降低计算成本的同时展现出强大的预测性能。我们还通过在替代模型固定时考虑风险因素基础模型参数的变化，研究了其在经济情景分布变化下的稳健性。这些结果使得所提出的方法特别适用于实际精算应用中的大规模敏感性分析和快速资产负债表评估。
英文摘要
In the insurance industry, Asset and Liability Management (ALM) models are key tools for numerous applications, including Solvency Capital Requirement (SCR) computation and asset allocation optimization. However, their use often entails a significant computational cost, especially when a large number of sensitivities or stressed balance-sheet evaluations must be performed. In this work, we propose an approximation framework for the outputs of an ALM model, such as the Value In Force or the Best Estimate, based on the theory of path signatures. More precisely, the proposed approach consists of approximating ALM outputs by a linear combination of signature terms derived from input economic scenarios. We show that the resulting surrogate is easy to calibrate, essentially through regularized linear regression, and exhibits strong predictive performance while drastically reducing computational costs. We further investigate its robustness under changes in the distribution of economic scenarios by considering variations in the parameters of the underlying model of risk factors while the surrogate model is kept fixed. These results make the proposed approach particularly suitable for large-scale sensitivity analyses and fast balance-sheet evaluations in practical actuarial applications.
