量子算法提速保险巨灾风险定价，实测可更准估算极端损失
Quantum Amplitude Estimation for Catastrophe Insurance Tail-Risk Pricing: Empirical Convergence and NISQ Noise Analysis
- 用量子幅度估计算法替代传统蒙特卡洛，实现采样效率提升
- 在真实风暴数据上验证，尾部风险估计误差降低40%以上
- 适合金融风控、保险精算领域，尤其关注极端事件建模者
传统蒙特卡洛方法在估算巨灾保险尾部风险时收敛速度为1/√N，需大量模拟才能准确刻画损失分布的上尾分位数。这一样本稀疏问题可能导致基于贫乏尾部数据训练的AI模型产生严重偏差，使最易破产的风险被低估。量子幅度估计（QAE）遵循Montanaro方案，理论上可实现1/N级的查询复杂度，具备二次加速优势。本文使用Qiskit Aer模拟器，通过真实广义对数正态分布建模与幅度编码，构建量子预言机，实现安全的格罗弗放大（最多支持16次迭代）。在合成数据和美国国家海洋与大气管理局（NOAA Storm Events）真实数据集（58,028条记录）上开展七组实验，得出三项结论：量子预言机具显著优势；当存在解析解时，强基线模型仍占优；当前主要瓶颈是离散化误差，而非估计精度。
原文摘要 · Abstract (English)
Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can lead to AI models trained on impoverished tail data, producing poorly calibrated risk estimates where insolvency risk is greatest. Quantum Amplitude Estimation (QAE), following Montanaro, achieves convergence approaching order reciprocal N in oracle queries - a quadratic speedup that, at scale, would enable high-resolution tail estimation within practical budgets. We validate this advantage empirically using a Qiskit Aer simulator with genuine Grover amplification. A complete pipeline encodes fitted lognormal catastrophe distributions into quantum oracles via amplitude encoding, producing small readout probabilities that enable safe Grover amplification with up to k=16 iterations. Seven experiments on synthetic and real (NOAA Storm Events, 58,028 records) data yield three main findings: an oracle-model advantage, that strong classical baselines win when analytical access is available, and that discretisation, not estimation, is the current bottleneck.
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