量子幅值估计在灾难保险尾部风险定价中的应用：经验收敛性与NISQ噪声分析
Quantum Amplitude Estimation for Catastrophe Insurance Tail-Risk Pricing: Empirical Convergence and NISQ Noise Analysis
AI总结：
本文研究量子幅值估计在灾难保险尾部风险定价中的应用，通过实验证明其在尾部风险估计中的优势，指出离散化是当前瓶颈。
摘要：
经典蒙特卡洛方法在定价灾难保险尾部风险时收敛速度为1/√N，需要大规模模拟预算来解析损失分布的上尾百分位数。此样本稀疏问题可能导致AI模型在贫乏的尾部数据上训练，产生校准不佳的风险估计，其中破产风险最大。量子幅值估计（QAE）在蒙塔诺罗的框架下，实现收敛速度接近1/N，即在Oracle查询中获得二次加速，这在规模上将使高分辨率尾部估计在实际预算内成为可能。我们使用Qiskit Aer模拟器和真实的Grover放大方法验证了这一优势。一个完整的管道将拟合的对数正态灾难分布编码到量子Oracle中，通过幅值编码产生小的读取概率，从而安全地进行Grover放大，最多支持k=16次迭代。在合成和真实（NOAA风暴事件，58,028条记录）数据上的七项实验得出三个主要发现：Oracle模型优势，当有分析访问时，强大的经典基线胜出，以及离散化而非估计是当前的瓶颈。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
