Quantum Amplitude Estimation for Catastrophe Insurance Tail-Risk Pricing: Empirical Convergence and NISQ Noise Analysis

TL;DR

This paper demonstrates that Quantum Amplitude Estimation can significantly improve tail-risk pricing for catastrophe insurance by providing a quadratic speedup over classical methods, validated through simulations on real and synthetic data.

Contribution

It empirically validates the advantage of QAE for tail-risk estimation in catastrophe insurance and analyzes the impact of NISQ noise and discretization bottlenecks.

Findings

QAE shows an oracle-model advantage in tail-risk estimation.

Classical methods outperform when analytical models are available.

Discretization, not estimation, limits current quantum approaches.

Abstract

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.