Quantum Amplitude Estimation for Catastrophe Insurance Tail-Risk Pricing: Empirical Convergence and NISQ Noise Analysis
This work addresses the sample-sparsity issue in tail-risk pricing for catastrophe insurance, which can lead to poorly calibrated AI models and insolvency risks, though it is incremental as it validates known quantum advantages with empirical data.
The paper tackled the problem of pricing catastrophe insurance tail risk by comparing Quantum Amplitude Estimation (QAE) to classical Monte Carlo methods, finding that QAE achieves a quadratic speedup in convergence (approaching order reciprocal N vs. reciprocal root N) but that discretisation, not estimation, is the current bottleneck in practical applications.
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.