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

Kirke, Alexis

arXiv.org Machine Learning

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.







ThetraininglossofCOMETis L= s ˆ s

Neural Information Processing Systems

However,inpractice, we did not find both effects inthe training. The last term in the loss function of COMET does not need the information from the dataset. This section contains the experiment details for cases tested in section 4. In section 4, there are 6 simple experiments performed todemonstrate the capability ofCOMET:(1) mass-spring, (2) 2D Case5: 2Dnonlinear spring.Weconsider acaseofamotion ofanobjectofmassm=1in2D where it is connected to the origin with a nonlinear spring with forceF = |r|2r where r is the position of the object in 2D coordinate. The constants of motion of this systems are the energy and the angular momentum,whichmakesnc=2. Case 6: Lotka-Volterraequation isanordinary differential equation modelling thepopulation of predatorandprey. The training loss in this case was composed of the reconstruction loss and the dynamics loss.


1 Data Ingestion

Neural Information Processing Systems

For all other remaining architectures, the reported results are from private datasets. Neck Shaft Angle(NSA) cannot be estimated. Additionally, [? ] requires estimation of the diaphysis Figure 4: Repeatability of the femur morphometry extraction method as measured by error distributions for a) the landmarks/anatomical sizes and b) axis alignment identified by the adapted method. Do the main claims made in the abstract and introduction accurately reflect the paper's Did you specify all the training details (e.g., data splits, hyperparameters, how they were Data splits are available in the GitHub repository. Did you report error bars (e.g., with respect to the random seed after running ex-67 Did you include the total amount of compute and the type of resources used (e.g., Did you mention the license of the assets?