Quantum Machine Learning for Personalized Insurance Premium Calculation

Abstract

Personalized insurance pricing requires robust estimation of conditional loss distributions from high-dimensional, heterogeneous data (demographics, medical records, telematics, claims histories). Classical ML techniques (gradient-boosted trees, deep neural networks, kernel methods) have advanced personalization but face computational and statistical limits when data are extremely high-dimensional, when nested Monte Carlo is required for capital calculations, or when richer uncertainty quantification is necessary. Quantum Machine Learning (QML) including quantum kernel methods, variational quantum circuits (VQCs), and amplitude-estimation-enabled Monte Carlo acceleration provides new algorithmic pathways that may (a) embed rich feature representations in high-dimensional Hilbert spaces, (b) offer different inductive biases than classical kernels, and (c) accelerate certain expectation-estimation tasks relevant to risk metrics. This paper (1) synthesizes QML theory with actuarial pricing objectives, (2) provides full mathematical formulations of candidate QML models and their training procedures for premium estimation, (3) designs hybrid quantum–classical deployment architectures suitable for insurers, (4) proposes reproducible experimental protocols and evaluation metrics, and (5) discusses regulatory, ethical, and practical limitations (NISQ constraints, data loading, governance).