Abstract
The increasing use of machine learning and artificial intelligence in insurance pricing has created new opportunities for modeling complex relationships between policyholder characteristics and insurance losses. Unlike conventional actuarial models, modern probabilistic machine-learning approaches can provide flexible predictive distributions and can potentially quantify different forms of predictive uncertainty. Nevertheless, the availability of sophisticated predictive distributions does not by itself solve the problem of decision-making under uncertainty. A pricing model must determine how uncertainty in the estimated loss distribution should affect the premium charged to an insured risk. Distributionally robust optimization provides a natural framework for addressing uncertainty in probability distributions by replacing a single reference distribution with an ambiguity set containing plausible alternatives. Although distributionally robust methods and their applications to insurance are already well established, an important methodological issue remains concerning the connection between predictive uncertainty generated by modern AI models and the construction of ambiguity sets for robust insurance pricing. In particular, ambiguity sets that are excessively small may fail to provide adequate robustness, whereas overly large sets can produce excessively conservative premiums. This paper develops a conceptual mathematical framework for uncertainty-calibrated distributionally robust insurance pricing. The framework connects four components: AI-based probabilistic risk prediction, predictive uncertainty quantification, statistically calibrated ambiguity-set construction, and robust premium determination. Particular attention is given to the relationship between predictive calibration, ambiguity-set size, robustness guarantees, and premium conservatism. The paper does not claim that distributionally robust insurance pricing or machine-learning-based insurance pricing is novel in isolation. Instead, it identifies a focused research direction concerning the mathematical calibration of distributional ambiguity from AI-derived predictive uncertainty and the characterization of its consequences for robust insurance premiums. The proposed framework provides a basis for future theoretical work on stability, sensitivity, convergence, and conservatism bounds in uncertainty-aware insurance pricing.