Research Article
Uncertainty-Calibrated Distributionally Robust Pricing for Insurance: From AI-Based RiskPrediction to Robust and Non-Conservative Premiums
Majid Ghorbani*
Issue:
Volume 1, Issue 2, June 2026
Pages:
48-53
Received:
20 August 2026
Accepted:
31 August 2026
Published:
18 September 2026
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.
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 c...
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Methodology Article
Mathematical Modelling of Light Propagation in Optical Fibers: From Maxwell’s Equations to Split-Step Simulation of Dispersive and Nonlinear Pulse Dynamics
Randriana Heritiana Nambinina Erica*,
Ando Nirina Andriamanalina
Issue:
Volume 1, Issue 2, June 2026
Pages:
54-63
Received:
10 October 2026
Accepted:
20 October 2026
Published:
31 October 2026
DOI:
10.11648/j.sdmath.20260102.12
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Abstract: Optical fibers carry most of the world’s long-distance data traffic, and reliable mathematical models are essential for designing, optimizing and teaching the systems built on them. This work presents a self-contained mathematical model of light propagation in single-mode optical fibers and its numerical implementation in Python. Starting from Maxwell’s equations, we derive the guided-mode eigenvalue problem of the step-index fiber, the frequency dependence of attenuation and chromatic dispersion from the Sellmeier equation and empirical loss models, and the nonlinear Schrödinger equation (NLSE) governing the slowly varying pulse envelope under the combined effects of loss, dispersion and the Kerr nonlinearity. Closed-form results for Gaussian pulse broadening, self-phase modulation (SPM) and soliton propagation are used as analytical benchmarks and combined with a symmetric split-step Fourier method (SSFM) for the numerical solution. The numerical scheme is validated against these analytical solutions to a relative accuracy better than 10-12 for linear propagation, reproduces the expected number of SPM spectral peaks, preserves fundamental and third-order solitons over two soliton periods, and demonstrates the expected second-order convergence with step size. A link-level simulation of a 2.5 Gb/s amplified system, including amplifier noise, a square-law receiver and the resulting Q-factor, shows an optimum launch power that decreases from approximately +11 dBm to +5 dBm as the number of 80 km spans increases from three to six, illustrating the trade-off between noise accumulation and nonlinear distortion. The results show how a compact, physics-based model, implemented in a few dozen lines of code, reproduces the main performance trade-offs of fiber-optic transmission and provides a validated basis for further studies including polarization effects, Raman scattering and multi-channel transmission.
Abstract: Optical fibers carry most of the world’s long-distance data traffic, and reliable mathematical models are essential for designing, optimizing and teaching the systems built on them. This work presents a self-contained mathematical model of light propagation in single-mode optical fibers and its numerical implementation in Python. Starting from Maxw...
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