On the Closed-Form Characterisation of the Impact of Risk Misprofiling on Optimal Nigerian Insurance Pricing Models - Adewale, Taiwo Abiodun; Tinuoye, Oladipo Abiodun; Adebayo, Ajala Olusegun; Oluwaseyi, Olaiya Olumide; Olalekan, Owoade Olusegun; Damilare, Olaleye Peter (Mikailalsys Journal of Mathematics and Statistics, 2026)
This study addresses the underexplored issue of risk mis-profiling in optimal insurance pricing models and its implications for solvency and regulatory compliance within the insurance industry. It aims to mathematically analyse the effects of classification errors on premium determination, quantify pricing deviations, and assess sensitivity to misclassification biases. Adopting a quantitative research design, the study utilises insurance data spanning 2010–2020, with computational implementation in Python 3.12.3 (2025) and calibration in Weka 3.9.6 (2022). Policyholders were categorised into low-, medium-, and high-risk groups using confusion matrices, while premiums were derived under exponential utility and deterministic-equivalent principles. Analytical techniques included cumulant generating function expansions, Taylor–Lagrange remainder approximations, and optimisation frameworks. The results indicate that even minor classification errors significantly influence premium estimates, particularly due to exponential tilting, variance underestimation, and tail sensitivity. These distortions align with theoretical expectations and highlight solvency vulnerabilities when premiums fall below actuarially fair values. The study concludes that systematic mis-profiling introduces pricing inefficiencies and potential insolvency triggers. Theoretical contributions include the extension of utility-based pricing principles to account for classification uncertainty, while practical implications call for insurers and regulators to adopt robust pricing adjustments, monitor classifier accuracy, and integrate misclassification-aware pricing mechanisms. Future research directions include extending the framework to portfolio-level analysis, applying robust stochastic optimisation, and investigating the effects of machine learning classification errors on pricing precision.