The Extreme Value Theory for Demographical Risk Analysis and Assessment: Peaks Over Random Threshold Value-at-Risk Analysis of Regional Prevalence Data with a Demographical Case Study

This study presents a novel application of Extreme Value Theory (EVT) to analyze and quantify the risk associated with disability prev lence across regions in Saudi Arabia. Leveraging advanced actuarial risk modeling techniques including Value-at-Risk (VaR), Tail Value-at-Risk (TVaR) , Mean of Order P (MOP), and the Peaks Over Random Threshold Value-at-Risk (PORT-VaR) framework, we provide a robust statistical assessment of regional disparities and extreme disability risk. Using demographic data from the 2016 national survey, our analysis identifies critical outliers and quantifies extreme thresholds at varying confidence levels (55%–95%). The Northern Border region emerges as a high-risk area, with over 285,000 individuals living with disabilities, significantly exceeding other regions. Our PORT-VaR and Peaks Over Random Threshold Mean of Order P (PORT-MOP) models highlight urgent policy targets and resource allocation needs, particularly for older adults and low-income populations who are disproportionately affected. This work contributes to the growing field of actuarial statistical modeling by demonstrating how EVT-based tools can enhance public health planning and support evidence-based decision-making in social policy development. By aligning traditional actuarial methodologies with contemporary public health challenges, the study underscores the relevance of predictive modeling and quantitative risk management in addressing complex societal issues such as disability prevalence.