Extreme Value Theory: Modelling Catastrophic Losses In Sports Injury

Abstract

Using Extreme Value Theory with a peaks-over-threshold method, we modelled the top 2% of sports-injury losses from 200,000 simulated claims. A generalized Pareto fit via MLE yielded a positive shape (? = 0.783), indicating a fat tail where rare injuries dominate severity. Q–Q and P–P diagnostics show good agreement between model and data. The implied 100-year loss is round 3.31 billion (currency units), and TVaR confirms that conditional on approaching the tail, predicted losses increase quickly. These findings support need for capital buffer to mitigate costly injuries, severe-scenario stress testing, and pricing loadings that specifically consider for costly but rare injuries.