9 - The Modeling of Extreme Events

Summary

Almost by definition of risk, rare events play a crucial role. We tackle this problem by presenting some basic tools from extreme value theory (EVT). From a statistical point of view, the workhorses are the block maxima method (BMM) and the peaks over threshold method (POTM). Besides giving the mathematical formulation, we exemplify both approaches via simulated examples. Once these tools are in place, we can provide estimators of the relevant risk measures such as high-exceedance probabilities, quantiles and return periods. In a crucial part of the book, we then estimate these quantities for sea-level data at Hoek van Holland near Rotterdam. We obtain estimates, including confidence intervals, for a necessary dike height withstanding a required 1 in 10 000 years storm event. Further applications concern financial data and data from the L’Aquila earthquake. For the latter, we present dynamic models for earthquake aftershocks. After an excursion to the world of records in athletics, we present the signature application of EVT through the story of the sinking of the MV Derbyshire. We show how an application of EVT techniques has saved many lives at sea.