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Extreme Value Theory (EVT) is a statistical framework used to model and assess the risk of extreme events in various domains such as finance, insurance, environmental studies, and actuarial science. In actuarial economics, EVT is particularly important for evaluating rare but high-impact events such as catastrophic losses, large claims, or extreme mortality events. The application of EVT involves a series of structured steps to ensure the accurate modeling of tail risks, and these steps can be outlined comprehensively as follows. The first step in applying EVT is data collection and preparation. This involves gathering historical data relevant to the variable of interest, such as insurance claims, loss amounts, or financial returns. In the context of actuarial economics, the data must be accurate, complete, and representative of the underlying risk profile. After collection, the data is cleaned to remove outliers, inconsistencies, and missing values. This step may also involve data transformation, such as converting raw loss amounts to standardized values, log-transformations to stabilize variance, or aggregating data over suitable time periods. The objective at this stage is to create a dataset suitable for the modeling of extremes while preserving the integrity of the tail behavior. The second step is identifying the extreme values within the dataset. EVT primarily focuses on modeling the behavior of extremes rather than the entire distribution. There are two common approaches to selecting extremes: the block maxima method and the peaks-over-threshold (POT) method. In the block maxima approach, the dataset is divided into non-overlapping blocks (e.g., monthly, yearly, or quarterly), and the ____ _______ ________ ________ _________ ___.
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