Modelling Extremal Events: For Insurance and Finance

By Paul Embrechts
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"Modelling Extremal Events" by Paul Embrechts offers a comprehensive overview of the statistical models and methodologies used in the analysis of extreme events. The book begins by introducing the concept of extreme value theory and its applications in various fields, such as hydrology, finance, insurance, and climate science.

Embrechts dives into the mathematical foundations of extreme value theory, presenting detailed explanations of different types of extreme value distributions, including the classical, general, and non-parametric approaches. He also covers tail estimation techniques, extreme quantile estimation, and peak-over-threshold models.

Throughout the book, Embrechts discusses real-world case studies and provides practical insights into modeling extreme events with a focus on accuracy and reliability. He explores the challenges associated with the extrapolation of extreme value estimates, highlighting the importance of robustness and sensitivity analysis.

The book concludes with a discussion on multivariate extreme value models, addressing the modeling of both dependent and independent extreme events. Embrechts emphasizes the importance of copula functions in capturing the dependency structure and provides guidance on their implementation.

"Modelling Extremal Events" is a valuable resource for researchers, practitioners, and students interested in understanding and modeling the statistical behavior of extreme events. Embrechts' clear and concise writing style, combined with numerous examples and exercises, makes it an accessible reference for those new to the subject, while also offering advanced insights for experienced statisticians and risk analysts.
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