Rare events such as extreme weather phenomena, large insurance claims and financial crashes are of prime concern for society. The aim of this course is to provide an introduction the mathematical and statistical modelling of extremal events.

Topics include: (1) an introduction to the mathematical foundations of classical univariate extreme-value theory, the Fisher-Tippett Theorem for block maxima and the Pickands-Balkema-de Haan Theorem for threshold exceedances, maximum domain of attraction and the concept of regular variation;

(2) statistical models and methods for extremes, estimation of high quantiles and return levels, likelihood inference, Hill estimation, threshold selection and bias reduction techniques;

(3) extensions to extremes for non-stationary and dependent sequences, the point process approach for the characterization and modelling of extremes.  

Modeling Extremal Events by P. Embrechts, C. Klüppelberg and T. Mikosch, Springer 1997.

·       Statistics of Extremes by J. Beirlant, Y. Goegebeur, J. Segers and J. Teugels, Wiley 2004.

·      Extreme Values, Regular Variation and Point Processes by S. I. Resnick, Springer 1987 (2nd Ed. 2007).

·      Extreme Value Theory by L. de Haan and A. Ferreira, Springer 2006.

·      An Introduction to Statistical Modeling of Extreme Values by S. Coles, Springer 2001

Students will acquire a good understanding of theoretical and practical aspects of  univariate EVT. Moreover, they will be able to analyze data with EVT.

at least 80% of the units

Classroom teaching; project and group work

The course assessment will be based on project work and on an oral presentation of the project.

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