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; (3) extensions to extremes for non-stationary and dependent sequences, the point process approach for the characterization and modelling of extremes; (4) extremes in the multivariate and spatio-temporal context.  

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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