Syllabus
The course covers selected advanced topics from probability, mathematical statistics, econometrics and financial mathematics.
Teachers and topics change every term.
First term 2023/24
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 to the mathematical and statistical modelling of extremal events, show how to implement the techniques with R and apply them in risk management and the environmental sciences.
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 more complex data, such as non-iid sequences, stationary time series, multivariate data, and spatio-temporal processes.
Annotation
This is a course for PhD students, eventually for Master students. The course covers selected advanced topics from probability, mathematical statistics, econometrics and financial mathematics.