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Last update: T_KPMS (06.05.2014)
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Last update: doc. Ing. Marek Omelka, Ph.D. (25.05.2023)
To deepen understanding of students in probability theory, mathematical statistics, econometrics and financial mathematics. |
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Last update: RNDr. Jitka Zichová, Dr. (29.10.2019)
Exam. The requirements change each year, are determined by the teacher. |
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Last update: doc. Ing. Marek Omelka, Ph.D. (27.09.2023)
Various journals on probability theory, mathematical statistics, econometrics and financial mathematics.
First term 2023/24:
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 |
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Last update: T_KPMS (06.05.2014)
Lecture. |
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Last update: RNDr. Jitka Zichová, Dr. (29.10.2019)
The requirements change each year, are determined by the teacher. |
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Last update: doc. Ing. Marek Omelka, Ph.D. (27.09.2023)
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.
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