Extreme Value Theory

• Master Mathematik (optional)
• Master Wirtschaftsmathematik (optional)
• Master Mathematische Biometrie (optional)
• Master of Finance (optional)
• Master CSE (optional)

News:

Please note the updated schedule!

More information and materials (e.g. lecture notes and exercise sheets) will be provided on Moodle. The password to register for the course will be given to you in the first lecture.

Lecture: Tuesdays, 12-2 p.m., He22 E.04

Exercise Class: Thursdays, 2-4 p.m., N24-131 (biweekly)

The lectures will start on Tuesday, 23rd of April. The first exercise class will take place on Thursday, 2nd of May.

Please note the following deviations from the schedule above:

• Instead of the lecture on Tuesday, 30th April, a lecture will take place on Thursday, 25th of April, 2-4 p.m., room N24-131.
• Instead of the lecture on Tuesday 4th of June, a lecture will take place on Thursday, June 6th, 2-4 p.m., room N24-131.
• Instead of the lecture on Tuesday, 23rd of July, a lecture will take place on Thursday, 11th of July, 2-4 p.m., room N24-131.

Final Exam:

Details tba

Prerequisites:

Measure Theory (or Introduction to Measure Theoretic Probability), Elementary Probability Theory and Statistics, Stochastics I

Contents:

In many applications, the biggest or smallest values of a sample are of particular relevance. For example, in finance and insurance - particular in risk assessment and management - many decisions have to be based on the behavior of extreme values. Likewise, extreme value theory is of utmost importance in areas like ecology, hydrology, and climatology.

The course will cover the following topics:

• Classical extreme value theory for i.i.d. observations, e.g. characterizing the possible limit distribution of extremal events and their domains of attraction
• Points over threshold method, i.e. finding the probability that a given (high) threshold is exceeded
• Related statistical techniques
• Discussion of applications in various fields

 Literature:

•  Coles, S. (2001), An Introduction to Statistical Modelling of Extreme Values, Springer
• Embrechts, P., Klüppelberg, C., and Mikosch,  T. (1997), Modelling Extremal Events for Insurance and Finance, Springer
• Leadbetter, M.R., Lindgren, G., and Rootzén, H. (1983), Extremes and Related Properties of Random Sequences and Processes, Springer
• Resnick, S. (1987), Extreme Values, Regular Variation and Point Processes, Springer

Exercise sheets:

Moodle

Moodle