This entry is from Summer semester 2021 and might be obsolete. No current equivalent could be found.

# Extreme Value Theory (dt. Extremwerttheorie)

 Level, degree of commitment Specialization module, compulsory elective module Forms of teaching and learning,workload Lecture (3 SWS), recitation class (1 SWS), 180 hours (60 h attendance, 120 h private study) Credit points,formal requirements 6 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics. Duration,frequency One semester, Regularly alternating with other specialization modules Person in charge of the module's outline Prof. Dr. Markus Bibinger

## Contents

We introduce the basic stochastic extreme value theory, which investigates the behavior of extreme values (so-called ''outliers''), especially their asymptotic distributions. Important aspects will be extreme value distributions, the theorem by Fisher-Tippett, ''domain of attraction'', order statistics and point processes. Methods for statistical inference are discussed. In addition, applications of extreme value theory in financial risk management and for climate data are given as examples.

## Qualification Goals

The students shall

• acquire knowledge in the field of specialization of extreme value theory as a subfield of stochastics,
• understand the differences between methods based on mean values or order statistics,
• learn techniques for statistical analysis,
• learn about interdisciplinary application possibilities, especially in risk management,
• improve their communication skills in the recitation class.

## Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Probability Theory, Internship Stochastics.

## Applicability

The module can be attended at FB12 in study program(s)

• B.Sc. Mathematics
• M.Sc. Data Science
• M.Sc. Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Applied Modules in Business Mathematics.

The module can also be used in other study programs (export module).