###### Main content

This entry is from Winter semester 2021/22 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
• B.Sc. Business Mathematics
• M.Sc. Data Science
• M.Sc. Mathematics
• M.Sc. Business Mathematics

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

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

## Recommended Reading

• Will be announced at the beginning of the course.

## Please note:

This page describes a module according to the latest valid module guide in Winter semester 2021/22. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.