Seminar Supervisor

Prof. Dr. Evgeny Spodarev

Seminar Advisor

Albert Rapp, M. Sc.

Date and Place

Depending on the number and preferences of the participants we will meet weekly or only once.  
Place: TBA.

Prerequisites

The level of difficulty in this seminar is varying between the different topics. The audience is at least supposed to be familiar with basic probability, statistics, basic analysis and measure theory. We ensure the participants that most of the 'beyond' knowledge will be learned during the seminar.

Intended Audience

Bachelor and Master students in any mathematical programme of studies. 

Content

The notion of heavy-tails frequently arises in extreme-value theory and studies phenomena whose behavior is mainly dominated by large rather than small movements. For instance, an insurer concerned with covering storm damages will observe that it is the large but rare rather than the small but frequent storms that drive the total amount of claims. Thus, that insurer will have to rely on methods from heavy-tail analysis to make inferences about future claim sizes.

Of course, actuarial science is not the only field relying on heavy-tail analysis since other applications come from all sorts of fields such as finance, network analysis and many more. However, from this short example the significance of heavy tails for real-world applications becomes abundantly clear. Mathematically speaking, heavy-tail analysis offers a rich blend of methods from pure mathematics such as the theory of regularly varying functions, probability theory and statistics.

In this seminar, we want to explore this wide variety of mathematical fields by following the book “Heavy-Tail Phenomena: Probabilistic and Statistical Modeling” by Sidney I. Resnick. A preview of all chapters of this book is available on the Springer homepage (Link) and students can express their interests regarding preferred topic/chapter or whether they are interested in covering topics related to pure mathematics, probability theory or statistics.

Preliminary list of talks

We will restrict ourselves to the following chapters of the book and each chapter will be split into two talks. 

• Regular variation - Chapter 2
• Weak convergence - Chapters 3
• Statistical inference for heavy tails - Chapter 4
• The Poisson Process - Chapter 5
• Multivariate regular variation - Chapter 6
• Weak convergence and the Poisson Process - Chapter 7
• Applied Probabilty Models and Heavy Tails - Chapter 8

Registration

To register for the seminar, please write an E-Mail to Albert Rapp until March, 01. In the e-mail please give your name, matriculation number, your programme of studies and subjects you have taken in the area of Probability or Statistics. Also, please indicate what chapter of the book you're interested in.  

Criteria to pass the seminar

Each student is supposed to give a talk. Those who give a (good) talk together with written summary will pass the seminar. Talks will be held in German or English. A preliminary version of the Slides need to be submitted two weeks before each talk.

Literature

Sidney I. Resnick (2007), Heavy-Tail Phenomena: Probabilistic and Statistical Modeling, Springer-Verlag New York