## Seminar Supervisor

Prof. Dr. Evgeny Spodarev

MSc. Duc Tran Nguyen

## Date and Place

Weekly Meetings or Blocks (depending on the number of students). It can be virtual or actual seminar. Place: Moodle - BigBlueButton

## Prerequisites

The level of difficulty in this seminar is varying between the different topics. The audience is at least supposed to be familiar with Elementary Probability Theory and Statistics,  Probability Theory and Stochastic Processes.

## Intended Audience

Bachelor and Master Students in any mathematical programme of studies. PhD students are welcome to attend the seminar.  The "(B)" in the list of talks, means that this talk is supposed to be given by a Bachelor's Student or Master's Student.

## Content

Every elementary probability course discusses how to construct joint distribution functions of independent random variables, but joint distribution functions of dependent random variables are usually omitted. Obviously, the reason is that things are not as simple as in the independent case. In this matter, so-called copulas can be an elegant tool to investigate dependency structures other than independence.

A copula is a convenient function which links the marginal distributions of random variables to their joint distribution. Interestingly, one can use suitable copulas to model the marginal distributions of random variables and their dependence structure separately. This is also one of the reasons why copulas are highly popular in areas such as finance (e.g. portfolio modeling), insurance, communication networks and others.

The topics of the seminar are covered by two main blocks

• Constructions and Classes of Copulas

• Copulas Estimation

## Preliminary list of talks

Constructions and Classes of Copulas:

I. Basic Properties
- Talk 1:                       Definition and Sklar’s Theorem, Invariance Principle, Survival and Symmetric Copulas(Duc Nguyen) (pdf)
II. Method of Constructing Copulas
- Talk 2:                       Inversion Method + Algebraic Method(Duc Nguyen) (pdf)
- Talk 3:                       Geometric Method(Tim Donhauser) (pdf) (notes)
III. Classes and Families of Copulas
- Talk 4:                       Archimedean Copulas(David Ziener) (pdf) (notes)

IV. Dependence
- Talk 5:                       Concordance and Dependence Properties(Dr. Vitalii Markogin) (pdf)

Copulas Estimation:

V. Copulas Estimation
- Talk 6:                       Parametric Estimation(Artur Bille) (pdf)

- Talk 7:                       Non - parametric Estimation (Viet Hoang)
(pdf)
- Talk 8:                      Copulas Estimation via Maximum Mean Discrepancy (Albert Rapp) (pdf)

Registration

To register for the seminar, please write an e-mail to tran-1.nguyen@uni-ulm.de until the December, 30. In the e-mail please give your name,  matriculation number, your course of studies, and subjects you have taken in the area of Probability, Statistics.  The number of participants is limited to 15 students.

## 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 English.

## Literature

•  An Introduction to Copulas (Springer Series in Statistics)
•  Elements of Copula Modeling with R - Hofert, M., Kojadinovic, I., Mächler, M., Yan, J. (Springer Series in Statistics)

# Contact

Seminar Supervisor