Seminar Supervisor

Prof. Dr. Evgeny Spodarev

Seminar Advisor

Dr. Marco Oesting

Date and Place

June 29, 9.00-12.00 and 14.00-17.00, Place: TBA

July 6, 8.30-10.00 and 14.00-17.00, 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. There are a few talks that require the lecture Stochastics II.

Intended Audience

Bachelor and Master Students majoring in any mathematical course of studies.

Content

Extreme Value Theory: Extreme Value Theory deals with stochastic models for rare, "extreme" events. Its theoretical basis is formed by limit theorems for maxima of i.i.d. random variables and for exceedances over high thresholds, respectively. These limit results allow for the assessment of the probability of events beyond previous observations. Applications can be found in numerous fields such as finance, (re-)insurance, meteorology, hydrology or materials science.

Registration

To register for the seminar, please send an e-mail to marco.oesting(at)uni-ulm.de before March 30, 2018. (Extended deadline: April 20)

Criteria to pass the seminar

Each student is supposed to give a talk and to attend the seminar on a regular basis. Those who give a (good) talk and attend the seminar regularly will pass the seminar. Talks will be held in German or in English.

Schedule

June 29:

Morning Session (Helmholtzstr. 22, Room 1.42):

9.00 - 10.30 The Fisher-Tippett Theorem
10.30 - 12.00 The Max-Domain The Max-Domain of Attraction of Fréchet and Weibull Distributions

Afternoon Session (Helmholtzstr. 22, Room E.04):

14.00-15.30 The Max-Domain of Attraction of the Gumbel Distribution
15.30-17.00 The Pickands-Balkema-de Haan Theorem

July 6:

Morning Session (Helmholtzstr. 22, Room 1.42):

8.30-10.00 The Mean Excess Function and the Pareto Distribution

Afternoon Session (Helmholtzstr. 22, Room E.04):

14.00-15.30 Maxima of Stationary Sequences
15.30-17.00 Max-Infinitely Divisible Distributions and the Exponent Measure

Literature:

1.) Embrechts, P., Klüppelberg, C. & Mikosch, T. (1997). Modelling Extremal Events: for
Insurance and Finance. Springer.
2.) Resnick, S.I. (1987). Extreme Values, Regular Variation and Point Processes. Springer.