401-3919-60L An Introduction to the Modelling of Extremes
Semester | Spring Semester 2017 |
Lecturers | P. Embrechts |
Periodicity | yearly recurring course |
Language of instruction | English |
Courses
Number | Title | Hours | Lecturers | ||||
---|---|---|---|---|---|---|---|
401-3919-60 V | An Introduction to the Modelling of Extremes Offered for the last time in FS 2017, examination until summer 2018. | 2 hrs |
| P. Embrechts |
Catalogue data
Abstract | This course yields an introduction into the MATHEMATICAL THEORY of one-dimensional extremes, and this mainly from a more probabilistic point of view. |
Objective | In this course, students learn to distinguish between so-called normal models, i.e. models based on the normal or Gaussian distribution, and so-called heavy-tailed or power-tail models. They learn to do probabilistic modelling of extremes in one-dimensional data. The probabilistic key theorems are the Fisher-Tippett Theorem and the Balkema-de Haan-Pickands Theorem. These lead to the statistical techniques for the analysis of extremes or rare events known as the Block Method, and Peaks Over Threshold method, respectively. |
Content | - Introduction to rare or extreme events - Regular Variation - The Convergence to Types Theorem - The Fisher-Tippett Theorem - The Method of Block Maxima - The Maximal Domain of Attraction - The Fre'chet, Gumbel and Weibull distributions - The POT method - The Point Process Method: a first introduction - The Pickands-Balkema-de Haan Theorem and its applications - Some extensions and outlook |
Lecture notes | There will be no script available, students are required to take notes from the blackboard lectures. The course follows closely Extreme Value Theory as developed in: P. Embrechts, C. Klueppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer. |
Literature | The main text on which the course is based is: P. Embrechts, C. Klueppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer. Further relevant literature is: S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. Springer. S. I. Resnick (1987) Extreme Values, Regular Variation, and Point Processes. Springer. |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
ECTS credits | 4 credits |
Examiners | P. Embrechts |
Type | session examination |
Language of examination | English |
Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
Mode of examination | oral 20 minutes |
This information can be updated until the beginning of the semester; information on the examination timetable is binding. |
Learning materials
No public learning materials available. | |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |