NMAK13005U Introduction to Extreme Value Theory (IntroExtremValue)(AAM)
MSc Programme in Acturial Mathematics
MSc Programme in Statistics
MSc programme in Mathematics-Economics
In this course the student will learn about the basics of modern
extreme value theory.
These include the classical asymptotic theory about the weak limits
of standardized maxima and order statistics (Generalized Extreme
Value Distribution) and of the excesses above high thresholds
(Generalized Pareto Distribution) for sequences of iid random
variables. An important part occupies the classification of
distributions in different Maximum Domains of Attraction of the
limitng extreme value distributions. Based on this theory,
statistical tools and methods for detecting extremes and estimating
their distributions are considered. These include estimators
of the tail index of a Pareto-like distribution, the extreme
value index of a distribution, the parameters of an extreme value
distribution and the estimation of high/low quantiles
of a distribution and tail probabilities, possibly outside
the range of the data. We discuss notions such as Value at Risk and
Expected Shortfall which ate relevant for Quantitative Risk
Management and their relation with extreme value theory. In the end
of course, we discuss how the classical theory for independent
variables can be extended to dependent observations. Such
observations typically have clusters of extreme values. We will
learn about the extremal index which measures the size of clusters.
The theory will be illustrated by various data sets
from finance, insurance and telecommunications.
In this course, the student will learn about the basics of
modern extreme value theory.
Knowledge:
In particular, he/she will know about the following topics:
Classical limit theory for sequences of iid observations and their
excesses above high thresholds.
Exploratory statistical tools for detecting and classifying
extremes.
Standard statistical methods and techniques for handling extreme
values, including estimation for extreme value distributions and in
their domains of attraction, the Peaks over Threshold (POT)
method for excesses above high thresholds.
Standard notions from Quantitative Risk Management such as
Value at Risk, Expected Shortfall, return period, t-year event, and
their relation with extreme value theory.
The notion of cluster of extremes for dependent data and how to
measure the size of clusters.
Skills:
At the end of the course, the student will be able to read
books, articles and journals
which are devoted to topics of modern extreme value theory and
extreme value statistics.
Competences:
The student will be competent in modeling extremes of independent
and weakly dependent observations and be able to apply software
packages specialized for analyzing extreme values.
P. Embrechts, C. Klueppelberg, T. Mikosch. Modelling Extremal Events for Finance and Insurance. Springer, Heidelberg, 1997. 9th Printing 2012
- Category
- Hours
- Exam
- 66
- Lectures
- 35
- Theory exercises
- 105
- Total
- 206
As
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesWritten assignmentThe oral examination counts for 70% of the grade.
The remaining 30% correspond to a Mid Term (15%) and a Final Term Test (15%).
In the take home tests, the student will solve some theoretical problems and get estimation experience with simulated and real-life financial and insurance data. - Exam registration requirements
The student must have received more than 50% of the marks for each of the Mid Term and the Final Terms Tests.
- Aid
- Without aids
The oral final exam is without aids. All aids are allowed for the two tests,
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
- Re-exam
Oral examination (30 minutes) with internal censor without preparation time and notes.
The student is admitted to the re-examination if he/she has received more than 50% of the marks in both the Mid Term and Final Term Tests. If this has not been achieved at the time of the first examination the student may resubmit the two tests no later than two weeks before the beginning of the re-examination week.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK13005U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Thomas Valentin Mikosch (7-6f6b6d7175656a426f63766a306d7730666d)
Office. 04.3.10