Time and Place practical ,
This course offers an introduction into the mathematical aspects of risk theory and quantitative risk managment. We will discuss basic concepts like the loss distribution, risk measurement, risk measures based on the loss distribution, e.g. value at risk or expected shortfall, as well as standard methods to compute market risk. Further we will give a basic introduction of extreme value theory and copulas and discuss applications of those in risk theory and insurance analytics. We will also introduce the credit risk management and discuss different credit risk models like structural models of default, threshold models, and the mixture model approach. Finally we will also tackle dynamic credit risk models.
After the successful completion of this course the students will be able to deal will quantitative risk models. They will be familiar with the mostly used models, their applicability, as well as their advantages and disadvantages in different situations.
Chapter titles:
- Risk management perspective: background and goals
- Basic concepts in risk management
- Standard methods to access market risk
- Extreme value theory and the POT method
- Dependence models: multivariate distributions and copulas
- Credit risk (static and dynamic models)
The main sources:
H. Hult, F. Lindskog, O. Hammarlind, C.J. Rehn,
Risk and Portfolio Analysis: Principles and Methods
Springer Series in Operations Research and Financial Engineering, Springer, 2012.
A.J. McNeil, R. Frey und P. Embrechts,
Quantitative Risk Management,
Princeton Series in Finance, Princeton University Press, Princeton, NJ, 2005.
Other titles:
-
P. Embrechts, C. Klüppelberg und Th. Mikosch,
Modelling Extremal Events for Insurance and Finance,
Springer, Berlin, 1997. -
P. Embrechts, A.J. McNeil und D. Straumann,
Correlation and dependence in risk management:properties and pitfalls,
in Risk Management: Value at Risk and Beyond,M.Dempster, Hrsg.,
Cambridge University Press, Cambridge, 2002. -
R.B. Nelsen,
An Introduction to Copulas,
Springer, New York, 1999. -
S.I. Resnick,
Extreme Values, Regular Variation and Point Processes,
Springer Series in Operations Research and Financial Engineering, New York, 2007.
More specific references, especially related to proofs of theorems which will be discussed without proof in the lecture
-
Karamata's theorem:
N.H. Bingham, C.M. Goldie, J.L. Teugels,
Regular Variation,
Cambridge University Press, Cambridge, 1987. -
Theorems on the maximum domain of attraction of max-stable distributions:
P. Embrechts, C. Klüppelberg und Th. Mikosch,
Modelling Extremal Events for Insurance and Finance,
Springer, Berlin, 1997. -
Lemma of Leadbetter at al., 1983:
M.R. Leadbetter, G. Lindgren, und H. Rootzen,
Extremes and related properties of random sequences and processes,
Springer, Berlin, 1983.
The grade for the lecture will be the result of an oral examination.
The dates for the oral examination will be decided upon necessity and in agreement with the students.
The grade for the practical will be based on a continuous assessment in the practical units and a written examination on February 1, 2019.
The registration for the written examination should be done via TUGonline.
The success of the students in the practical will be measured in terms of points which can be collected during the term and at the written examination.
The maximum amount of collectable points at the written examination is 12 with a minimum of 4 points to be achieved in order to be positively graded for the practical. The maximum number of collectable points during the practical units is 12.
During the practical units students can collect points by preparing and presenting their solutions of the assignmemts; each correctly presented solution earns the presenter 2 points. A student has to present the solutions of at least six assignments in order to be positively graded for the practical. At the beginning of each practical unit the students should report which assignments they have prepared. Among all students who have prepared a certain assignment the instructor will select the candidate to present his/her solution on the board.
Points
The total number of collected points is given as follows
P= K + 12(P+B)/A where
| K | - points obtained at the written examination |
| P | - number of the prepared assignments |
| B | - points obtained for the presentation on the board |
| A | - overall number of assignments |
Grade obtained for the practical according to the overall score:
5 0 <= P <= 12
4 12 = P <= 15
3 15 < P <= 18
2 18 < P <=21
1 21< P
There will be a classical black-board lecture supported by slides the files of which will be uploaded here prior to each lecture.
- Slides of the lecture on October 1 (pdf)
- Slides of the lecture on October 4 (pdf)
- Slides of the lecture on October 8 (pdf)
- Slides of the lecture on October 15 (pdf)
- Slides of the lecture on October 17 (pdf)
- Slides of the lecture on October 22, first part- (pdf)
- Slides of the lecture on October 22- second part (pdf)
- Slides of the lecture on October 29 (pdf)
- Slides of the lecture on October 31 (pdf)
- Slides of the lecture on November 5 (pdf)
- Slides of the lecture on November 12 (pdf)
- Slides of the lecture on November 14 (pdf)
- Slides of the lecture on November 19 (Part 1) (pdf)
- Slides of the lecture on November 19 (Part 2) (pdf)
- Slides of the lecture on November 26 (pdf)
- Slides of (a part) of the lecture on November 28 (pdf)
Some lecture notes (in German, do not cover the whole course material!) can be downloaded here.
The work sheets
will also be published hier, usually one week ahead of the corresponding practical unit.
- 1st work sheet, to be discussed on October 11 (pdf)
- 2nd work sheet, to be discussed on October 24 (pdf)
- 3d work sheet, to be discussed on November 7 (pdf)
- 4th work sheet, published on November 15, to be discussed on November 21 and December 5 (pdf)
- 5th work sheet, to be discussed on January 9, (pdf)
cela@opt.math.tu-graz.ac.at.
Last update on December 2019