Risk theory and management in actuarial science
3 lecture + 1 practical
Department of Discrete Mathematics
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.
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.
More specific references, especially related to proofs of theorems which will be discussed without proof in the lecture
N.H. Bingham, C.M. Goldie, J.L. Teugels,
Cambridge University Press, Cambridge, 1987.
P. Embrechts, C. Klüppelberg und Th. Mikosch,
Modelling Extremal Events for Insurance and Finance,
Springer, Berlin, 1997.
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 result from oral exam.
The dates for the oral exam 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.
The success of the students will be measured in terms of points which can be collected during the term in the following ways.
The total number T of collected points is given as follows
T= 8P/A +12*(B/(4*P1)) where
|P||- number of the tasks worked on|
|P1||- number of the tasks presented on the board|
|B||- overall number of points obtained for presentations|
|A||- overall number of tasks|
5 0 <= T < 12
4 12 < T < 14
3 14 < T < 16
2 16 < T < 18
1 18< T
There will be a classical black-board lecture supported by slides the files of which will be uploaded in advance.
Some lecture notes (old, in German, covering around 75% of the whole course material!) can be downloaded here.
will also be published hier, usually one week ahead of the corresponding practical unit.
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Last update on January 2022