Risk theory and management in actuarial science
3 lecture + 1 practical
(MAT.522UF/MAT.523UF)

E. Dragoti-Çela
Department of Discrete Mathematics

• Time and Place lecture ,
  Time and Place practical ,
  

• Start: 5. October 2021, 1615-18:00, SR AE06, Steyrergasse 30, ground floor
• Registration
via TUGonline until October 17, 2021
• Mode
lecture and practical units in the classroom so far compliant with the pandemic regulations, otherwise online (webex)
• Contents

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)




• Literature

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.



• Assessment

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.

• by working on the tasks from the worksheets independently; at most 8 points;
  At the beginning of every practical class the participants have to declare which tasks they have worked on and are ready to present.
  At the end of the course they will be credited with the percentage of the tasks hey have succesfully worked on during the course multiplied by 8
• by presenting the solution of tasks in the class;
  For each presented task the students will be credited with at most 4 points corresponding to the correctness and completeness of the solution as well as the quality of the presentation. A minimum of 7 presentations is needed for a positive grade of the practical.



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


Grade obtained for the practical according to the overall score:


5    0 <= T < 12
4    12 < T < 14
3    14 < T < 16
2    16 < T < 18
1    18< T

Course mode and materials (pdf)

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.

The worksheets will also be published hier, usually one week ahead of the corresponding practical unit.

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  cela@opt.math.tu-graz.ac.at.

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Last update on January 2022

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