Risk Theory

Junior-Prof. Dr. Zakhar Kabluchko

Teaching Assistant

Wolfgang Karcher

Time and place


Monday  12-14  in H14
Tuesday 12-14  in H14

Exercise session:

Wednesday 16-18 in H12

First lecture: Monday, 19th April

First exercise session: Wednesday, 28th April


4 hours lecture + 2 hours exercises


Probability, Calculus

Intended audience

Graduate students in Mathematics, Business Mathematics and Finance


This course provides an introduction to the mathematical models of non-life insurance with emphasis on
  1. Distribution of claim sizes
  2. Distribution of the number of claims
  3. Distribution of the aggregate claim amount
  4. Simulation
  5. Premium calculation
  6. Reinsurance
  7. Risk reserves
  8. Ruin probabilities

Requirements to obtain the certificate (Übungsschein and/or DAV-Schein)

In order to obtain the certificate of the lecture (Übungsschein), one has to earn 50% of all homework credits and pass the written final exam.

At the end of this term, a certificate of the German Actuarial Society (DAV-Schein Schadensversicherungsmathematik) can be earned by passing the written final exam. In order to obtain the DAV certificate it is not necessary to earn 50% of home credits.

Lecture notes

Lecture notes of Prof. Evgeny Spodarev (Ulm) can be downloaded here.

Lecture notes of Prof. Klaus Schmidt (Dresden) can be downloaded here

Final exam

Monday, 19th July, 2010, 10:00 - 12:00 in H4/5

Auxiliary material for the final exam: 1 DIN A4 sheet with own notes, non-programmable pocket calculator, pens

Please use the following table to determine your grade. Half points are rounded up. For example, if your score is 18.5, you will get the grade corresponding to 19 points. For the DAV-Schein, you need at least 18.5 points.

Score       Grade

39-37         1.0
36-35         1.3
34-33         1.7
32-31         2.0
30-29         2.3
28-27         2.7
26-25         3.0
24-23         3.3
22-21         3.7
20-19         4.0
18-0           5.0

Exercise sheets

In order to receive credit points, a registration at SLC is required.

If you have no account at the SLC, please follow this link and choose "Weiter zur Online-Registrierung" there.


  • Asmussen, S.
    Ruin probabilities
    World Scientific, Singapore, 2000
  • Beard, R.E., Pentikäinen, T., Pesonen, E.
    Risk Theory
    Chapman and Hall, London - New York, 1984
  • Embrechts, P., Klüppelberg, C., Mikosch, T.
    Modelling extremal events
    Appl. Math., 33, Springer, Berlin, 1997
  • Heilmann, W.
    Grundbegriffe der Risikotheorie
    Verlag Versicherungswirtschaft, Karlsruhe, 1987
  • Hipp, C., Michel, R.
    Risikotheorie: Stochastische Modelle und Statistische Methoden
    Schriftenreihe Angewandte Versicherungsmathematik, Heft 24, Verlag Versicherungswirtschaft, Karlsruhe, 1990
  • Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.
    Modern actuarial risk theory
    Kluwer, Boston, 2001
  • Mack, T.
    Schriftenreihe Angewandte Versicherungsmathematik, Heft 28, 2. Auflage, Verlag Versicherungswirtschaft, Karlsruhe, 2002
  • Mikosch, T.
    Non-life insurance mathematics
    Springer, 2004
  • Rolski, T., Schmidli, H., Schmidt, V., Teugels, J.
    Stochastic Processes for Insurance and Finance
    J. Wiley & Sons, Chichester, 1998
  • Schmidt, K.
    Lectures on risk theory
    Teubner, Stuttgart, 1996
  • Straub, E.
    Non-life insurance mathematics
    Springer, Zürich, 1988

Further Literature

  • Daykin, C.D., Pentikäinen, T., Pesonen, M.
    Practical Risk Theory for Actuaries
    Chapman & Hall, London, 1994
  • Farny, D., Helten, E., Koch, P., Schmidt, R.
    Handwörterbuch der Versicherung
    Verlag Versicherungswirtschaft, Karlsruhe, 1988
  • Gerber, H.U.
    An Introduction to Mathematical Risk Theory
    Richard D. Irwin, Homewood, 1979
  • Wolfsdorf, K.
    Versicherungsmathematik. Teil 2: Theoretische Grundlagen, Risikotheorie, Sachversicherung
    Teubner, Stuttgart, 1988
  • Schwepcke, A.
    Rückversicherung. Grundlagen und aktuelles Wissen
    Swiss Re, Verlag Versicherungswirtschaft, Karlsruhe, 2001
  • Goovaerts, M.J., de Vylder, F., Haezendonck, J.
    Insurance premiums
    Elsevier, Amsterdam, 1984
  • Müller, A., Stoyan, D.
    Comparison methods for stochastic models and risks
    Wiley, 200
  • Klugman, S. A., Panjer, H. H., Willmot, G. E.
    Loss models. From data to decisions
    Wiley, 1998




Junior-Prof. Dr. Zakhar Kabluchko

  • Office hours: on appointment
  • Phone: +49 (0)731/50-23527
  • Homepage

Teaching Assistant

Wolfgang Karcher

  • Office hours: on appointment
  • Phone: +49 (0)731/50-23529
  • Homepage


  • The DAV certificates can be picked up in the office 1.06 (Helmholtzstr. 18)
  • Deadline for the registration for the second exam: 27th of September, 2010
  • Students who want to take the second exam: Please write an email to Wolfgang Karcher with your Matrikel number. Notice that you cannot get a DAV-Schein for the second exam any more.

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