Risk Theory

Prof. Dr. Evgeny Spodarev

Teaching Assistant
Judith Olszewski

Time and place

Monday 10-12 in H14
Thursday 12-14 in H12

Exercise session
Tuesday 16-18 in H14


4 hours lecture + 2 hours exercises


Probability Calculus

Intended audience

Master 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. Ruin probabilities

Requirements to obtain the certificate (Übungsschein)

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

Lecture notes

The lecture notes can be downloaded here.

Final exam

First exam:
The exam took place on July 23, 2014, in H4/5 at 12:00-14:00.

Second exam:
Thursday, October 9, 2014
The second exam will be oral and will take place in the office of professor Spodarev. The first student will start at 10 o'clock. The duration of each exam will be 30 minutes.

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

Exercise sheets

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

Exercise Sheet 1

Exercise Sheet 2

Exercise Sheet 3

Exercise Sheet 4

Exercise Sheet 5 in problem 4: number of claims 0,1,2, not 1,2,3

Exercise Sheet 6

Exercise Sheet 7

Exercise Sheet 8

Exercise Sheet 9

Exercise Sheet 10

Exercise Sheet 11 

Exercise Sheet 12 

Further information

The DAV-certificate "Schadenversicherungsmathematik" and "Statistische Methoden/Risikotheorie" can be obtained after passing both written exams of lecture courses "Risk Theory" and "Statistical methods of risk theory".

In order to get the DAV certificate, one has to earn 50% of all homework credits and to pass the first exam. If you do the second exam you can only get the certificate of the university. You don't need to have done the first exam in order to do the second exam (that is, the exam is open). If you are only doing the final exam in order to get the DAV certificate, please send a short email containing your name with the subject "Risk theory" to Renate Jäger: Link. We need this information to know the exact number of participants in the final exam. It is not necessary to send the email if you register for this exam in the "Hochschulportal", and the email does not replace registration 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
  • Bowers, N.L., Gerber, H.U., Hickman, J., Jones, D., Nesbitt, C.
    Actuarial Mathematics
    Society of Actuaries, Itasca, 1997
  • Daykin, C.D., Pentikäinen, T., Pesonen, M.
    Practical Risk Theory for Actuaries
    Chapman & Hall, London, 1994
  • Embrechts, P., Klüppelberg, C., Mikosch, T.
    Modelling extremal events
    Appl. Math., 33, Springer, Berlin, 1997
  • 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
  • Goovaerts, M.J., de Vylder, F., Haezendonck, J.
    Insurance premiums
    Elsevier, Amsterdam, 1984
  • 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
  • Klugman, S. A., Panjer, H. H., Willmot, G. E.
    Loss models. From data to decisions
    Wiley, 1998
  • Mack, T.
    Schriftenreihe Angewandte Versicherungsmathematik, Heft 28, 2. Auflage, Verlag Versicherungswirtschaft, Karlsruhe, 2002
  • Mikosch, T.
    Non-life insurance mathematics
    Springer, 2004
  • Müller, A., Stoyan, D.
    Comparison methods for stochastic models and risks
    Wiley, 2002
  • 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
  • Schwepcke, A.
    Rückversicherung. Grundlagen und aktuelles Wissen
    Swiss Re, Verlag Versicherungswirtschaft, Karlsruhe, 2001
  • Straub, E.
    Non-life insurance mathematics
    Springer, Zürich, 1988
  • Wolfsdorf, K.
    Versicherungsmathematik. Teil 2: Theoretische Grundlagen, Risikotheorie, Sachversicherung
    Teubner, Stuttgart, 1988





  • Sprechzeiten: Mitwoch 16:00-17:00 Uhr
  • Telefon: +49 (0)731/50-23530
  • Homepage


Judith Olszewski


  • Sprechzeiten: nach Vereinbarung
  • Telefon: +49 (0)731/50-23529


The exam will take place on July 23, 2014, in H4/5 at 12:00-14:00.