Risk Theory II


Prof. Dr. Mitja Stadje

Teaching Assistant

Thai Nguyen

Time and place

Time and place:

Tuesday: 10:00-12:00, H12 ( lecture)

Wednesday : 16:00-18:00, H13 (lecture)

Friday: 14:00-16:00, H3 (excercise)

Important News

  • The lecture and exercises are in English.
  • All further information on the lecture and all documents will be uploaded to moodle.


4 hours lecture + 2 hours exercises


Introduction to Probability Theory, Calculus.

Risk Theory I is strongly recommended

Intended audience

Master students in Mathematics, Master students in Business Mathematics and Master students in Finance

Key subjects

This course provides an introduction to the mathematical models of (non-life) insurance with emphasis on

  • Individual and collective model and their applications
  • Ruin probabilities
  • Stochastic ordering and premium calculation
  • Credibility Theory
  • Claim reserving
  • Reinsurance
  • Bonus-Malus System/Markov-Chains
  • Simulation
  • Biometric Actuarial Bases

    Further information

    The DAV-certificate can be obtained in the first final exam at the end of the semester only. DAV-certificates will not be awarded for passing the second exam!




       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 using R, Springer, 2008

       Klugman, S. A., Panjer, H. H., Willmot, G. E., Loss models. From data to decisions, Wiley, 1998

       Mack, T., Schadenversicherungsmathematik, 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