Risk Theory I


Prof. Dr. Mitja Stadje

Teaching Assistant

Dr. Thai Nguyen

Time and place


Tuesday, 12:15 to 2 pm (H14)
Wednesday, 12:15 to 2 pm (H14)


Exercise session

Friday, 12:15 to 2 pm (H14)

Important News

  • The lectures and exercises are in English.
  • Handing in Homework is compulsory.
  • All further information and all documents can be found in moodle.


4 hours lecture + 2 hours exercises


  • Introduction to Probability Theory
  • (Elementare Wahrscheinlichkeitstheorie), Calculus (Analysis)I,II,
  • Linear Algebra I,II.
  • Measure and Intregration Theory (Statistics and Measure Theory) or Introduction to Measure Theoretic Probability is recommended.

Intended audience

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

Key subjects

The content is guided by the standards of the DAV. This course provides an introduction to several stochastical and statistical methods of risk modeling and their applications.

Some of the subjects discussed in the lecture are:

  • Risk measurement using VaR and TVaR and convex risk measures
  • Relevant distribution families in risk theory
  • The collective model
  • Statistical methods in risk theory
  • Generalized linear models and their applications in risk theory
  • Credibility theory
  • Monte Carlo simulations
  • Markov chains, Time Series
  • Mortality modeling


    Final exam

    The exam is open, but only the first exam will lead to the DAV certificate.

    Date, Time and Place can be found on the moodle page.

    Handing in homework is mandatory. The prerequisite to register for an exam will be announced in the lecture. To get points in the homework, it is necessary to be registered in moodle.

    Further information

    The DAV-certificate "Stochastische Risikotheorie/ Risikotheorie I" can be obtained after passing the (first) final exam at the end of the semester. The second exam will not lead to the DAV-certificate.


    • 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
    • Gerber, H.U.  An Introduction to Mathematical Risk Theory, Richard D. Irwin, Homewood, 1979
    • 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
    • Mikosch, T.  Non-life insurance mathematics, Springer, 2004