Type

4 hours lecture + 2 hours exercises

Prerequisites

• 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:

• Stochastic processes in risk theory with focus on (compound)
• Poisson processes
• Markov chains and Markov processes
• Introduction to the collective model
• Relevant distribution families in risk theory
• Time Series Analysis
• Life-time models and mortality modeling
• Generalized linear models and their applications in risk theory
• Credibility theory
• Dependencies and Copulas
• Monte Carlo simulations
• Risk measurement using VaR and TVaR

Final exam

The exam is open.

The date of the exam will be announced later.

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.

Literature

• 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