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.
Lecturer
Exercises
DAV Supplement
Lecture Format
The course will be held in English.
We are planning to do the course mainly in presence. The exercises have to be handed in online.
Time and place
Lecture
- Thursday, 12:15-13:45 in H12
- Friday, 12:15-13:45 in N24 226
Exercise session
- Tuesday, 12:30-14:00 in H3
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 in moodle.
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 "Angewandte Stochastik" can be obtained after passing the final exam at the end of the semester and passing the DAV supplement exam.
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