Lecturer
Junior-Prof. Dr. Zakhar Kabluchko

Teaching Assistant

Wolfgang Karcher

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Time and place

Lecture

Monday  12-14  in H14
Tuesday 12-14  in H14

Exercise session:

Wednesday 16-18 in H12

First lecture: Monday, 19th April

First exercise session: Wednesday, 28th April

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Type

4 hours lecture + 2 hours exercises

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Prerequisites

Probability, Calculus

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Intended audience

Graduate students in Mathematics, Business Mathematics and Finance

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Content

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. Risk reserves
8. Ruin probabilities

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Requirements to obtain the certificate (Übungsschein and/or DAV-Schein)

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

At the end of this term, a certificate of the German Actuarial Society (DAV-Schein Schadensversicherungsmathematik) can be earned by passing the written final exam. In order to obtain the DAV certificate it is not necessary to earn 50% of home credits.

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Lecture notes

Lecture notes of Prof. Evgeny Spodarev (Ulm) can be downloaded here.

Lecture notes of Prof. Klaus Schmidt (Dresden) can be downloaded here

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Final exam

Monday, 19th July, 2010, 10:00 - 12:00 in H4/5

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

Please use the following table to determine your grade. Half points are rounded up. For example, if your score is 18.5, you will get the grade corresponding to 19 points. For the DAV-Schein, you need at least 18.5 points.

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Exercise sheets

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

If you have no account at the SLC, please follow this link and choose "Weiter zur Online-Registrierung" there.

• Blatt 1
• Blatt 2    Supplement
• Blatt 3
• Blatt 4
• Blatt 5
• Blatt 6
• Blatt 7
• Blatt 8     Proof of Corollary 11.5
• Blatt 9
• Blatt 10
• Blatt 11
• Blatt 12

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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
• 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
• Mack, T.
  Schadenversicherungsmathematik
  Schriftenreihe Angewandte Versicherungsmathematik, Heft 28, 2. Auflage, Verlag Versicherungswirtschaft, Karlsruhe, 2002
• Mikosch, T.
  Non-life insurance mathematics
  Springer, 2004
• 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
• Straub, E.
  Non-life insurance mathematics
  Springer, Zürich, 1988

Further Literature

• Daykin, C.D., Pentikäinen, T., Pesonen, M.
  Practical Risk Theory for Actuaries
  Chapman & Hall, London, 1994
• 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
• Wolfsdorf, K.
  Versicherungsmathematik. Teil 2: Theoretische Grundlagen, Risikotheorie, Sachversicherung
  Teubner, Stuttgart, 1988
• Schwepcke, A.
  Rückversicherung. Grundlagen und aktuelles Wissen
  Swiss Re, Verlag Versicherungswirtschaft, Karlsruhe, 2001
• Goovaerts, M.J., de Vylder, F., Haezendonck, J.
  Insurance premiums
  Elsevier, Amsterdam, 1984
• Müller, A., Stoyan, D.
  Comparison methods for stochastic models and risks
  Wiley, 200
• Klugman, S. A., Panjer, H. H., Willmot, G. E.
  Loss models. From data to decisions
  Wiley, 1998