University of Ulm: Department of Stochastics

University of Ulm, Faculty of Mathematics and Economics - Department of Stochastics

Risk Theory

Schedule

Winter term 2004/05
Lecture:	Tuesday, 10.15-12.00 am, H11 Wednesday, 1.30-3.00 pm, H14
Homework session:	Thursday, 4.15-6.00 pm, H13

Type

Lecture (4 hours/week)
Homework session (2 hours/week)

Requirements

Undergraduate lectures
Probability Theory

Lecturer: Prof. Dr. Evgueni Spodarev

Office hours: by appointment

Teaching assistant:Hendrik Schmidt

Office hours: by appointment

General Remarks

At the end of this term, a certificate of the German Actuarial Society (DAV-Schein Schadensversicherungsmathematik) can be earned by taking the written DAV-exam.
In order to earn a certificate (Übungsschein), one has to pass a written final exam. For admission to this final exam, 50% of all homework credits are required.
In case of failing the exam or missing it (with written excuse), there exists the possibility of repeating the final exam (however not the DAV-exam!).
For MSc Finance students (Wirtschaftswissenschaften) it is possible to choose this course as Vertiefungsfach Mathematik.
NOTICE: Please enroll in this course with SLC. Without your electronic registration, participation in this course is not possible.
Your anonymous (critical) comments on this course are welcome!

Important hints for the final exam and the exam in "Schadenversicherungsmathematik"

Final exam (incl. exam "Schadenversicherungsmathematik", see extra hints below): February 25, 2005, 10 am, H16.
Exam "Schadenversicherungsmathematik": to be held in German, see hints below.
Which aids are allowed during the final? Non-programmable pocket calculator and inkstand.
Do not forget to have your student ID card with you
To be eligible for the "Übungsschein" you need at least 270 homework credits.
In case of failing the final exam or missing it (with written excuse) there exists the opportunity to repeat the exam. Date and form of such an exam will be posted on this page at any one time. The exam "Schadenversicherungsmathematik" can not be repeated.

The repetition of Final is schedeuled for March 31st, 10 am.

Wichtige Hinweise zur Klausur "Schadenversicherungsmathematik"

Datum, Zeit und Ort: 25. Februar 2005, 10 Uhr, H16.
Die Klausur in Schadenversicherungsmathematik wird in deutscher Sprache durchgeführt. Die Antworten müssen ebenfalls in deutscher Sprache gegeben werden.
Erlaubte Hilfsmittel für die Klausur? Nichtprogrammierbarer Taschenrechner und Schreibzeug.
Bitte Studentenausweis mitbringen
Für die Klausur in Schadenversicherungsmathematik kann, im Falle des Nichtbestehens, keine Nachklausur angeboten werden.

News

Klausureinsicht: 9. März 2005, 10 Uhr in He146
Post-exam review: March 9, 10 am in He146
Grades (points) are online now (SLC) for non-Master students
Students with 50 points or more pass the exam
The repetition of the Final is schedeuled for March 31st, 10 am. Please contact us at March 9, 10 am (He 146) in case you want to participate.
The fifth chapter of the lecture notes (in German) is online! See Downloads...
As of now it is possible for students to present solutions of exercises during homework sessions. Exercises suitable for student presentations are marked with an asterisk *. Students who wish to make a presentation, have to show their solution of the chosen exercise to Hendrik Schmidt at least one day prior to the presentation. Students earn 10 homework credits for each presentation (maximal number of credits earned this way is limited to 20 and no student can present more than one exercise per homework session).
NOTICE: Please enroll in this course with SLC.

Topics

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

Distribution of claim sizes
Distribution of the number of claims
Distribution of the aggregate claim amount
Simulation
Premium calculation
Reinsurance
Risk reserves
Ruin probabilities

Lectures will be held in English.

Literature

(also available in .ps-format

or in .pdf-format

)

1. Asmussen, S. Ruin probabilities. World Scientific, Singapore, 2000

2. Beard, R.E., Pentikäinen, T., Pesonen, E. Risk Theory. Chapman and Hall, London - New York, 1984

3. Bowers, N.L., Gerber, H.U., Hickman, J., Jones, D., Nesbitt, C. Actuarial Mathematics. Society of Actuaries, Itasca, 1997

4. Daykin, C.D., Pentikäinen, T., Pesonen, M. Practical Risk Theory for Actuaries. Chapman & Hall, London, 1994

5. Embrechts, P., Klüppelberg, C., Mikosch, T. Modelling extremal events. Appl. Math., 33, Springer, Berlin, 1997

6. Farny, D., Helten, E., Koch, P., Schmidt, R. Handwörterbuch der Versicherung. Verlag Versicherungswirtschaft, Karlsruhe, 1988

7. Gerber, H.U. An Introduction to Mathematical Risk Theory. Richard D. Irwin, Homewood, 1979

8. Goovaerts, M.J., de Vylder, F., Haezendonck, J. Insurance premiums. Elsevier, Amsterdam, 1984

9. Heilmann, W. Grundbegriffe der Risikotheorie. Verlag Versicherungswirtschaft, Karlsruhe, 1987

10. Hipp, C., Michel, R. Risikotheorie: Stochastische Modelle und Statistische Methoden. Schriftenreihe Angewandte Versicherungsmathematik, Heft 24, Verlag Versicherungswirtschaft, Karlsruhe, 1990

11. Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M. Modern actuarial risk theory. Kluwer, Boston, 2001

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

13. Mack, T. Schadenversicherungsmathematik. Schriftenreihe Angewandte Versicherungsmathematik, Heft 28, 2. Auflage, Verlag Versicherungswirtschaft, Karlsruhe, 2002

14. Mikosch, T. Non-life insurance mathematics. Springer, 2004

15. Müller, A., Stoyan, D. Comparison methods for stochastic models and risks. Wiley, 2002

16. Rolski, T., Schmidli, H., Schmidt, V., Teugels, J. Stochastic Processes for Insurance and Finance. J. Wiley & Sons, Chichester, 1998

17. Schmidt, K. Lectures on risk theory. Teubner, Stuttgart, 1996

18. Schwepcke, A. Rückversicherung. Grundlagen und aktuelles Wissen. Swiss Re, Verlag Versicherungswirtschaft, Karlsruhe, 2001

19. Straub, E. Non-life insurance mathematics. Springer, Zürich, 1988

20. Wolfsdorf, K. Versicherungsmathematik. Teil 2: Theoretische Grundlagen, Risikotheorie, Sachversicherung. Teubner, Stuttgart, 1988

Any questions? Just email us!

Last update: January 26, 2005

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