Ruinteori Home Page; Block 2, 2009-10

Course Details:

Lecturer: Jeffrey Collamore; ph.: 3532 0782; e-mail: collamore-at-math.ku.dk.
Lectures: Wednesday 10:15-12:00 in Aud. 6; Wednesday 13:30-15:15 in Aud. 6.

Evaluation: There will be a 30-minute oral exam and exercises. Your grade will be based primarily on the oral exam, although the exercises will also count for a small part of the grade. Moreover, it is a requirement that all the exercises are attempted and the exercise set is "passed" in order to participate in the oral exam.

Prerequisites: The course may be taken independently of "SkadeStok." While there are no specific requirements, a basic course in measure-theoretic probability theory will generally be assumed.

Course material: A.J. McNeil, R. Frey and P. Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton Univ. Press, 2005. (The text may be purchased from the university bookstore or from various other sources, such as Amazon.co.uk.)

Course description: Starting in 2009, this will actually be a course in quantitative risk management. (For administrative reasons, the title cannot be changed until 2010, at which time it will indeed be called "Quantitative Risk Mangement" instead of "Ruin Theory.") Topics will include: risk measures; statistical methods in extreme value theory; multivariate distributions and dependence; elliptical distributions and copulas; credit risk modeling; insurance-based models for operational risk. The present (required) course will serve as good background for an optional course in risk management, which will be offered by Jostein Paulsen in Block 4.

Notes: For those that have had the old "Ruin Theory" course, the present course can be taken as an optional course. For those that have taken but not passed the old "Ruin Theory" course, the reexam may either be taken using the new or the old pensum, but in either case, it will be an oral exam.

Schedule for the lectures:

All reading material is taken from the book of McNeil, Frey and Embrechts (written "MFE" below).

11.11.09: MFE, Ch.1 (optional); Ch.2, pp. 25-48.
18.11.09: MFE, Ch. 2, pp. 48-60.
25.11.09: MFE, Ch. 3 (mainly pp. 89-103): spherical and elliptical distributions.
02.12.09: MFE, Ch. 5 (all): copulas.
08.12.09: MFE, Sec. 7.2, 7.4 (esp. Hill method, POT method): extreme value theory.
09.12.09: MFE, Ch. 5, cont.: copulas. MFE, Ch. 8, pp. 327-367: intro. to credit risk.
16.12.09: MFE, pp. 327-367 (cont.): credit risk. MFE, Ch. 10 (all): operational risk.

Exam dates: January 25 and 26.
Reexam date: June 11 (note change of date).

Homework:

Exercises.

Data sets needed for the exercises: DAX-returns; BMW-returns.

You may work in groups of two, and should hand in all problems by Thursday, January 14, at the latest. (Submissions after Monday, December 21, must be done electronically to my email address.) In your solutions, it is important that you explain all steps completely (and provide the code for any numerical work). The correct approach is the important part, more so than whether there is an error in the actual computation.

Exam questions:

The exam will consist of two parts. First, you will draw a number randomly and present one of the topics below. Then you will be asked general questions, most likely, dealing with a different topic from the one you selected in the first half.

1. Loss operators, risk measures.
2. Computing VaR and ES (elementary methods and importance sampling).
3. Extreme value theory methods (and their general relation to risk management).
4. Elliptical distributions.
5. Copulas, I: Basics, dependence properties.
6. Copulas, II: Examples, statistical fitting to data.
7. Credit risk.
8. Operational risk.

Reexam information:

This will take place on Friday, June 11, 10:00-13:00, in Room 04.04.01 (seminar room on the fourth floor of the mathematics building). The format of the exam is the same as for the original exam, and the prepared questions are the same as those listed above. The precise schedule is the following:

1. Veronica.
2. Kasper.
3. Astrid.
4. Any further students.*

*The homework assignment needs to be handed in first (by June 9, say, to my mailbox at the secretariat on the first floor) in order to participate.

We will begin at 10:00 and continue until we are finished with all the exams. Thus, you should come at 10:00 sharp, at least to notify us that you are coming (as there are often many "no-shows" for reexams, and we will leave as soon as there are no more students waiting for the exam).