SkadeStok Home Page; Block 1, 2009-10

Course Details:

Lecturer: Jeffrey Collamore; ph.: 3532 0782; e-mail: collamore-at-math.ku.dk
Lectures: Thursday 8-10 in Aud. 5; Thursday 13-15 in Aud. 6.
Exercises: Tuesday 8-11 in Aud. 7.

Evaluation: Your grade will be based entirely on a three-hour written exam, to be given on October 29.

Prerequisites: Together with the course "Ruinteori," this forms a two-part sequence. Roughly, the prerequisites for the sequence are an introductory, bachelor-level course in non-life insurance mathematics, and an introductory measure-theoretic course in probability theory.

Course material: R. Norberg, Topics in Non-life Insurance Mathematics: Lecture Notes to FM2, Ch. 8.
H. Schmidli, Lecture Notes on FM2, Ch. 1-3.
In addition, supplementary notes on ruin in the presence of stochastic investments (handwritten).

The main references, namely the notes of Norberg and Schmidli, can be obtained here under "Ruin." (These are the first two items listed there.) Alternatively, the material may also be downloaded at Absalon.

The following references are also recommended, if you would like a second point of view on some of the topics:
S. Asmussen, Ruin Probabilities, World Scientific, 2000.
S. Asmussen, Applied Probabilities and Queues, 2nd ed., Springer, 2003.
P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events. For Insurance and Finance, Springer, 1997.
H. Bühlmann, Mathematical Methods in Risk Theory, Springer, 1970. (Ch. 6 describes the dividend barrier problem.)

Course description: Starting this year the topics of the course will change, as follows. As in previous years, we will begin with survey of utility theory and its application to insurance risk (about three weeks). However, the remainder of the course will now focus on ruin theory. Emphasis will be given to the proofs of the Lundberg bound (via martingale techniques), the Cramer-Lundberg estimate (via the renewal theorem), Laplace transform techniques, subexponential claims, and the renewal risk model. In the final week of the course, we will discuss some modern topics such as, for example, ruin with investments.

Schedule for the lectures:

01.09.09: Introduction; RN Ch. 8.
03.09.09: HS Sec. 1.8, RN Ch. 8 (zero utility premium, risk aversion function).
10.09.09: RN Ch. 8 (optimal contracts, multiple risks).
17.09.09: RN Ch. 8 (Pareto optimal exchange); HS Sec. 1.1-1.3, 1.5.
24.09.09: HS Sec. 2.1-2.5 (C-L model, Lundberg ineq.), 1.4 (renewal theory).
01.10.09: HS Sec. 2.6, 2.9 (C-L estimate, Laplace transforms), HS 1.7 (subexponential distributions).
06.10.09: HS Sec. 2.11 (ruin-subexponential case). Note: Lecture instead of discussion: 8-10.
08.10.09: HS Sec 3.1-3.2, 3.4 (renewal risk model); ruin with investments.
15.10.09: Discussion instead of lecture: 8-10 (and 13-15 if necessary).

The ordinary exam is scheduled for October 29, while the reexam is scheduled for January 6 (1 1/2-hr. written exam) and January 7 (30-minute oral exam). However, the date of the oral reexam will be changed to the last week in December prior to the Christmas holiday. Please contact me immediately if you have a problem with this.

Schedule for the exercise sessions:

01.09.09: Lecture instead of discussion (from 8-10).
08.09.09: Homework 1. Solutions. Group presentations as follows: Problem 1-Group 1; Problem 2-Group 2; Problem 3-Group 3; Problem 4-Group 4.
15.09.09: Homework 2. Solutions. Problem 1-Group 5; Probl. 2-Group 1; Probl. 3-Group 2; Probl. 4-Group 3.
22.09.09: Homework 3. Solutions. Problem 1-Group 4; Probl. 2-Group 5; Probl. 3-Group 1; Probl. 4-Group 2.
29.09.09: Homework 4. Solutions. Problem 1-Group 3; Probl. 2-Group 4; Probl. 3-Group 5; Probl. 4-Group 1.
06.10.09: Lecture instead of discussion (from 8-10).
13.10.09: Homework 5. Solutions. Problem 1-Group 2; Probl. 2-Group 3; Probl. 3-Group 4; Probl. 4-Group 5.
15.10.09: Homework 6. Solutions. Problem 1-Group 1; Probl. 2-Group 2; Probl. 3-Group 3; Probl. 4-Group 4.

Some old exams: 2005, 2006, 2007.
Solutions: 2005.

Reexam information:

Written exam: Tuesday, February 2, 15:30-17:00. (Room: A105.)
Oral exam: Friday, February 5, 10:00-12:00. (Room: A103.)

Topics for the oral reexam:
1. Utility theory, I (everything except the topics listed in "II" below).
2. Utility theory, II (multiple risks and Pareto optimal exchange).
3. The Cramer-Lundberg estimate and its extension in the renewal risk model.
4. The Lundberg estimate and its extension in the renewal risk model.
5. The Cramer-Lundberg estimate in the subexponential case.
6. Ruin with stochastic investments.

Oral reexam schedule:
10:00: Michael.
10:30: Elisabeth.
11:00: Sha Sha.