SkadeStok Home Page; Block 1, 2018


Course Details:

Lecturer: Jeffrey Collamore; ph.: 3532 0782; e-mail: collamore-at-math.ku.dk

Lectures: Tuesday 10-12 in Aud. 7; Thursday 10-12 in Aud. 7.
Exercises: Thursday 13-16 in Auditorium Syd, Nørre Alle 51.

Evaluation: Your grade will be based entirely on a three-hour written exam (open book).

Prerequisites: Together with the course "Quantitative Risk Management (QRM)," 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: H. Schmidli, Lecture Notes on FM2, Ch. 1-3.
J. F. Collamore, Supplementary notes on ruin with stochastic investements and related problems.
J. Paulsen, Claim reservation in non-life insurance. 30 pp.

The main references can be downloaded from Absalon.

The following references are also recommended, if you would like a second point of view on some of the topics:
S. Asmussen and H. Albrecher, Ruin Probabilities, 2nd ed., World Scientific, 2010.
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.

Course description: In the first part of the course, we will focus on ruin theory. Emphasis here 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, the renewal risk model, and the numerical technique of importance sampling. We will also discuss a few modern topics; in particular, ruin with investments and its connection to certain problems in financial time series modeling. In the final part of the course, we will focus on claims reserving.


Schedule for the lectures:

04.09.18: Introduction; HS Ch. 2 (Cramer-Lundberg model); HS Sec. 1.1-1.5 (background on probability theory).
06.09.18 (Lecture 1): HS Sec. 1.1-1.5 (background on probability theory, continued); HS Sec. 2.5 (Lundberg inequality).
06.09.18 (Lecture 2): HS Sec. 2.5 (Lundberg inequality, cont.); HS Sec. 1.4 (renewal theory).
11.09.18: HS Sec. 2.6 (Cramer-Lundberg estimate).
13.09.18: HS Sec. 2.6 (Cramer-Lundberg estimate, cont.); HS Sec. 2.9 (Laplace transforms).
18.09.18: HS Sec. 1.7 (subexponential distributions); HS Sec. 2.11 (ruin in the subexponential case).
20.09.18: HS Sec. 2.11 (subexponential ruin). Note: This lecture will take place from 11-12 and 13-14.
25.09.18: HS Sec. 3.1-3.2 (renewal risk model); HS Sec. 3.3 (Lundberg inequality for renewal risk model).
27.09.18: HS Sec. 3.4 (Cramer-Lundberg estimate for renewal risk model).
02.10.18: Importance sampling; ruin with investments.
04.10.18 (Lecture 1): Ruin with investments: stochastic fixed point equations; connections to the GARCH financial models.
04.10.18 (Lecture 2): Ruin with investments: the Kesten-Goldie theorem.
09.10.18: Claims reserving: JP notes, Sec. 1.1-1.2.
11.10.18: Claims reserving: JP notes, mainly Sec. 1.1-1.2 (final lecture).

"HS" refers to the lecture notes by Hanspeter Schmidli; "JP" refers to the lecture notes by Jostein Paulsen.

The above schedule is tentative; there might be slight changes to the schedule as we proceed through the course.


Schedule for the exercise sessions:

06.09.18: Lecture in place of discussion.
13.09.18: Homework 1.
20.09.18: Homework 2. Note: There will be lecture 13-14 and discussion 14-16.
27.09.18: Homework 2 cont. (if necessary); Homework 3.
04.10.18: Lecture in place of discussion.
11.10.18: Homework 4.
18.10.18: Efteraarsferie.
23.10.18: Homework 5. Note: This discussion will take place 10-12 in Aud. 7, i.e. in place of lecture.
25.10.18: Homework 6.