Lecturer:Jeffrey
Collamore; ph.: 3532 0782; e-mail: collamore-at-math.ku.dk Lectures: Tuesday 8-10 in Aud. 5; Thursday 10-12 in Aud. 10 (Weeks 36-41, 43). Exercises: Thursday 13-16 in Aud. 6.
Evaluation: Your grade will be based entirely on a three-hour
written exam (open book), to be given on November 10.
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.
The main references, namely the notes of Norberg and Schmidli, 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, 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. (Although not strictly part of the
course, Ch. 6 describes the dividend
barrier problem.)
Course description: We will begin
with survey of utility theory and its application to insurance risk
(about three weeks). In the remainder 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,
and the renewal risk model. In the final week of the course, we will
discuss a more modern topic, namely ruin with investments.
Schedule for the lectures:
06.09.11: Introduction; RN Ch. 8.
08.09.11: Lecture 1: HS Sec. 1.8 (concave functions, Ohlin's lemma).
08.09.11: Lecture 2: RN Ch. 8 (zero-utility premium, risk aversion function).
13.09.11: RN Ch. 8 (optimal contracts).
15.09.11: RN Ch. 8 (multiple risks; Pareto optimal exchange).
20.09.11: RN Ch. 8 (Pareto optimal exchange cont.).
22.09.11: HS Sec. 1.1-1.5 (background in probability
theory).
27.09.11: HS Sec. 2.1-2.5 (Cramer-Lundberg model, Lundberg inequality).
29.09.11: Lecture 1: HS Sec. 1.4 (renewal theory);
HS Sec. 2.6 (CL estimate).
29.09.11: Lecture 2: HS Sec. 2.6 cont.
04.10.11: Discussion instead of lecture.
06.10.11: Lecture cancelled.
11.10.11: HS, Sec. 2.9 (Laplace transforms); HS 1.7 (subexponential distributions).
13.10.11: HS Sec. 2.11 (ruin in subexponential case).
18.10.11/20.10.11: Efterårsferie.
25.10.11: HS Sec. 3.1-3.2 (renewal risk model), 3.4 (CL theory for the renewal risk model).
27.10.11: Ruin with investments (handout).
Exam date: November 10. Reexam date: February 2.
Schedule for the exercise sessions (discussions):
08.09.11: Lecture in place of discussion.
15.09.11: Homework 1.
22.09.11: Homework 2.
29.09.11: Lecture in place of discussion.
04.10.11: Homework 3. Note: this discussion will take place at the time of the lectures, i.e., 8-10 in Aud. 5.
06.10.11: Homework 4.
13.10.11: Homework 5.
20.10.11: Efterårsferie.
27.10.11: Homework 6.
All homework sets can be downloaded from Absalon (and all are now posted there).
Reexam information:
06.02.12: The reexams have just been received. The results will be posted by exam number when they are ready, but this will take several days (probably Friday of this week or sometime early next week).