Portfolio theory
2007-2008

Aim

To make students familiar with the mathematical fundamentals of portfolio selection.

Contents

In this course we treat fundamental economic notions as preference relations and utility functions and show how these are applied in portfolio optimization and measure of risk. This will be done first for static markets and extended later on to a dynamic setting, where time is discrete. Finally we will consider American options both in discrete and continuous time, and we will show how stochastic control theory can be applied to find hedging or super hedging strategies.

Prerequisites

Introductory course in mathematical finance, like Stochastic Processes for Finance and knowledge of stochastic integration, for instance as offered in Stochastic integration.

Literature

The course is partly based on H. Föllmer and A. Schied, Stochastic Finance, An Introduction in Discrete Time. During the course lecture notes will be written. Please, check these carefully, and report errors of any kind. These lecture notes have been subject to many revisions. The current version uses another section numbering than earlier ones. The current number of a section is the old number minus 1 (and then also 2.1 becomes 1.1 for example). There will also be a set of complementary exercises for the first two weeks.

Examination

Take home exercises (you are strongly encouraged to work in pairs) and oral exam. Deadlines for homework: solutions have to be handed in within one week!

People

Lectures by Bert van Es and by Peter Spreij.

Schedule

Fall semester, Thursdays 10.00-12.45, room I.103 (Universiteit van Amsterdam), the course will start on September 6. Note that classes start at 10.00 sharp (new UvA rules)! No classes on October 25 and on November 22.

Programme

1
 Class: most of sections 1.1-1.3 up to the statement of Theorem 1.31
Homework: Read examples and parts of the book that have been skipped and make exercises 1, 2, 3.
2
 Class: From Theorem 1.31 to the end of Section 1.4
Homework: exercises 4(i) and 5 (4(ii) is the same as exercise 2 and thus redundant)
3
 Class: From the lecture notes most of sections 3.1, 3.2
Homework: exercises 3.1, 3.3, 3.5 (lecture notes, section 3.3)
4
 Class: Section 4
Homework: exercises 4.1, 4.2, 4.3
5
 Class: Most of Section 5
Homework: 5.2, 5.4, 5.6 (If you find errors, or strange things, please inform me immediately)
6
 Presentations: Demeter Kiss and Attila Herczegh
Class: Mainly Section 6.1, Section 6.2 very briefly
Homework: 6.1, 6.2, 6.4
7
 Class: Most of section 7.1
Homework: 7.5, 7.6
8
 Class: Sections 7.2 and 8.1
Homework: 7.2, 8.2, 8.3
9
 Class: Sections 9.1 and 9.2
Homework: 9.1 and 9.3 (Warning: I have no clear idea of what comes out of this. Just give it a try and report your findings)
10
 Class: Section 9.3
Homework: 9.4, 9.5 (if you want, you ignore the statement about completeness in (a))
11
 Class: Sections 9.4, 9.5 and a bit of 10.1
Homework: none (but maybe 9.8 next week)
12
 Class: Sections 10.1 and 10.2
Homework: 10.4 (skip (c) if this results in long, tedious and not informative computations), 10.5 (this is actually a conjecture, investigate whether it is true or not), 10.6 (this should be easy since the R_t are independent, but who knows ......?)
13
 Class: Section 10.3
Homework: Exercise 10.7



Links

Korteweg-de Vries Institute for Mathematics
Master Stochastics and Financial Mathematics