Portfolio theory (ST407026)
2010-2011

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 show how stochastic control theory and dynamic programming can be applied to problems of portfolio optimization.

Prerequisites

Basic concepts of probability and measure theory, for instance at the level of Measure theoretic probability.

Literature

The course is mainly based on H. Föllmer and A. Schied, Stochastic Finance, An Introduction in Discrete Time and on S.R. Pliska, Introduction to Mathematical Finance: Discrete Time Models. A set of lecture notes partly based on these sources contains the contents of the course.

Related course

Students are advised to also take the course Financial Stochastics on derivative pricing in continuous time.

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, homework grading by Peter Spreij.

Schedule

Fall semester, Thursdays 14.00-17.00, September 9 - October 21: room A1.06, November 4 - December 16: room G2.04. Location: Science Park 904; see the map of Science Park and the travel directions. The course will start on September 9. Changes in the schedule will appear here.

Programme
(weekly updated, last modified: )

1
Class: Sections 1.1, 1.2 up to Theorem 1.15
Homework: Exercises 1.1, 1.3.
2
Class: Section 1.2 from Definition 1.16, Section 1.3
Homework: Exercises 1.2, 1.4, 1.5.
3
Class: Most of Sections 2.1, 2.2 (skip Proposition 2.10)
Homework: Exercises 2.1, 2.3, 2.5.
4
Class: Section 3.1 up to Lemma 3.7
Homework: Exercise 3.1
5
Class: Section 3: Theorem 3.9, Section 4.1
Homework: Exercises 3.3, 4.1, 4.2
6
Class: Sections 4.2, 5.1
Homework: Exercises 5.2, 5.5
7
Class: Section 6.1
Homework: Exercises 6.2, 6.3
8
Class: Section 7.1
Homework: Exercises 7.1, 7.3 (look at Definition 6.12 of the relative entropy), 7.4
9
Class: Sections 8.1, 8.2
Homework: Read the end of Section 8.2 and make exercises 8.1, 8.2, 8.3
10
Class: Section 8.3 and part of Theorem 8.22
Homework: Exercises 8.5, 8.6
11
Class: Sections 8.4, parts of Section 9.1
Homework: Read Section 8.5, make Exercises 8.8, 9.2
12
Class: Remainder of Section 9.1, parts of Sections 9.2, 9.3
Homework: Exercises 9.4, 9.7
13
Class:
Homework: Exercises




Links

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