This is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximization.
A related course is 401-3913-01L Mathematical Foundations for Finance (3V+2U, 4 ECTS credits). Although both courses can be taken independently of each other, only one will be recognised for credits in the Bachelor and Master degree. In other words, it is not allowed to earn credit points with one for the Bachelor and with the other for the Master degree.
A knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory").
This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II.
For an overview of courses offered in the area of mathematical finance, see link.
We will mainly use D-Math Forum to answer questions. Please sign up for an account (your ethz.ch or uzh.ch email is required). The assistants of Group 3 (Probability Theory, Insurance Mathematics and Stochastic Finance) offer regular office hours for questions on courses and exercises taught by the professors in the group. See here for the detailed information.
Lecture notes covering the material addressed during the lectures will be made available to the students in the Polybox folder. The link to the Polybox folder has been sent to you by mail. You will receive the password from the lecturer. Please note that the content of the notes sometimes goes beyond that of the lectures, though only the material covered in class and during the exercise sessions is exigible.
Please find a set of practice questions here.
You are welcome to submit your solutions to zhouyi.tan(AT)math.ethz.ch, even though it is not obligatory. In case you decide to submit your solutions, this needs to be done before 18:00 of the corresponding due date (typically on Monday). Your solutions will then be corrected and returned by e-mail. Please follow the instructions below:
1. Scan your solution into a single PDF file.
2. Name the created file in the {email_address}_{assignment number}.pdf format, e.g. mathfin@example.com_1.pdf.
| Exercise Sheet | Due Date | Solutions |
|---|---|---|
| Assignment 1 (Recording) | March 8th | Solutions 1 |
| Assignment 2 (Recording) | March 15th | Solutions 2 |
| Assignment 3 (Recording) | March 22th | Solutions 3 |
| Assignment 4 (Recording) | March 29th | Solutions 4 |
| Assignment 5 (Recording) | April 12th | Solutions 5 |
| Assignment 6 (Recording) | April 19th | Solutions 6 |
| Assignment 7 (Recording) |
| Solutions 7 |
| Assignment 8 (Recording) | May 10th | Solutions 8 |
| Assignment 9 | May 17th | Solutions 9 |
| Assignment 10 (Recording) | May 24th | Solutions 10 |
| Assignment 11 | May 31th | Solutions 11 |
| Assignment 12 | June 7th | Solutions 12 |