Mathematical Foundations for Finance Fall 2022

Prof. Dr. Martin Schweizer
Benjamin Kotlov

This course gives a first introduction to important modelling ideas and mathematical tools from quantitative finance. It is aimed mainly at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced mathematical course) may also find this of interest. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.

Topics to be covered include:


Results and facts from measure-theoretic probability theory as in the book "Probability Essentials" by Jean Jacod and Philip Protter will be used freely. The book can be downloaded from Springer (within the ETH network or using VPN) for free. Especially participants without a direct mathematical background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. In the lecture notes, Chapter 8 (which will not be presented in class) has a short overview of frequently used concepts.

For those who are not sure about their background, we suggest to have a look at the exercises in Chapters 8, 9, 22-25, 28 in the "Probability Essentials" book. If these pose problems, you will have a hard time during the course. So be prepared.

Lectures take place live on Tuesdays 8:00-10:00 and Thursdays 13:00-14:00, in HG G5. There will be no recordings.

The first lecture is on September 20.

Lecture Notes

The lecture notes can be found online here. The password will be emailed to the enrolled students.

Note that the lecture notes are protected by copyright, and their dissemination in any form is strictly prohibited.

Exercise classes take place live on Fridays 8:00-10:00 (for last names A-L) and 10:00-12:00 (for last names M-Z), in HG D5.2.

The first exercise class is on September 23, in the first week of the semester.

Exercise Sheets

New exercise sheets are uploaded below on Wednesdays before the corresponding Friday exercise class, along with solutions to the exercise sheet from the previous week.

While handing in your solutions is not compulsory, experience shows that being able to solve the exercises independently goes a long way towards good exam performance. We strongly encourage you to hand in written solutions. This can be done electronically. Please follow the instructions below.

  1. Scan your solution into a single PDF file.
  2. Name the created file as {email address}_{exercise sheet number}.pdf (e.g. andrey.kolmogorov@probability.com_1.pdf).
  3. Upload your solution using the button below before 12:00 on the indicated Wednesday. The password will be emailed to the enrolled students.

Late submissions will not be considered. In case you submit your solution early and then decide to change something and submit again, we will only consider the most recent submission.

Exercise Sheet Due by Solutions
Exercise Sheet 1 September 28, 2022 Solution 1
Exercise Sheet 2 October 5, 2022 Solution 2
Exercise Sheet 3 October 12, 2022 Solution 3
Exercise Sheet 4 October 19, 2022 Solution 4
Exercise Sheet 5 October 26, 2022 Solution 5
Exercise Sheet 6 November 2, 2022 Solution 6
Exercise Sheet 7 November 9, 2022 Solution 7
Exercise Sheet 8 November 16, 2022 Solution 8
Exercise Sheet 9 November 23, 2022 Solution 9
Exercise Sheet 10 November 30, 2022 Solution 10
Exercise Sheet 11 December 7, 2022 Solution 11
Exercise Sheet 12 December 14, 2022 Solution 12
Exercise Sheet 13 December 21, 2022 Solution 13
Exercise Sheet 14 Not for hand-in Solution 14

Office hours during the semester with assistants from group 3 are available on Mondays and Thursdays starting from the fourth week of the semester. More information can be found here. Note that you can also ask questions during the exercise classes.

The forum for this course can be found here.

The grade for this course is based solely on the (written) final exam. The exam will cover all the material discussed during the lectures and all the material from the exercise sheets (except if explicitly stated otherwise).

Old Exams

Some old exams can be found here. However, note that past experience shows that preparing from old exams only could well not be enough to ensure a passing grade.

Exam Inspection

Details on how and when to view your marked exam can be found here.

Office Hours

Office hours during the winter break with assistants from group 3 will be available in the last two weeks before the exam session. More information can be found here.