Mathematical Foundations for Finance Autumn 2020

Prof. Dr. Martin Schweizer
Martin Stefanik

This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims 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 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 given 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 familiarize themselves with those tools before (or very quickly during) the course.

A possible alternative to the above textbook are the ETH lecture notes for the standard course on Probability Theory. These lecture notes are available here. The password will be distributed at the beginning of the semester.

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.

Update (November 3, 2020):

Lectures take place on Tuesdays, 8:00-11:00. They will be live streamed here. Recordings of the lectures will be made available online with a small delay here. Starting November 3, 2020, the lectures cannot be attended in person.

The first lecture takes place on Tuesday, September 15.

Lecture Notes

Lecture notes that will usually be closely followed during the lectures are available here. The lecture notes will keep getting extended throughout the semester. The required password will be distributed to the students enrolled in the course via email. The lecture notes are protected by copyright, and their dissemination in any form is strictly prohibited.

Update (November 3, 2020):

Physical exercise session are canceled and starting November 6, 2020, there will be only one exercise session held via Zoom at the following Zoom link. The recordings of this exercise session will be available here.

The first exercise class takes place on Friday, September 18.


Friday 08:00-10:00 online Martin Stefanik or Thea Kosche

Exercise Sheets

New exercise sheets will be uploaded here on Wednesdays before the corresponding Friday exercise class, along with a model solution to the exercise sheet from the previous week. Note that handing in your solutions is not obligatory. However, experience shows that being able to solve the exercises independently goes a long way towards good exam performance.

In case you decide to hand in your solutions, this will be done exclusively electronically. Please follow the instructions below.

  1. Scan your solution into a single PDF file. File format other than PDF will not be accepted. In case you do not have access to a scanner, scanning to a single PDF can be done efficiently using mobile applications such as Google Drive or Adobe Scan and many other ones. Please make sure that your scans are of good quality if you use these apps.
  2. Name the created file as {email address}_{exercise sheet number}.pdf. The parts surrounded by brackets are placeholders that should be replaced by the email address at which you want to receive the corrected solution and the number of exercise sheet for which you are submitting a solution, respectively. A correctly named solution file for exercise sheet 1 is for instance given by andrey.kolmogorov@probability.com_1.pdf.
  3. Upload your solution using the button below before 12:00 on the indicated Wednesday.

Several comments are in order:

Exercise sheet Due by Solutions Extra material
Exercise sheet 1 September 23, 2020 Solution 1 Slides 1
Exercise sheet 2 September 30, 2020 Solution 2 Slides 2
Exercise sheet 3 October 7, 2020 Solution 3 Slides 3
Exercise sheet 4 October 14, 2020 Solution 4 Slides 4
Exercise sheet 5 October 21, 2020 Solution 5 Slides 5
Exercise sheet 6 October 28, 2020 Solution 6 Slides 6
Exercise sheet 7 November 4, 2020 Solution 7 Slides 7
Exercise sheet 8 November 11, 2020 Solution 8 Slides 8
Exercise sheet 9 November 18, 2020 Solution 9 Slides 9
Exercise sheet 10 November 25, 2020 Solution 10 Slides 10
Exercise sheet 11 December 2, 2020 Solution 11 Slides 11
Exercise sheet 12 December 9, 2020 Solution 12 NA
Exercise sheet 13 December 16, 2020 Solution 13 Slides 12
Exercise sheet 14 Not to be submitted Solution 14 NA

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

Old Exams

Some old exams can be found here on the homepage of Group 3. Note, however, that students are highly discouraged from preparing from old exams only. Experience shows that this will most likely not be enough to ensure a passing grade.

Exam Inspection

Details on how and when to inspect your exam and the mistakes you have made can be found here.

Office Hours / Q&A Sessions

Office hours for the exams are usually offered during the last two weeks before the exam session. Details on this as well as udpates can he found here.

For computational aspects, you can for example consult the following books: