Mathematical Finance (MAC 410)

  • General Information

    Welcome to the webpage of the course  Mathematical Finance. The course will take place live via Zoom but all material of the course will be additional available online afterwards in some form. If you are interested in taking the course, please sign up by writing me an email to

    proemel ( a t )

    providing your full name. This will help us to provide you with information regarding the course and does not mean that you have to do the exam in the end.

    • some basics from probability theory: conditional expectation, filtrations, stopping times
    • martingale theory
    • modeling of financial markets in discrete time, e.g., the binomial model of Cox, Ross and Rubinstein
    • arbitrage theory: in particular, fundamental theorems of asset pricing (FTAP), pricing and hedging of European options in complete and incomplete models
    • portfolio optimization
    • risk measures
    • American option and optimal stopping stopping
    • Some basics in continuous-time mathematical finance: Black-Scholes model, Black-Scholes formula and “Greeks“
    • a bit of elementary functional and convex analysis
  • Team

    Lecturer: Prof. Dr. David Prömel

    Tutors: Sam Baguley, Paul Nikolaev

  • Lectures and Notes


    Tues B3 (12:00 - 13:30) in WIM-ZOOM-05
    Thurs B3 (12:00 - 13:30) in WIM-ZOOM-05

    The lectures will be live via Zoom but will also be recorded and made available on YouTube afterwards. Of course, the recommendation of the university is in place: „During virtual lectures or courses of a similar nature, students are not obliged to enable video and sound transmission and may use a pseudonym to participate.“

    The lecture notes will be updated and corrected regularly during the term. Please check always for the latest version. You can aso find the notes of each lecture below.


  • Tutorials

    Schedule: Tues B4 (13:45-15:15) in WIM-ZOOM-05

    - The tutorials will be live via Zoom but not recorded.

    - You are strongly encourage to actively participate in the tutorials.

    - The tutorials will not be recorded but the notes will made available after the tutorials.

    Below you can find the notes of each tutorial:

  • Problem Sheets and Help Desk

    Please submit your solutions to Paul Nikolaev via Email to

    pnikolae( a t )

    If this is not possible, you can submit your solutions in paper form in the box at B6, 26, level 4.

    There will be a help desk every Monday from 11 am to 13 am online (Zoom) or in person in office B4.03 in B6 provided by Paul. If you have questions regarding the his corrections or the problem sheets, please write Paul an email or use the help desk.

    Below you can find the problem sheet and the corresponding solutions.

    1. Problem sheet (due on 02/10) - Solutions

    2. Problem sheet (due on 09/10) - Solutions

    3. Problem sheet (due on 14/10) - Solutions (corrected)

    4. Problem sheet (due on 23/10) - Solutions

    5. Problem sheet (due on 30/10) - Solutions

    6. Problem sheet (due on 06/11) - Solutions

    7. Problem sheet (due on 13/11) - Solutions

    8. Problem sheet (due on 20/11) - Solutions

    9. Problem sheet (due on 27/11) - Solutions

    10. Problem sheet (due on 04/12) - Solutions

    11.Problem sheet (due on 11/12) - Solutions

    12. Problem sheet (due on 18/12) - Solutions


  • Exam

    Post-exam review: The post-exam review is postponed until the university opens again for students. Please contact me via email if you would like to review your exam earlier for a good reason (e.g. as preparation for the second exam, completion of your Bachelor/Master degree, etc.).

    Style: written exam of 90 min

    Date: 11/01/2021

    - Requirement for the exam are at least 50% of the points on the problem sheets.

    - It will be standard written exam of 90 min.

    - The exam questions are in English only.

    - You may reply in English or German.

    - You are allowed to use a non-programmable calculator but (I think) you do not need it.

    - Everything (lectures, problem sheets, tutorials) is relevant for the exam except lecture 25/Chapter 8.

    - Questions-answer session on Thursday, January 7, 2-3.30 pm in Zoom-room 01.

    - Here a sample exam with solutions if you like to get some more practice.

    - Last minute emails regarding the course will not be answered from from Friday, January 8, 5pm, on.