Stochastic Calculus (MAA 519)

  • General Information

    Welcome to the webpage of the course Stochastic Calculus. If you are interested in taking the course, please sign up by writing me an email to

    proemel ( a t ) uni-mannheim.de

    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. The course will cover the following topics:

    • Brownian motion and martingales in continuous time
    • Stochastic Integration and Ito formula
    • solution theory for stochastic differential equations
      (strong solutions, linear SDEs)
    •  change of measure (Girsanov theorem)
    •  martingale representation theorem

    A PDF with all information can be found here.

    Please note that this course is recommended as foundation for the courses Advanced Topics in Mathematical Finance, Computation Finance, Numerics of Stochastic Differential Equations, ...

  • Team

    Lecturer: Prof. Dr. David Prömel

    Tutor: Anna Kwossek

    Bonus material: David Scheffels

  • Lectures and Notes

    The videos to the lecture can be found on the YouTube channel „Mathe Mannheim“.

    Schedule:

    Tues B4 (13:45 – 15:15): Consultation-hour on Zoom (see Portal2)
    Thurs B4 (13:45 – 15:15):  Consultation-hour in C 014 (A 5)

    The video of the lecture will be uploaded on the YouTube channel „Mathe Mannheim“.

    The lecture notes will be updated and corrected regularly during the term. Please always check for the latest version.

     

  • Tutorials

    Schedule: Thursdays B5 (15:30-17:00) in  C 014 (A 5)

    The tutorials will take place as personal meetings, but all material will be available here.

    1. Tutorial (16.09.21) – Additional Material

    2. Tutorial (23.09.21) – Additional Material

    3. Tutorial (30.09.21) – Additional Material

    4. Tutorial (07.10.21) – Additional Material

    5. Tutorial (14.10.21) – Additional Material

  • Problem Sheets

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

    1. Problem sheet (due on 14/09) – Solutions

    2. Problem sheet (due on 21/09) – Solutions

    3. Problem sheet (due on 28/09) – Solutions

    4. Problem sheet (due on 05/10) – Solutions

    5. Problem sheet (due on 12/10) – Solutions

    6. Problem sheet (due on 19/10) – Solutions

    7. Problem sheet (bonus sheet, due on 26/10) – Solutions

    Please note:

    • You are encouraged to submit your solutions in pairs.
    • For each problem you can get up to 5 points.
    • Please submit your solution either in paper form in the post box in A5 part C or via email to akwossek (-at-) mail.uni-mannheim.de.
  • Exam

    Style: oral exam of 30 min

    Date: to be agreed on. Please contact me asap if you did not receive my emails regarding possible dates for the oral examination.

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

    - You may reply in English or German.

    - Everything (lectures, problem sheets, tutorials) is relevant for the exam.

  • Programming exercises

    Python exercises

    On each exercise sheet, there will be one additional programming exercise. We recommend to deal with them in Python but R or Matlab would work equally well. Solving these programming exercises is optional and you should not hand them in. They have no direct relevance for the exam, but of course  they contribute to get a better understanding of the lecture topics.

    Sample solutions

    We will upload sample solutions to these exercises on our GitHub account:

    https://github.com/fima-unima?tab=repositories.

    You don’t need an account on GitHub to download the solutions.

    Since we are no experts in Python programming, we believe that you could find “nicer” solutions to the exercises. If this is the case, please send us your solution to

    fima.unima (-at-) gmail.com.

    We will then upload your nicer solutions also to GitHub.

    Installation, introduction into Python and further material

    We recommend you to use the editor Visual Studio. A good explanation for the installation of Python and Visual Studio on MAC OS and Windows can be found here:

    https://github.com/FelixRb96/Python_kurs_RTG/blob/main/materialien/0_installation_und_entwicklungsumgebung.ipynb.

    On the parent folders of the upper link you can also find an introduction into Python:

    https://github.com/FelixRb96/Python_kurs_RTG/blob/main/materialien/1_python_uebersicht.ipynb

    as well as into the packages numpy (which is needed for any mathematical calculations), matplotlib and pandas. You can learn how to install packages on the very last point of that introduction.

    If you want to learn even more about Python, you can find the material from the Python course held by STADS in 2020 here:

    https://stads-mannheim.github.io/pythonkurs2020_1_get_started.

    If you need more detailed help with the installation, you can also have a look at these videos:

    https://www.youtube.com/watch?v=qn96nt-9jaU (for Windows),

    https://www.youtube.com/watch?v=9h5V4XxNm_4 (for MAC OS),

    but note that you do not need to install Git and Poetry for the purpose of this course.