Stochastic Calculus (MAA 519)
Welcome to the webpage of the course “Stochastic Calculus”, which provides the mathematical foundation for understanding and modeling random phenomena, making it an essential tool for financial engineering, machine learning, and many applications in the natural and social sciences. The course covers, in particular, 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.
Please note that this course is recommended as foundation for the many other courses like “Advanced Topics in Mathematical Finance”, “Computational Finance”, and “Numerics of Stochastic Differential Equations”.
General Information
The course will be based on pre-recorded lectures, with tutorials taking place in person at the university.
For the schedule and location of the tutorials, please see Portal2. All course materials (lecture notes, problem sheets, etc.) as well as further information will be made available in the course’s ILIAS group.
If you are interested in attending the course, please register for the ILIAS group. This ensures that you receive all relevant information about the course, but it does not obligate you to take the exam.
Team
Lecturer: Prof. Dr. David Prömel
Tutor: Mihriban Ceylan
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.
- You may reply in English or German.
- Everything (lectures, problem sheets, tutorials) is relevant for the exam.