University of Duisburg-Essen

Faculty of mathematics, Campus Essen

Prof. Martin Hutzenthaler

Special topic course with integrated block seminar (2SWS+2SWS)
in the
winter term 2020/21 (3,6 or 9 ECTS)

**Backward stochastic differential equations**

*What should I know if I want to participate:*

This special topic course (Vertiefungsbereich Stochastik) is offered as part of the Master Program in Mathematics. Nevertheless, if you are interested in probability theory you are very welcome to participate. Preknowledge in probability theory (as covered by Probability Theory II
or chapters 1-10,21 in Klenke's book) are required. Don't hesitate to send me an e-mail for more information:

*Online course:*

Due to the Corona pandemia,
we are recommended to reduce contact as much as possible.
For this reason will be online only.

*When does the course start?*

The first video-conference will be on moodle on Monday, November 2nd, 2020, at 14:15.
Please let me know if you prefer a different day or time.

*How many credits do I get?*

This course has a block seminar (in February or March 2021) integrated.
The topics will usually be papers which rely on the material presented in the class. It will take place in the end of the winter semester break. If you only attend the course and pass an oral exam, then you get **3 CTS**
in Vertiefungsbereich Stochastik.
Alternatively, if you attend the course and
present a paper in the block seminar, then you get
**6 CTS** either in Vertiefungsbereich Stochastik or as Master Seminar.
Alternatively, if you attend the course and
present two papers in the block seminar, then you get
**9 CTS** as Master Seminar.

*Content:*

- Reminder: Martingale theory
- Reminder: Brownian motion
- Reminder: Ito Integrals
- Reminder: Stochastic differential equations
- Reminder: Feynman-Kac formula
- Backward stochastic differential equations
- Numerical approximations of BSDEs

*Moodle page:*

You will find all material on the moodle course page
to which everyone should
register.
News and messages will be sent over this moodle platform.
password is 20BSDE

*Language:*

The language will be English
or - if preferred - German.

*Literature:*

- Pardoux and Rascanu; Stochastic differential equations, Backward SDEs, Partial Differential Equations; Springer; 2014
- Rogers and Williams; Diffusions, Markov Processes and Martingales 2: Ito Calculus; Cambridge University Press; 2000
- Oksendal; Stochastic differential equations (6th edition); Springer; 2003
- Achim Klenke; Wahrscheinlichkeitstheorie; Springer; 2006
- Achim Klenke; Probability theory; Springer; 2008; translation of the book from 2006