Stochastic Differential Equations
Dr. Alexander Kalinin
Schedule and Venue
| Events | Date/Time | Room |
|---|---|---|
| Seminar Dr. Alexander Kalinin | Wednesday, 10:15 - 11:45 | B251 |
The course is organised via Moodle. If you want to attend the course, please register in Moodle.
In this seminar, we will analyse one-dimensional stochastic differential equations (SDEs) driven by a Brownian motion. To this end, a short review of semimartingales, stochastic integrals and Itô's formula will be discussed. Under Lipschitz conditions on the drift and diffusion coefficients of the SDE, we will derive unique strong solutions. In particular, we will recover the Brownian bridge, the geometric Brownian motion and the Ornstein-Uhlenbeck process as solutions of affine SDEs.
- Revuz, D. and Yor, M.: Continuous martingales and Brownian motion, Springer-Verlag, 1999.
- Ikeda, N. and Watanabe, S.: Stochastic differential equations and diffusion processes, North-Holland Publishing Co., 1989.
Both books are available as PDF files for LMU students at the university library.
Target Participants: Master students in Mathematics and Financial and Insurance Mathematics.
Pre-requisites: Probability theory and measure and integration theory.
Applicable credits: 3 ECTS. Students may apply the credits from this course to the
- Master in Mathematics, PO 2021 (any seminar module, such as WP 12 or WP 15),
- Master in Financial and Insurance Mathematics, PO 2021 (P 3 or WP 17), PO 2019 (P 3 or WP 18).