Financial Modelling with Stochastic Partial Differential Equations
Dr. Alexander Kalinin
Schedule and Venue
| Events | Date/Time | Room |
|---|---|---|
| Lectures Dr. Alexander Kalinin | Tuesday, 14:15 - 15:45 First lecture: Tuesday, 18 October | B041 |
| Exercise Classes | Tuesday, 16:00 - 17:30 First exercise: Tuesday, 18 October | B041 |
| Final Exam | 15 February, 14:00 - 16:00 | B006 |
The course is organised via Moodle at https://moodle.lmu.de and the lecture and exercise sessions will also be held online via zoom if there are students joining the sessions in the beginning. If you want to attend the course, please register in Moodle and send an e-mail from your LMU address to kalinin@math.lmu.de.
The aim of this course is to give a concise introduction to a class of parabolic stochastic partial differential equations with a particular focus on financial modelling. In the first part of the semester, we will deal with Gaussian processes, including fractional Brownian motions, Ornstein-Uhlenbeck processes and white noises, and consider the Kolmogorov-Chentsov continuity theorem in a multidimensional setting. In the second part, we will derive unique solutions to such stochastic equations, analyse their path and probabilistic properties and consider relevant applications in mathematical finance.
- Dalang R., Khoshnevisan D., Mueller, C., Nualart, D. and Xiao, Y.: A Minicourse on Stochastic Partial Differential Equations, Springer, 2009.
- Lototsky S. V. and Rozovsky, B. L.: Stochastic Partial Differential Equations, Springer, 2017.
- Röckner, M. and Liu, W.: Stochastic Partial Differential Equations: An Introduction, Springer, 2015.
- Hairer, M.: An Introduction to Stochastic PDEs, arXiv preprint, 2009.
All three books are available as PDF files for LMU students at the university library and the article, cited in the fourth place, is publicly available.
Target Participants: Master students of Financial and Insurance Mathematics or Mathematics.
Pre-requisites: Probability theory and foundations of stochastic processes in continuous time.
Applicable credits: 6 ECTS. Students may apply the credits from this course to:
- the Master in Financial and Insurance Mathematics, PO 2021 (WP 13), PO 2019 (WP 14)
- the Master in Mathematics, PO 2021 (WP 42 or WP 11 + WP 13), PO 2011 (WP 47.2+3 or WP 15)