Financial Modelling with Stochastic Partial Differential Equations
Lecturer: Dr. Alexander Kalinin
Schedule and Venue
| Lectures Dr. Alexander Kalinin |
Dates and Times: Tuesday, 16:15 - 17:00 and Wednesday, 12:15 - 13:45 First lecture: Tuesday, 13 April |
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Exercises Dr. Alexander Kalinin |
Dates and Times: Tuesday, 17:00 - 17:45 First exercise: Tuesday, 13 April |
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| Final Exam | Thursday, 5 August, 9:00 - 12:00 |
The lectures and the exercise sessions will be held online via zoom and all the course material will be available in Uni2work at https://uni2work.ifi.lmu.de. If you want to attend the course, please register as soon as possible in Uni2work or send an e-mail from your LMU address to kalinin@math.lmu.de.
Course Description
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.
References
- 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 (https://www.en.ub.uni-muenchen.de/index.html) and the article, cited in the fourth place, is publicly available.
For who is this course?
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 2019 (WP14)
- the Master in Mathematics (WP 47.2+3 or WP 15)
Exam
The online exam will take place on Thursday, 5 August, from 9 am to 12 pm by means of Uni2work.