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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

Exercises

Dr. Alexander Kalinin

Dates and Times:

Tuesday, 17:00 - 17:45

First exercise: Tuesday, 13 April

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.