Numerical Approximation of Stochastic Differential Equations

Professor: JProf. Dr. Diyora Salimova
E-Mail Professor: diyora.salimova@mathematik.uni-freiburg.de
Lecture: Tuesday, Friday 12-14 Uhr, SR 226, Hermann-Herder-Str. 10
Office Hours: by arrangement, R 208, Hermann-Herder-Str. 10
Tutorial: Tuesday, 16-18 Uhr, SR 226, Hermann-Herder-Str. 10
Computer Exercise: Thursday, 14-16 Uhr, CIP-Pool, Hermann-Herder-Str. 10
Assistant: M.Sc. Ilkhom Mukhammadiev
E-Mail Assistant: ilkhom.mukhammadiev@mathematik.uni-freiburg.de
Office Hours: by arrangement, R 211, Hermann-Herder-Str. 10

Updates

  • The course takes only place in the first half of the semester, until the end of November.
  • Oral exams take place in the week of December 2nd - 6th. Please contact the lecturer in advance, latest until November 1st, for fixing the exact date.
  • Tutorials and computer exercises begin during the second week of lectures.

Content

The aim of this course is to enable the students to carry out simulations and their mathematical analysis for stochastic models originating from applications such as mathematical finance and physics. For this, the course teaches a decent knowledge on stochastic differential equations (SDEs) and their solutions. Furthermore, different numerical methods for SDEs, their underlying ideas, convergence properties, and implementation issues are studied. The topics we will cover
  • Preliminaries from measure and probability theory
  • Generation of random numbers
  • Monte Carlo integration methods
  • Stochastic processes and Ito calculus
  • Stochastic difeerential equations (SDEs)
  • Numerical approximations for SDEs
  • Applications to computational finance: Option valuation

Studien-/Prüfungsleistungen

Studienleistung: Achieving 50 % of exercise points.

Prüfungsleistung: Completion of the Studienleistung and successful participation in the oral exam.

Lecture Notes

The hanwritten lecture notes will be regularly uploaded online:

Exercise Groups

Tutorials and computer exercises begin during the second week of lectures and take place weekly.

Exercise Sheets

Submission at the letterbox NASDE next to CIP-Pool (Hermann-Herder-Str. 10) or via e-mail until Friday. The exercise sheets can be submitted in groups of two.

 Sheet Uploaded Submission deadline
Sheet 1 18.10.2024 25.10.2024
Sheet 2 25.10.2024 04.11.2024 (since 01.11 is a public holiday)
Sheet 3 01.11.2024 08.11.2024
Sheet 4 08.11.2024 15.11.2024
Sheet 5 15.11.2024 22.11.2024
Sheet 6 22.11.2024 29.11.2024

MATLAB

For the programming of practical sheets we will use MATLAB. Details on the usage of MATLAB as well as its installation on your computer you find hier.

Computer exercises

Computer exercises take place weekly in CIP-Pool (Hermann-Herder-Str. 10). Please solve your problems with MATLAB und send your solutions as a zip-Data (except of the case it is just one file) per E-Mail to Ilkhom. You can submit in a group of two.

 Sheet Code Uploaded Submission deadline
Practical sheet 1 18.10.2024 01.11.2024
Practical sheet 2 01.11.2024 15.11.2024
Practical sheet 3 15.11.2024 29.11.2024

Literature

  1. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations Springer-Verlag, Berlin, 1992.
  2. Bernt Oksendal: Stochastic Differential Equations Springer, 2003.