Universität Wien

250016 VO Mathematical Finance (Continuous Time) (2025S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
Mo 28.04. 08:00-09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

The lectures on monday will start only at 9:00.

  • Monday 03.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.03. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.03. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.03. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.04. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.04. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.04. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.05. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.05. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.05. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.05. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.06. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.06. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.06. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.06. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.06. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

* Fundamentals of continuous times processes relevant to finance: martingales, Brownian motion, geometric Brownian motion, stochastic integration, Ito formula, Ito processes, Girsanov theorem, martingale representation, etc.
* Fundamental aspects of continuous time mathematical finance: trading, super/sub hedging, replication, pricing of options, martingale measures, no-arbitrage, the fundamental theorem of asset pricing, market completeness, Black-Scholes formula, hedging within the Black-Scholes model, exotic options, model calibration given option prices, etc. If time permits we will cover stochastic optimal control problems in finance, such as utility maximization.
We will start the lecture with a brief introduction to discrete time stochastic processes and discrete time mathematical finance. Then we introduce the necessary machinery from continuous time stochastic processes. We apply this machinery towards building a continuous time theory of mathematical finance.

Assessment and permitted materials


Only a final exam. Depending on the size of the class, either oral or written (closed book) exam.

Minimum requirements and assessment criteria

Examination topics

The material from the lectures.

Reading list

For the elements of discrete time stochastic processes / mathematical finance, you may consult the book 'Stochastic Finance' by Föllmer and Schied.
For continuous time processes / finance, good references are 'Introduction to stochastic calculus applied to finance' by Lamberton and Lapeyre, 'Stochastic calculus for finance II: continuous-time modelr' by Shreve, or 'Arbitrage theory in continuous time' by Björk.

Association in the course directory

MSTV

Last modified: Fr 28.02.2025 16:46