Universität Wien

250016 VO Mathematical Finance (Continuous Time) (2024S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 04.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.04. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.04. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.05. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.05. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 04.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.06. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.06. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.06. 11:30 - 13:00 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 Lecture Notes from Christa Cuchiero or Mathias Beiglböck (provided in the lecture) or 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: We 30.04.2025 09:27