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250016 VO Mathematical Finance (Continuous Time) (2022S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The intention is to hold the lectures on campus.

Tuesday 01.03. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 02.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 08.03. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 09.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 15.03. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 16.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 22.03. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 23.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 29.03. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 30.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 05.04. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 06.04. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 26.04. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.04. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 03.05. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 04.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 10.05. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 11.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 17.05. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 18.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 24.05. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 25.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 31.05. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 01.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 08.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 14.06. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 21.06. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 22.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 28.06. 11:30 - 12:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

* Fundametals 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.

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

Depending on the size of the class, either oral or written exam.

Minimum requirements and assessment criteria

Examination topics

The material from the lecture

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: Tu 28.02.2023 14:48