250016 VO Mathematical Finance (Continuous Time) (2023S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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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

Julio Daniel Backhoff-Veraguas

Classes (iCal) - next class is marked with N

Wednesday 01.03. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 02.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 08.03. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 09.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.03. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 16.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 22.03. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 23.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.03. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 30.03. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.04. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 20.04. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.04. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 27.04. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.05. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 04.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.05. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 11.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.05. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.05. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 25.05. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 31.05. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 01.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 07.06. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 14.06. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 15.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 21.06. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 22.06. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 28.06. 13:15 - 14:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 29.06. 11:30 - 13:00 Seminarraum 11 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: Tu 13.02.2024 15:06