## Mathematical Finance 2019

Find here the material of the first three weeks of the lecture course. A fourth draft of the lecture notes from 2013 and 2017 together with the **exam questions** can be found **here**. Two ipython notebooks on learning arbitrages and simulating semi-martingales are provided. Several examples from my course **Machine Learning in Finance** are used to illustrate concepts and to demonstrate the effectiveness of machine learning technology in Finance.

Please notice that parts of the lecture will be considerably different from these notes (sometimes simpler), also the following articles will play a major role in the exposition:

**
**- [K09] Kostas Kardaras, Generalized Supermartingale deflators under limited information.
- [BS98] Werner Brannath, Walter Schachermayer, A Bipolar Theorem for subsets of L0+.
- [T15] Josef Teichmann, Talk on FTAP for large financial markets, Pittsburgh, 2015.
- [T14] Josef Teichmann, Talk on FTAP, St Petersburg, 2014.
- [K97] Youri Kabanov, On the FTAP of Kreps-Delbaen-Schachermayer.
- [CS84] Christophe Stricker, Caracterisation des semimartingales, Seminaire de probabilites de Strasbourg, Volume 18 (1984) p. 148-153 .
- [63] Christa Cuchiero, Irene Klein, Josef Teichmann: A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting , arXiv:1705.02087, submitted, 2017.
- [56] Christa Cuchiero, Irene Klein, Josef Teichmann: A new perspective on the fundamental theorem of asset pricing for large financial markets, arXiv/1412.7562, TVP (Theory of Probability and Its Applications) 60 (4), 561-579, 2016.
- [52] Christa Cuchiero, Josef Teichmann: A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing, arXiv/1406.5414, Finance and Stochastics, 19 (2015), volume 4.