Lecturer

Josef Teichmann

Coordinator

David Pires Tavares Martins
david.martins@

Lectures: Tue 8-10 LFW B 1, Thu 8-10 ML F 36.

Exercise classes: Fri 10-12 ML F 38.

Course description

This (401-4889-00L Mathematical Finance) is an advanced course on mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this mostly in continuous-time models.

Some of the topics are:
- semimartingales and general stochastic integration
- absence of arbitrage and martingale measures
- fundamental theorem of asset pricing
- option pricing and hedging
- hedging duality
- optimal investment problems.

Prerequisites

Students are assumed to be familiar with the content of the standard courses:
- 401-3601-00L Probability Theory,
- 401-3642-00L Brownian Motion and Stochastic Calculus.
This course is the continuation of the Spring semester course
- 401-3888-00L Introduction to Mathematical Finance,
which focuses on models in finite discrete time. Although that course is not required, students who have attended it will have an advantage in terms of the ideas and concepts, so it is advisable for students to attend that course before the present one, when possible.

For an overview of courses offered in the area of mathematical finance, see link. More information about the prerequisite (and other) courses is available on the Group 3 website.

Learning materials

Learning materials used in the course will be uploaded here.
Josef Teichmann - Foundations of Martingale Theory and Stochastic Calculus from a Finance Perspective
Lecture notes from 2013 and 2017
Some additional information about this course can also be found in the personal website of the lecturer.

Exercise classes

Exercise sheets should be submitted by 12 on Thursday before the class, to the assistant's box next to HG G 53.2, or by email to the assistant. The sheets will be uploaded a week in advance.

Announcement:

Due to the ongoing crisis, exercise classes will be conducted online (via Zoom) starting from October 30th and until further notice. In order to participate in the exercise classes, please contact the teaching assistant. Solutions submitted in physical format will be returned to the box.

Exercise sheet	Due by	Solution
Sheet 1	24 September 2020	Solutions 1
Sheet 2	1 October 2020	Solutions 2
Sheet 3	8 October 2020	Solutions 3
Sheet 4	15 October 2020	Solutions 4 Python 4
Sheet 5	22 October 2020	Solutions 5
Sheet 6	29 October 2020	Solutions 6
Sheet 7	5 November 2020	Solutions 7
Sheet 8	12 November 2020	Solutions 8
Sheet 9	19 November 2020	Solutions 9
Sheet 10	26 November 2020	Solutions 10
Sheet 11	3 December 2020	Solutions 11
Sheet 12	10 December 2020	Solutions 12
Sheet 13	17 December 2020	Solutions 13

Literature

On the FTAP of Kreps-Delbaen-Schachermayer by Y. Kabanov
Caracterisation des Semimartingales by C. Stricker
A Convergence Result for the Emery Topology and a Variant of the Proof of the Fundamental Theorem of Asset Pricing by C. Cuchiero, J. Teichmann
A New Perspective on the Fundamental Theorem of Asset Pricing for Large Financial Markets by C. Cuchiero, I. Klein, J. Teichmann
A Fundamental Theorem of Asset Pricing for Continuous Time Large Financial Markets in a Two Filtration Setting by C. Cuchiero, I. Klein, J. Teichmann
"Stochastic Integration and Differential Equations" by P. Protter (Springer 2005)
The Work of Kyosi Itô by P. Protter
"Semimartingale Theory and Stochastic Calculus" by S. He, J. Wang, J. Yan (CRC Press 1992)
Almost Sure by G. Lowther
"Continuous-time Stochastic Control and Optimization with Financial Applications" by H. Pham (Springer 2009)