- Lecturer
- Josef Teichmann
- Coordinator
- David Pires Tavares Martins

Lectures: Tue 8-10 HG E 1.1, Thu 8-10 ML F 39.

Exercise classes: Fri 10-12 ML F 38.

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.

- 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. Some additional information about this course can also be found in the personal website of the lecturer.

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

Note that the first class will be held on 27.09.

Exercise sheet | Due by | Solution |
---|---|---|

Sheet 1 | 3 October 2019 | Solutions 1 |

Sheet 2 | 10 October 2019 | Solutions 2 |

Sheet 3 | 17 October 2019 | Solutions 3 Python 3 |

Sheet 4 | 24 October 2019 | Solutions 4 |

Sheet 5 | 31 October 2019 | Solutions 5 |

Sheet 6 | 7 November 2019 | Solutions 6 Python 6 |

Sheet 7 | 14 November 2019 | Solutions 7 |

Sheet 8 | 21 November 2019 | Solutions 8 |

Sheet 9 | 28 November 2019 | Solutions 9 |

Sheet 10 | 5 December 2019 | Solutions 10 |

Sheet 11 | 12 December 2019 | Solutions 11 |

Sheet 12 | 19 December 2019 | Solutions 12 |

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)