# Finanzmathematik II

## Prof. Dr. Thilo Meyer-Brandis, Hannes Hoffmann

## Schedule and Venue

LecturesProf. Dr. Thilo Meyer-Brandis |
Tue 10:15-11:45
Thu 10:15-11:45 First lecture: 07.10. |
B 006
B 006 |

ExercisesHannes Hoffmann |
Wed 16:15-17:45 | B 006 |

Tutorium |
Thu 16:30-18:00
The tutorial is every second week starting from 30.10. |
B 133 |

Final Exam |
Tue 27.01. 10:00-12:00 | B 006 |

Retake Exam |
Fri 10.04 10:00-12:00 | B 005 |

## Exam results

The retake exam results are now available in front of office B234. You can review the retake exam this week in office B235.

## Course Description

The lecture provides an introduction to stochastic calculus with an emphasis on the mathematical concepts that are later used in the mathematical modelling of financial markets. In the first part of the lecture the theory of stochastic integration with respect to the Brownian motion and Ito processes is developed. Important results such as the Girsanov theorem and the martingale representation theorem are also covered. The first part concludes with a chapter on the existence and uniqueness of strong and weak solutions of stochastic differential equations. The second part of the lecture gives an introduction into the arbitrage theory of financial markets in continuous time driven by Brownian motion. Key concepts are the absence of arbitrage, market completeness, and the risk neutral pricing and hedging of contingent claims. Particular attention will be given to the the Black-Scholes model and the famous Black-Scholes formulae for pricing call and put options.

## References

C. Dellacherie and P. A. Meyer. Probabilities and Potential B: Theory of Martingales. North-Holland, Amsterdam, 1982.

I. Karatzas and S. E. Shreve. Brownian Motion and Stochastic Calculus. Springer, New York, second edition, 1991.

B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, sixth edition, 2003.

Continuous Time Finance:

T. Björk. Arbitrage Theory in Continuous Time. Oxford University Press, New York, third edition, 2009.

I. Karatzas and S. E. Shreve. Methods of Mathematical Finance. Springer, New York, 1998.

B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, sixth edition, 2003.

## For whom is this course?

**Target Participants:** Master students of Business Mathematics or Mathematics.

**Pre-requisites: **Probability Theory.

**Applicable credits: ** Students may apply the credits from this course to Masterprüfungen Wirtschaftsmathematik (WP12) and Mathematik (WP23).

## Exercises

Please try to solve every problem sheet. Those problem sheets which are marked as "bonus system" sheets on top, can be handed in and will be corrected. They can be handed in either in the next exercise or in my office B235 before this exercise. If you are able to solve 50% of every of these bonus problem sheets and if you pass the exam, you will get a bonus of 0.3 for the exam grade and 0.7 if you additionally solve more than 80% of the problem sheets.

**Exercise Handouts:** Problem sheets will be uploaded at the bottom of this page during the course.

## Final Exams

The exam is a 120 minutes written exam. In order to participate in the retake exam you have to participate in the first exam or to hand in a doctors's certificate.