# Finanzmathematik II

## Dr. Andreas Groll, Sorin Nedelcu

## Schedule and Venue

LecturesDr. Andreas Groll |
Tue 10:15 to 11:45 and Thu 10:15 to 11:45 | Room B 132 |

ExercisesSorin Nedelcu |
Thu 14:15 to 15:45 | Room B 132 |

TutorialRebecca Declara |
Mon 16:15 to 17:45 | Room B 040 |

Final Exam |
Tue 4 Feb. 10:00 to 12:00 |
Room B 005 |

Retake Exam |
Friday 11 April. 10:00 to 12:00 |
Room B138 |

** The grades of the students who attended the retake-exam are displayed on the panel in front **

** of Room 233 . **

**The students have the possibility to review their exam result on Wed, 16.04.2014,**

** from 13:00 - 14:00 in Room 229.**

## 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.

**Lecture Notes** - Chapters 1-4

## 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

Correcting your answers and thinking through the exercises is the best preparation for the exam. The solutions need not be submitted, but if you wish them to be corrected, please submit your exercise solutions.

**Exercise Handouts:** Problem sheets and Solutions will be uploaded here during the course.

**Korrektor: **Aron Folly E-mail: aronfolly@gmail.com

Problem Sheet 1 | |

Problem Sheet 2 | |

Problem Sheet 3 | |

Problem Sheet 4 | |

Problem Sheet 5 | |

Problem Sheet 6 | |

Problem Sheet 7 | |

Problem Sheet 8 | |

Problem Sheet 9 | |

Problem Sheet 10 | |

Problem Sheet 11 | |

Problem Sheet 12 |

## Final Exams

## List of Grades

IMPORTANT UPDATE:

Tuesday, **4 February 2014**, from **10:00** to **12:00** in Room B 005