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Finanzmathematik II

Prof. Dr. Thilo Meyer-Brandis, Martin Bauer, Daniel Ritter


Schedule and Venue

Lectures

Prof. Dr. Thilo Meyer-Brandis

Tue 12.00 - 14.00

Thu 10.00 - 12.00

First Lecture: Tue 16.10.18

Room B 005

Room B 005

Exercise Classes

Martin Bauer, Daniel Ritter

Wed 16.00 - 18.00

First Exercise Class: Wed 17.10.18

Room B 005

Supplementery Exercise Classes

Martin Bauer

Thu 31.01.19  16.00 - 18.00 (Mock Exam)

Fri 01.02.19    16.00 - 19.00 (Correction Mock Exam)

Wed 06.02.19 18.00 - 19.00

Room B 121

Room B 005

Room B 005

Repetitorium

Martin Bauer

Mon 04.02.19 16.00 - 19.00


Room B 121

Final Exam

Thu 07.02.19, 10.00 - 12.00 s.t.

Room B 005

Retake Exam

Tue 16.04.19, 12.15 - 14.15 s.t.

Room B 139


Course Description

The lecture provides an introduction to stochastic calculus with an emphasis on the mathematical concepts that are later used in the mathematical modeling of financial markets. In the first part of the lecture course the theory of stochastic integration with respect to Brownian motion and Ito processes is developed. Important results such as Girsanov's 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 course gives an introduction to 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 formula for pricing call and put options.


References

Stochastic calculus:

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. Please try to solve every problem sheet. Exercises marked with a star (*) will be valid for a bonus system for the final exam. This exercise can be handed in for correction, either in the next exercise class or in our offices B235/B236 before this class. Each "star exercise" will be worth a certain number of points (not necessarily the same). Collecting at least 75% of the total points available during the whole semester will result, upon passing the exam, in a 0.3/0.4 bonus on the final grade.


Final Exams

The exam is a 120-minutes written test. It is not an open book exam. That is, you are not allowed to bring with you the lecture notes or any other means of help. Please bring your identity and student card.


Lecture Notes