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Finanzmathematik II

Prof. Dr. Ari-Pekka Perkkiö, Martin Bauer

Schedule and Venue


Prof. Dr. Ari-Pekka Perkkiö

Tue 10.00 - 12.00

Thu 10.00 - 12.00

First Lecture: Tue 17.10.17

Room B 006

Room B 006


Martin Bauer

Wed 8.30 - 10.00

First Exercise: Wed 18.10.17

Room B 006

Additional Exercises

Martin Bauer

Mock Exam: Wed 07.02. 16.00-18.30

Solutions:    Thu 08.02. 16.00-18.00

Questions:   Mon 12.02. 14.00-17.00

Room B 121

Room B 134

Room B 121

Final Exam

Thu 15.02.2018, 13.00

Room B 139

Retake Exam

Fri 06.04.2018, 09.00

Room B 005

The results of the retake exam can now be found in the box opposite room B233. The review is possible on monday April 9th from 10-11 in room B229. If you cannot come during this time, please send me an email until latest monday April 9th 12 o'clock to arrange some time.

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.


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).


Please try to solve every problem sheet. One or more specific exercises in each problem sheet, marked with a star "*", will be valid for a bonus system for the final exam. This exercise can be handed in, either in the next exercise class or in my office B236 before this class, and will be corrected. Each "star exercise" will be worth a certain number of points. Collecting at least 70% of the total points available during the whole semester will result, upon passing the exam, in a 0.3 or 0.4 bonus on the final grade.

Final Exams

The exam is a 120 minutes written exam. There is no examination support material allowed. Please bring your identity and student card. There is no registration for the exam. You are allowed to attend the retake exam also if you did not participate in the regular exam. The final grade is the better of the two exams.

Lecture notes