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Finanzmathematik II

Prof. Dr. Ari-Pekka Perkkiö, Martin Bauer


Schedule and Venue

Lectures

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

Exercises

Martin Bauer

Wed 8.30 - 10.00

First Exercise: Wed 18.10.17

Room B 006

Final Exam

Thu 15.02.2018, 13.00-16.00

Room B139

Retake Exam

TBA

TBA

Problem Sheet 11 is now online.


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

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

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.


Lecture notes