Finanzmathematik II/Stochastic Calculus and Arbitrage Theory in Continuous Time
Prof. Dr. Thilo Meyer-Brandis, Martin Bauer
Schedule and Venue
Lectures Prof. Dr. Thilo Meyer-Brandis |
Wed 10.00 - 12.00 Thu 10.00 - 12.00 |
Room B 006 Room B 005 |
Exercise Classes Martin Bauer |
Wed 16.00 - 18.00 |
Room B 005 |
Supplementary Exercise Classes Martin Bauer |
Fri 13.00 - 16.00 |
Room B 004 |
Final Exam |
Thu, February 6th, 10.00-12.00 |
Room B 005 |
Retake Exam |
Thu, April 2nd, 16.00 - 18.00 |
TBA |
The results of the exam can be found in the box opposite of room B233. The review of the exam is possible on Wednesday 19th, 13.00-14.00 in room B229.
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
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 Financial and Insurance Mathematics or Mathematics.
Pre-requisites: Probability Theory.
Applicable credits: Students may apply the credits from this course to Masterprüfungen Finanz- und Versicherungsmathematik (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 my office 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.
Exercise Sheets
- Sheet 1
- Sheet 2
- Sheet 3
- Sheet 4
- Sheet 5
- Sheet 6
- Sheet 7
- Sheet 8
- Sheet 9
- Sheet 10
- Sheet 11
- Sheet 12
- Sheet 13
- Sheet 14
- Sheet 15
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.