Mathematical Finance

First lecture
Tuesday 16/09/2014
First exercise class
Friday 19/09/2014

Course description

This is an advanced level introduction to mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this in both discrete- and continuous-time models. Topics include absence of arbitrage and martingale measures, option pricing and hedging, optimal investment problems, and probably others.

Topics

• absence of arbitrage and martingale measures
• option pricing and hedging
• optimal investment problems
• additional topics

Prerequisites

Prerequisites are probability theory and stochastic processes as taught in the courses "Wahrscheinlichkeitstheorie/Probability Theory" and "Brownian Motion and Stochastic Calculus". Lecture notes for both courses can be be purchased during the assistant hour ("Präsenz").

Lecture notes

No official lecture notes are available.

Exercise classes

Details of the exercise classes can be found here.

Assistant hour ("Präsenz") and office hour

There are regular assistant hours ("Präsenz") on Mondays and Thursdays, 12:00-13:00 in HG G 32.6.

Examination details

A numerical grade and ECTS points for the course are based only on the final 30 minutes oral examination. Exams will be during the standard exam period in January/February 2015.

References

• N.H. Bingham, R. Kiesel, "Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives", second edition, Springer, 2004
• T. Björk, "Arbitrage Theory in Continuous Time", third edition, Oxford University Press, 2009
• J. Cvitanić, F. Zapatero, "Introduction to the Economics and Mathematics of Financial Markets", MIT Press, 2004
• H. Föllmer, A. Schied, "Stochastic Finance: An Introduction in Discrete Time", third edition, de Gruyter, 2011
• M. Jeanblanc, M. Yor, M. Chesney, "Mathematical Methods for Financial Markets", Springer, 2009.
• G. Kallianpur, R.L. Karandikar, "Introduction to Option Pricing Theory", Birkhäuser, 2000
• D. Lamberton, B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance", second edition, Chapman-Hall, 2008
• A.N. Shiryaev, "Essentials of Stochastic Finance: Facts, Models, Theory", World Scientific, 1999