Mathematical Finance

Beginning of the lecture: September 21, 2010

Conditions to obtain the certificate (Testat): 2/3 of all exercises reasonably tackled.

Exercises: Click here for information on the exercise classes.

Lecture Notes: Lecture notes for probability theory and stochastic processes can be bought at the Präsenz of Gruppe 3 (HG G 32.6, Mondays and Thursdays from 12 to 13).

Contents and Prerequisites

This is an advanced level introduction to mathematical finance for students with a good background in probability. We want to give an overview of the 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, superreplication, American options, optimal investment problems, basic notions of fixed income markets, and perhaps others.
Prerequisites are probability theory and stochastic processes (for which lecture notes are available).

Some References

• "Stochastic Finance: An Introduction in Discrete Time", H. Föllmer, A. Schied, de Gruyter, 2004.
• "Introduction to Stochastic Calculus Applied to Finance", D. Lamberton, B. Lapeyre, Chapman-Hall, 2008.
• "Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives", N.H. Bingham, R. Kiesel, Springer, 2004.
• "Introduction to the Economics and Mathematics of Financial Markets", J. Cvitanić and F. Zapatero, MIT Press, 2004.
• "Methods of Mathematical Finance", I. Karatzas and S.E. Shreve, Springer, 1998.

Examination and ECTS Points

Session examination, oral 30 minutes. 12 ECTS credit points.

Tentative Schedule