Mathematical Finance

First lecture
Wed 18/09/2013
First exercise class
Thu 19/09/2013

Course description

This course gives an advanced-level introduction to mathematical finance for students with a strong background in probability. It presents an overview of the main concepts, questions and approaches in the field, both in discrete and continuous time.

Topics

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

Prerequisites

Students are expected to have a solid knowledge of (measure-theoretic) probability 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.

Complementary Material: 

• A proof of the Doob Meyer Theorem can be found here.
  
• A proof of Bichteler-Dellacherie Theorem can be found here or here.
• A note on stochastic integration can be found here.
  

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 in January/February 2014.

References

• "Foundations of Modern Probability", O. Kallenberg, Second Edition, Springer, 2002.
  
• "Stochastic Integration and Differential Equations", P. Protter, Second Edition, Springer, 2005.
  

• "Stochastic Finance: An Introduction in Discrete Time", H. Föllmer, A. Schied, de Gruyter, 2011.
• "Mathematical Methods for Financial Markets", M. Jeanblanc, M. Yor, M. Chesney, Springer, 2009.
• "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.
• "Martingales and Stochatic Integration I", P.-A. Meyer, Lecture Notes in Mathematics 284, Springer Verlag,