Lecture Winter Term 2016/2017

Financial Mathematics 1





Robert Stelzer

Class Teacher:

Johanna Vestweber

Tutorial Teacher:

Imma Curato


MSc Finance compulsory course

Bachelor/Master Mathe: Wahlpflichtmodul im Bereich Angewandte Mathematik 

Bachelor/Master WiMa: Wahlplichtmodul im Bereich SOF 



!!!!The time of lecture and exercise course have changed!!!!

First lecture: 20/10/2016; Thursday 12.15-14, H3



Time and Venue:

Lecture:  Thursday, 12.15-14, H3; Friday 10.15 -12, H12

First Lecture: 20/10/2016;

Exercise Course: Tuesday, 14.15-16, H3;

First Exercise Classes: 25/10/2016;

Tutorial (only MSc Finance students): Friday, 14-16, He120

First tutorial: 28/10/2016.



Final Exam:

Rooms for the exam on Tuesday, 28. February:

Those of you, who just write the normal exam, go to room H22. 

Those of you, who write the exam for the DAV certificate, go to room H4/5. 


written and closed (that means, that you have to write the exam at the first date and only if you fail, you can write the retake.)

First date: 28.02.2017

Retake: 05.04.2017  (no possibility to get the DAV certificate)

Prerequisite: 50% of exercise points.



Analysis I+II; Lineare Algebra I+II; Stochastik I; Elementary Probability, Statistics and Measure Theory or Introduction to Measure Theoretic Probability (can be attended in the same winter term, beginning on 05/10/2015).



This course covers the fundamental principles and techniques of financial mathematics in discrete- and continuous-time models.  Specific topics are

  • Financial market models in discrete time: arbitrage freeness and completeness     
  • Conditional expectation and discrete time martingales
  • Valuation of European, American and path-dependent options
  • Foundations of continuous time market models and of the Black-Scholes
  • Interest rate models and derivatives
  • Risk measures
  • Portfolio optimisation and CAPM

  • Baxter, M.; Rennie, A.: Financial Calculus: An introduction to derivative pricing. (Cambridge University Press), 1996.
  • N.H.Bingham & R.Kiesel, Risk Neutral Valuation (2nd edition), Springer 2004.
  • Björk, T.: Arbitrage theory in continuous time. (Oxford University Press,
    Oxford) 2.edn. 2003.
  • H. Föllmer & A. Schied, Stochastic Finance: An introduction in discrete time, de Gruyter, 2004.
  • Korn, R.; Korn, E.: Option Pricing and Portfolio Optimization. (American Mathematical Society, Providence), 2001.
  • Musiela, M.; M. Rutkowski: Martingale methods in financial modelling. (Springer, New York), 2nd ed. 2004.
  • S. Shreve, Stochastic Calculus for Finance I: The  Binomial Asset Pricing Model, Springer, 2004.
  • S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.

Exercise sheets:               




Lecture notes: