Financial Mathematics I


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 model
  • Interest rate models and derivatives 
  • Risk measures
  • Portfolio optimisation and CAPM

More information is given in Moodle. Please inscribe there for the course.


A list of reference books would cover the following works:

  • A. Irle, Finanzmathematik: Die Bewertung von Derivaten, Vieweg + Teubner, 2012.
  • N.H.Bingham & R.Kiesel, Risk Neutral Valuation, 2nd ed., Springer, 2004.
  • H. Föllmer & A. Schied, Stochastic Finance: An introduction in discrete time, de Gruyter, 2004.
  • P.K. Koch & S. Merino, Mathematical Finance and Probability: A Discrete Introduction, Springer, 2013.
  • M. Musiela & M. Rutkowski, Martingale methods in financial modelling, 2nd ed., Springer, 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.


Alexander Lindner

Class teacher

Merve Kutlu

Time and Venue

Teaching will take place online using the university's moodle system. Further information is available on the moodle system.


MSc. Finance: compulsory course
Bachelor/Master Mathematik: Wahlpflichtmodul im Bereich Angewandte Mathematik
Bachelor WiMa: Wahlpflichtmodul im Bereich SOF
Master WiMa: Wahlpflichtmodul im Bereich SOF


  • 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, more information can be found here).