Discrete Time Financial Mathematics

Information about the course


This course covers the fundamental principles and techniques of financial mathematics in discrete-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
  • Interest rate models and derivative
  • Portfolio optimisation
  • Risk measures


  • Bachelor Mathematische Biometrie (optional)
  • Bachelor/Master Mathematik (optional)
  • Bachelor/Master Wirtschaftsmathematik (optional)
  • Master Wirtschaftswissenschaften (optional)
  • Master of Finance-Major Financial Mathematics (obligatory)
  • Master of Finance-Major Financial Economics (obligatory)
  • Master of Finance-Major Actuarial Science (obligatory)
  • Prerequisites
    • Analysis I+II
    • Lineare Algebra I+II
    • Stochastik I 
    • Elementary Probability, Statistics
    • Measure Theory or Introduction to Measure Theoretic Probability (can be attended in the same winter term)

Time and Venue

Discrete Time Financial Mathematics is a (2+1)-course and there will be 2 hours of lecture every week and 2 hours of exercise every second week.

  • Lecture: Friday 8:15-9:45 in N24 H14
  • Exercise Class: Thursday 16:15-17:45 in N24 H14

Lecture Notes and Exercises

All materials will be available on Moodle.



Alexander Lindner

Class teacher

Merve Kutlu


  • Date of the first lecture: Friday, 22.10.2021 8:15-9:45
  • Date of the first Exercise Class: Thursday, 04.11.2021 16:15-17:45


  • 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.