Lecture Winter Term 2018/2019

Financial Mathematics I


Alexander Lindner
Class and Tutorial Teacher:
Jana Reker

MSc. Finance: compulsory course

Bachelor/Master Mathematik: Wahlpflichtmodul im Bereich Angewandte Mathematik 

Bachelor WiMa: Wahlpflichtmodul im Bereich SOF

Master WiMa: Wahlpflichtmodul im Bereich SOF


On Thursday, 7th of February, we have the opportunity to hear a talk on Financial Mathematics in practice during the time of the lecture. The invited speakers are Dr. Christian Hering and Eva Mayer-Amhof (Landesbank Baden-Württemberg).

Time and Venue:


  • Tuesday, 14-16 pm, N25-H3.
  • Thursday, 12-14 pm, N25-H3.

Exercise Class:

  • Friday, 10-12 am, N24-H12.
Tutorial Course:
  • Friday, 14-16 pm, He18 - 1.20.

Final Exam:

The final exam will be written on Monday, 25th February 2019 in H1 and H4/5, either from 13 to 16 pm or from 13 to 15 pm, depending on whether the participant additionally writes the DAV supplement exam or not.

A retake will take place on Tuesday, 9th April 2019.

Authorized Auxiliaries (FiMa I):

  • a non-programmable calculator (no smartphone, smartwatch or similar, even if the calculator app is non-programmable),
  • one A4 sheet or equivalent 2 pages of handwritten notes,
  • a permanent pen.

The Financial Mathematics I exam is open. That means that you can choose the date at which you want to write the exam. Note that, if you want to write also the DAV part, you have to write the exam at the first appointment.

You will need to achieve 50% of the overall exercise points to attend the final exam.

To participate in the final exam, you have to register first for the precourse (Vorleistung) at campusonline.uni-ulm.de until Friday, 15th of February 2019. 

Afterwards we will enter whether you have passed the precourse or not in the system. If you have passed the precourse, you can register for the Financial Mathematics I exam until Thursday, 21st of February 2019. If you miss to register for either the precourse or the exam, you cannot attend the final exam.


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).


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


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.

Exercise sheets:


Lecture notes: