Lecture Winter Term 2017/2018

Financial Mathematics I


Alexander Lindner
Class and Tutorial Teacher:
Dirk Brandes

MSc. Finance: compulsory course

Bachelor/Master Mathematik: Wahlpflichtmodul im Bereich Angewandte Mathematik 

Bachelor WiMa: Wahlplichtmodul im Bereich SOF

Master WiMa: Pflichtmodul 


The first lecture is scheduled on Thursday, 19th October 2017, in N25-H3 from 12 pm to 14 pm.

There is an additional lecture on Tuesday, 24th October, in N25-H3 from 14 pm to 16 pm.

The first exercise class takes place on Friday, 27th October, in N24-H12 from 10 am to 12 am.

To provide information for the lecture and the exercise sheets, we are using Moodle. The password you need to enter the course was given to you in the first lecture.

The DAV supplement takes place on every Monday and Wednesday between 06/11/2017 and 29/11/2017, 18:00 - 19:30, N24-H14. For more details and future information see DAV Supplement.

Time and Venue:


  • Thursday, 12-14 pm, N25-H3.
  • Friday, 10-12 am, N24-H12.
  • First lecture: 19/10/2017

Exercise Class:

  • Tuesday, 14-16 pm, N25-H3.
  • First Exercise Class: Friday, 27/10/2017, N24-H12.
Tutorial Course:
  • Friday, 14:00-16:00, He18 - 1.20.
  • First Tutorial Course: 27/10/2017

Final Exam:

written, 26th of February 2018 and 10th of April 2018.

The Financial Mathematics I exam is open. That means that you can chose 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, 26th of February 2018.

Prerequisite: 50% of the overall exercise points.

To participate in the final exam, you have to register first for the precourse (Vorleistung) at campusonline.uni-ulm.de until February the 9th 2018. 

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 February the 22nd 2018. If you miss to register for either the precourse or the exam, you cannot attend the final exam.

Authorized Auxiliaries (FiMa I):

  • a non-programmable calculator (no smartphone),
  • one A4 sheet or equivalent 2 pages of handwritten notes,
  • a permanent pen.

Authorized Auxiliaries (DAV-Part):

  • a non-programmable calculator (no smartphone),
  • a permanent pen.


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 09/10/2017).


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: