Optimization Methods in Finance


Prof. Friedrich Eisenbrand


Dr. Thomas Rothvoß



Many computational problems in finance can be solved by optimization techniques. This course will cover a selection of such methods which are nowadays the basis of many products offered by financial service providers. The students will get to learn the main optimization techniques and will be anabled use them to solve typical optimization problems arizing in finance.
Especially the following topics will be covered.

  • Learning and games: Experts advice, zero sum games and investment strategies
  • Linear Programming: Computing a dedicated bond portfolio, asset pricing
  • Quadratic Programming: Portfolio Optimization (Markowitz model)
  • Integer Programming: Constructing an index fund
  • Dynamic Programming: Option Pricing, Structuring asset backed securities
  • Stochastic Programming: Asset/Liability management

The lectures and the exercises will be given in English. We assume basic knowledge in linear algebra and basic programming knowledge in C++ or Matlab. The lecture announcement can be found here.


Your grade will be determined by a written final exam. You can collect bonus points by  the following means:

  • Scribing one lecture (5 pts)  Here is a guideline on how to scribe and the file scribe.sty
  • Presenting a theoretical exercise (2 pts)
  • Solving practical exercises (3 pts)

Each of these means to collect bonus points are assessed and graded during the semester. If you obtain 4 bonus points, your final grade will be improved by half a point. If you receive 8 or more bonus points the grade of your final exam will be improved by a full grade.

Please be aware: The bonus points can only improve your grade but cannot turn a failure in the exam into a passing of the entire course! 

This is a 4-credit course. 



Lectures: Wednesday, 14:15-15:45, MA A3 31 (First Lecture: 22.09.10)

Exercise session: Wednesday, 16:00-17:30, MA A3 31 (First exercise session: 29.09.10)


The exercises will take place as follows: For the i-th exercise sheet the students are supposed to solve the assignments in the tutorial in week 2i+1. The solutions will be discussed in week 2i+2.


There is no text for this course. We will provide inks to original literature and chapers of books as we proceed. Furthermore, there will be handouts (scribenotes) prepared by the students and edited by the lecturer.

  • Lecture 1 (Scribe by Fritz Eisenbrand): Following experts advice. latex-file
  • Lecture 2 (Scribe by Miroslav Popovic): Randomized weighted majority algrithm, zero sum games
  • Lecture 3 (Scribe by Yoav Zemel, updated 18.10.10): The Minimax theorem
  • Lecture 4 (Scribe by Sezin Afsar): Online portfolio selection
  • Lecture 5 (Scribe by Julien Damond, updated 5.11.10): Mean variance portfolio optimization and Lagrange Duality
  • Lecture 6 (Scribe by Nancy Moret): The ellipsoid method
  • Lecture 7 (Scribe by Rached Hachouch): Linear programming, dedicated bond portfolios
  • Lecture 8 (Scribe by Parmeet Bhatia, updated 22.11.10): The fundamental theorem of asset pricing
  • Lecture 9: (Scribe by Yankai Shao): Dynamic Programming
  • Lecture 10: (Scribe by Anu Harjula): The knapsack problem
  • Lecture 11: (Scribe by Boris Oumow): Integer Programming and Branch & Bound
  • Lecture 12: (Scribe by Thomas Schandlong): Two person games, Brouwers Fix Point Theorem

Practical exercises



Previous exams: