Practical Financial Optimization

Course content

Week One

Day 1 Introduction to GAMS using mean variance/ mean standard deviation optimization.

Day 2 Continued introduction to GAMS. Adding practical constraints such as fixed costs, size constraints and gearing to the mean variance model. Analysing the results in Excel.

Day 3 Continued introduction to GAMS. Introducing classical concepts in fixed income modelling and management: yield curve generation, portfolio dedication and immunization.

Day 4 and 5 Project work. The participants will be asked to formulate, solve and analyse a GAMS model based on a given problem formulation. The results should be presented at the end of week 1.

Week Two

Day 1 Scenario generation and optimization. Case: index tracking and regret minimization.

Day 2 Scenario optimization continued. Case: Value at Risk and Conditional Value at Risk.  

Day 3 Stochastic programming. Case: Mortgage loan refinancing.   

Day 4 The final project will be introduced. We will work together on developing a back-testing framework for use in the final project.

Day 5 We will work on the final project in the class. By the end of this day the students should be able to perform independent work on the project.

Learning outcome


The course gives an introduction to the domain of practical financial risk and portfolio management. Participants will work with problem areas that can be attacked using optimization models. 


Participants will be trained in quantitative evaluation of risk-return trade-offs, and learn how to model, solve, and document large, practical problems.

The course also gives an introduction to the programming language GAMS (General Algebraic Modelling Systems), which will be used extensively in all the cases and examples.

Participants who have followed the course will be able to formulate and solve optimization problems in GAMS in particular within the following areas:

  • Measuring and managing return and risk trade offs
  • Adding practical constraints to financial optimization problems
  • Immunization and dedication of a bond portfolio
  • Modelling Value at Risk and Conditional Value at Risk
  • Back-testing results of ex-ante optimization


See course contents above.

3 hours of lectures and 3 hours of tutorials on each of the 10 (week)days August 4 to 15.

After that (or: during the 2nd week) students are given an assigment to which they must (before the regular teaching block begins) hand in written answers (a report).

Reading material will be sent out in July.

Example of course literature:

“A GAMS Tutorial”:

Zenios, Stavros A. (2008), "Practical Financial Optimization: Decision Making for Financial Engineers", Blackwell.

An introductory course in finance, an introductory course in operations research, and basic programming literacy. (The first two years of the Math/Econ-education will do nicely.)

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Oral examination, 15 minutes
Written assignment, 7 days
Type of assessment details
No preparation time. The report will be the focal point of the examination.
The grade will be given based on an overall evaluation.
Only certain aids allowed

The student can bring the report for the examination.

Marking scale
7-point grading scale
Censorship form
No external censorship
Severel internal examiners

15 minutes oral exam (excl. grading) with all aids, but no preparation time. Here, the student will draw a question from a pre-specified list covering the full course contents.

Criteria for exam assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 30
  • Preparation
  • 70
  • Exercises
  • 30
  • Project work
  • 70
  • Exam Preparation
  • 6
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master
Summer course,
August 4-29, 2025
Week 1 and 2: Lectures, tutorials, and supervised project work
Week 3: Unsupervised project work and report writing
A report-based oral exam is held in week 4.
On-campus attendance is required only for the first two weeks.

Workload: Pre-lectures preparation 71 hours, 2*45 hours for the two lecture weeks, 45 hours in total the week after the lectures to finish the final project + prepare for examination
Summer course; August 4 - 29, 2024 (teaching two first weeks, exam in the last week)
The number of places might be reduced if you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Rolf Poulsen   (4-83807d77517e7285793f7c863f757c)
Saved on the 14-02-2024

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