Practical Financial Optimization
Day 1 Introduction to GAMS using mean/variance or 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.
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.
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
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 7 to 17.
In the 2nd week students are given an assignment to which they must hand in written answers (a report) by August 25 and defend at an oral exam on August 31.
Reading material will be sent out in July.
Example of course literature:
“A GAMS Tutorial”: http://www.gams.com/dd/docs/gams/Tutorial.pdf
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.
- 7,5 ECTS
- Type of assessment
Oral examination, 15 minutesWritten assignment, 7 days
- Type of assessment details
- The oral exam takes place on August 31. It consists of a
defense/discussion of the student's report.
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
Criteria for exam assessment
See Learning Outcome
Single subject courses (day)
- Project work
- Exam Preparation
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
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.
7 August - 1 September 2023
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Rolf Poulsen (4-7774716b457266796d33707a336970)
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Courseinformation of students