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.
Knowledge:
See course contents above.
Skills:
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
Competencies:
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.
3 hours of lectures and 3 hours of tutorials on each of the 10
(week)days August 4 to 15.
The lectures and tutorials are taught online.
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).
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.
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.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral exam on basis of previous submission, 15 minutes
- 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. - Aid
- 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
- Re-exam
-
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
Kursusinformation
- Language
- English
- Course number
- NMAK15000U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Placement
- Summer
- Schedulegroup
-
4-29 August 2025
Online summer course:
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. - Capacity
- 40
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. - Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Rolf Poulsen (4-75726f69437064776b316e7831676e)
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