NMAK20000U Changed: Polynomial Utility Optimization

Volume 2020/2021

MSc Programme in Actuarial Mathematics


Selection of topics related to dynamic optimization with respect to investment of capital in a financial market. Polynomial utility functions and how they can be used to approximate non-polynomial utility functions are central topics.

Learning Outcome

At the end of the course the student is expected to have:


  • Knowledge about optimization of investment strategies with respect to a given utility function.


  • Skills to formulate practical investment problems in a theoretical framework.
  • Skills to present key aspects of the topics covered in the course, and discuss the discrepancies between real-world applications and theoretical models.

Competences in:

  • Structuring optimization problems into control processes and objective functions.
  • Using polynomial utility functions to approximate the optimal control of a given non-polynomial utility function.
  • Understanding how divergence of polynomials affects the optimal control, and how undesired properties of polynomial utility functions can be deminished.
  • Having an overview over what types of problems lead to what type of solutions.
  • Being able to derive and interpret the life-cycle nature of the optimal control processes.
Continuous Time Finance (FinKont).
Academic qualifications equivalent to a BSc degree in Actuarial Mathematics is recommended.
Lectures, 5 per week for 7 weeks. In addition to this, a total of 4 hours of exercise classes where the students can work on their mandatory assignment.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 166
  • Theory exercises
  • 4
  • Exam
  • 1
  • Total
  • 206
Continuous feedback during the course of the semester
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Oral examination, 30 minutes.
Oral exam without preparation.
Exam registration requirements

To participate in the exam, the mandatory assignment must be passed.

All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal censor.

Same as the ordinary exam. If the homework set is not approved before the ordinary exam, the non-approved set must be approved no later than three weeks before the beginning of the re-exam week. 

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.