Consumption-Investment Problems

Course content

We consider personal financial optimization in the course by looking at different consumption-investment problems. 

We formulate modern investor preferences and derive optimal consumption, investment and insurance strategies for different preferences, such as classical constant relative risk aversion, the inclusion of state dependency, and state versus risk preferences. 

The various problems are discussed, and the structures of solutions are understood as different patterns of consumption, investment, and insurance over the life cycle.


MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics

Learning outcome

Knowledge: About dynamic optimization problems concerning consumption, investment and insurance decision-making.

Competences: Confidence in formulation and solution of stochastic control problems. Insight into problems and corresponding solutions within personal finance optimization. Ability to read original papers in finance and actuarial journals. 

Skills: At the end of the course, the student is expected to be able to formalize, discuss and solve problems within personal financial optimization. The starting point is Merton's consumption-investment problem in continuous time and from there we generalise to state-dependent utility and applications of equilibrium theory.

4 hours of lectures per week for 7 weeks. The students get to see the course contents in regular lectures. Since the core content concern individual preferences and individual decision making, the students' preferences and decision making is discussed with the students during the lectures.

Continuous-Time Finance (e.g. the course FinKont) including Ito Calculus and pricing and hedging of contingent claims in diffusive markets. A Bachelors degree is recommended.

Continuous feedback during the course of the semester
Feedback by final exam (In addition to the grade)

Continuous feedback during the course of the semester is given during discussions about the students' preferences and decision making.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Type of assessment details
Without preparation time
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

As the ordinary exam

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
  • 28
  • Preparation
  • 177
  • Exam
  • 1
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 1
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Julie Søe   (2-79824f7c7083773d7a843d737a)
Saved on the 28-02-2023

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