NMAA05113U Continuous Time Finance (FinKont)

Volume 2023/2024

MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics



  • Stochastic integrals and Ito formula
  • Stochastic differential equations
  • Arbitrage
  • Complet markets
  • Martingale methods in finalcial mathematics
Learning Outcome

Ito calculus, stochastic differential equation and methods applied in continuous time financial models.

At the end of the course, the students are expected to be able to

  • Apply theorems on stochastic integrals and stochastic differential equations, including theorems such as: Ito's formula, Feynman-Kac representations, martingale representations, Girsanov's theorem.
  • Determine arbitrage free prices of financial claims including determining partial differential equations for price functions.
  • Deduce if a diffusion model for the market is arbitrage free and if it is complete and to be familiar with the 1st and 2nd fundamental theorems of asset pricing including the determination of martingale measures.
  • Apply concepts for portfolios including self financing and replicating.
  • Apply the theory to determine the Black-Scholes price for a call option.


To provide operational qualifications and insight in modern financial methods.

Example of course litterature:

Thomas bjork: "Arbitrage Theory in Continuous Time"

Sandsynlighedsteori (Sand) - alternatively Mål- og integralteori (MI) from previous years.
Either Stochastic Processes 2 or Advanced Probability Theory 1 (VidSand1).
Either Finansiering 1 (Fin1), Grundlæggende livsforsikringsmatematik 1 (Liv1), or similar.

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 154
  • Theory exercises
  • 21
  • Exam
  • 3
  • Total
  • 206
Continuous feedback during the course of the semester

Upon active participation in  exercise classes, teaching assistant will provide feedback

7,5 ECTS
Type of assessment
Written examination, 3 hours
Type of assessment details
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.

30 minutes oral exam without preparation time and no aids, with several internal examiners.

Criteria for exam assesment

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