Continuous Time Finance (FinKont)

Course content

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

MSc Programme in Actuarial 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.

Blended teaching and learning: 4 hours of video lectures per week for 7 weeks. Worksheets with exercises/problem solving will be provided for the students for in-depth engagement with the course material. There will be regular meetings with the lecturer for discussions of the course material and the exam.

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.

This course is only available to students enrolled in the MSc Programme in Actuarial Mathematics in the study year 2023/24 and earlier.


Upon active participation in meetings for discussions of the course material. 

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

Same 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.

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 163
  • Theory exercises
  • 14
  • Exam
  • 1
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 2
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Jesper Lund Pedersen   (6-716c7a776c794774687b6f35727c356b72)
Phone+ 45 35 32 07 75, office: 04.3.11
Saved on the 21-02-2024

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students