# Continuous Time Finance (FinKont)

### Course content

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

MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics

Learning outcome

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

Skills:
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.

Competencies:
To provide operational qualifications and insight in modern financial methods.

4 hours of lectures and 3 hours of exercises per week for 7 weeks.

Example of course litterature:

Thomas bjork: "Arbitrage Theory in Continuous Time"

Mål og integralteori (MI), Stochastic Processes 2/Advanced Probability Theory 1 (VidSand1) and either FInansiering 1 (Fin1), Grundlæggende livsforsikringsmatematik 1 (Liv1), or similar

ECTS
7,5 ECTS
Type of assessment
Written examination, 3 hours
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Aid
All aids allowed
Marking scale
Censorship form
No external censorship
One internal examiner.
##### Criteria for exam assessment

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

Single subject courses (day)

• Category
• Hours
• Lectures
• 28
• Preparation
• 154
• Theory exercises
• 21
• Exam
• 3
• English
• 206