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"

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.

Continuous feedback during the course

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

ECTS
7,5 ECTS
Type of assessment
Written examination, 3 hours
Type of assessment details
---
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

Kursusinformation

Language
English
Course number
NMAA05113U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 2
Schedulegroup
A
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
Contracting department
• Department of Mathematical Sciences
Contracting faculty
• Faculty of Science
Course Coordinator
• Jesper Lund Pedersen   (6-6f6a78756a77457266796d33707a336970)
Phone+ 45 35 32 07 75, office: 04.3.11
Saved on the 28-02-2022

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