Program Overview

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Program Details

Course Overview

The course examines mathematical concepts for stochastic calculus, including:

• Introduction to continuous time stochastic processes
• Definition and properties of Brownian motion
• Semimartingales
• Stochastic integration
• Itô (change of variable) formula
• Theorems for applications (e.g., Girsanov’s theorem)

Education

This course is part of the following programs:

• MSc Programme in Mathematics-Economics
• MSc Programme in Mathematics
• MSc Programme in Statistics
• MSc Programme in Mathematics with a minor subject

Learning Outcomes

Upon completion, students will have:

Knowledge:

• Continuous time stochastic processes
• Stochastic integrals
• Itô formula and applications
• Continuous semimartingales
• Stochastic differential equations

Skills:

• Ability to explain central concepts of continuous time stochastic processes
• Apply results from stochastic integration
• Apply Ito's formula
• Apply theorems from stochastic calculus such as Girsanov's theorem
• Describe properties of stochastic differential equations

Competencies:

• Ability to discuss and apply central methods and results from stochastic calculus
• Evaluate models based on stochastic integrals

Teaching and Learning Methods

The course consists of:

• 4 hours of lectures per week for 7 weeks
• 2 hours of exercises per week for 7 weeks

Literature

Course literature is available on Absalon.

Recommended Prerequisites

• Sandsynlighedsteori 2 (Sand 2)
• Academic qualifications equivalent to a BSc degree are recommended

Remarks

This course is equivalent to the first seven weeks of NMAK24001U Mathematical Finance.

Exam Details

• Type of assessment: Oral examination, 30 minutes (no preparation)
• Aid: No aids allowed
• Marking scale: 7-point grading scale
• Censorship form: No external censorship
• Exam period: Several internal examiners
• Re-exam: 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.

Course Type and Workload

• Course type: Single subject courses (day)
• Workload:
  • Lectures: 28 hours
  • Preparation: 163 hours
  • Theory exercises: 14 hours
  • Exam: 1 hour
  • Total: 206 hours

Language and Course Details

• Language: English
• Course number: NMAK24000U
• ECTS: 7.5 ECTS
• Programme level: Full Degree Master
• Duration: 1 block
• Placement: Block 1
• Schedule group: A
• Capacity: No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.

Contracting Department and Faculty

• Contracting department: Department of Mathematical Sciences
• Contracting faculty: Faculty of Science

Course Coordinator

• Jesper Lund Pedersen

Timetable

• 25E-B1-1; Hold 01 Stoch; Stochastic Processes in Continuous Time

Study Board

• Study Board of Mathematics and Computer Science

University Details

• University of Copenhagen
• Nørregade 10
• 1165 København K

Final Notes

This course provides a comprehensive introduction to stochastic processes in continuous time, covering key concepts and theorems in stochastic calculus. It is designed for students in various master's programs and aims to equip them with the knowledge, skills, and competencies necessary for advanced studies and applications in mathematics and related fields.