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Course Information

NMAK24000U Stochastic Processes in Continuous Time

Education

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

Content

This 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)

Learning Outcome

• 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 of 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

Literature

See course literature for details.

Recommended Academic Qualifications

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

Teaching and Learning Methods

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

Remarks

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

Workload

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

Exam

• Credit: 7.5 ECTS
• 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 Information

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

Study Board

• Study Board of Mathematics and Computer Science

Contracting Department

• Department of Mathematical Sciences

Contracting Faculty

• Faculty of Science

Course Coordinators

• Jesper Lund Pedersen

Timetable

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