MAT4720 – Stochastic analysis and stochastic differential equations

Course description

• Course content
• Learning outcome
• Admission
• Prerequisites

• Overlapping courses
• Teaching
• Examination
• Evaluation

Course content

The course gives a thorough basis for understanding stochastic dynamics and models. We will in particular study Brownian motion and martingales, Ito’s stochastic calculus, stochastic integration and martingale representation theorems, Ito’s Formula. We will present stochastic dynamical models via stochastic differential equations and study existence and uniqueness of solutions, linear stochastic differential equations, theory for diffusion processes, Markov processes, Dynkin’s Formula, Girsanov’s Theorem. The course gives an introduction to the most common numerical methods for stochastic differential equations. 

Learning outcome

After completing the course you will:

• have a throrough understanding of stochastic methods that are inbetween mathematical analysis and probability theory;
• know how to use the fundamental tools in stochastic analysis;
• be familiar with numerical methods for stochastic differential equations;
• know how to use methods of stochastic analysis for modeling in different application areas like finance, industry, thecnology, biology, etc.

Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Prerequisites

Recommended previous knowledge

• MAT3400 - Lineær analyse med anvendelser / MAT4400 - Lineær analyse med anvendelser
• One of the following three courses will also give you an advantage, but it is not required to pass the course:
  STK-MAT3700/STK-MAT4700
  MAT2700 - Matematisk finans og investeringsteori
  STK4510 - Innføring i finansmatematiske metoder og teknikker

Overlapping courses

• 10 credits overlap with MAT9720 – Stochastic analysis and stochastic differential equations
• 8 credits overlap with MAT4701 – Stochastic analysis with applications (continued)
• 4 credits overlap with STK4510 – Introduction to methods and techniques in financial mathematics (discontinued)

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

4 hours of lectures/exercises every week throughout the semester.

Examination

1 mandatory assignment.

Final written examination.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

• Explanation of grades and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.