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SF2971 Martingales and Stochastic Integrals 7.5 credits

Information per course offering

Termin

Information for Spring 2025 TTMAM m.fl. programme students

Course location

KTH Campus

Duration
14 Jan 2025 - 16 Mar 2025
Periods
P3 (7.5 hp)
Pace of study

50%

Application code

61209

Form of study

Normal Daytime

Language of instruction

English

Course memo
Course memo is not published
Number of places

Places are not limited

Target group

Elective for all programmes as long as it can be included in your programme.

Planned modular schedule
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Schedule
Schedule is not published

Contact

Examiner
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Course coordinator
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Teachers
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Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus SF2971 (Spring 2022–)
Headings with content from the Course syllabus SF2971 (Spring 2022–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Conditional expectation, martingales and stochastic integrals in discrete time, stopping times, Girsanov Theorem.

  • Martingales in continuous time, Brownian motion, Ito integral and Ito Lemma.

  • Martingale representation Theorem, stochastic differential equations, Ito diffusions, Kolmogorov equations, Feynman-Kac formula, stopping times and optional stopping.

Intended learning outcomes

After passing the course, the students should be able to

  • formulate and explain central definitions and theorems within the theory of martingales and stochastic integrals;

  • solve basic problems within the theory of martingales and stochastic integrals, and apply its methods to stochastic processes.

Literature and preparations

Specific prerequisites

  • English B / English 6
  • Completed advanced course in probability theory (SF2940 or equivalent)

Recommended prerequisites

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Equipment

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Literature

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Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F

Examination

  • TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

Mathematics

Education cycle

Second cycle

Add-on studies

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