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Conditional expectation, martingales and stochastic integrals in discrete time, stopping times, Girsanov Theorem.
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Martingales in continuous time, Brownian motion, Ito integral and Ito Lemma.
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Martingale representation Theorem, stochastic differential equations, Ito diffusions, Kolmogorov equations, Feynman-Kac formula, stopping times and optional stopping.
SF2971 Martingales and Stochastic Integrals 7.5 credits
Information per course offering
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
- [object Object]
- Schedule
- Schedule is not published
Contact
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–)Content and learning outcomes
Course contents
Intended learning outcomes
After passing the course, the students should be able to
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formulate and explain central definitions and theorems within the theory of martingales and stochastic integrals;
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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
Equipment
Literature
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
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
Opportunity to raise an approved grade via renewed examination
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.