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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
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About course offering
For course offering
Spring 2025 TTMAM m.fl. programme students
Target group
Elective for all programmes as long as it can be included in your programme.
Part of programme
Master's Programme, Applied and Computational Mathematics, åk 1, Optional
Master's Programme, Applied and Computational Mathematics, åk 1, FMIA, Conditionally Elective
Master's Programme, Industrial Engineering and Management, åk 1, FMIB, Conditionally Elective
Periods
P3 (7.5 hp)Duration
Pace of study
50%
Form of study
Normal Daytime
Language of instruction
English
Course location
KTH Campus
Number of places
Places are not limited
Planned modular schedule
Course memo
Course memo is not publishedSchedule
Schedule is not publishedApplication
For course offering
Spring 2025 TTMAM m.fl. programme students
Application code
61209
Contact
For course offering
Spring 2025 TTMAM m.fl. programme students
Contact
Boualem Djehiche (boualem@kth.se)
Examiner
No information insertedCourse coordinator
No information insertedTeachers
No information insertedContent 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.