SF2971 Martingales and Stochastic Integrals 7.5 credits

Martingaler och stokastiska integraler

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Course information

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.

Course Disposition

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Literature and preparations

Specific prerequisites *

SF2940 Probability theory.

Recommended prerequisites

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Equipment

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Literature

Djehiche Boualem: Stochastic Calculus, An Introduction with Applications. Compendium from KTH.

Examination and completion

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.

Other requirements for final grade *

Written examination (7,5 university credits)

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

Thomas Önskog

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2971

Offered by

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

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Contact

Kevin Schnelli (schnelli@kth.se)

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.