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FSF3971 Optimal Stochastic Control and Backward Stochastic Differential Equations 7.5 credits

About course offering

For course offering

Spring 2024 Start 16 Jan 2024 programme students

Target group

PhD students only

Part of programme

No information inserted


P3 (3.0 hp), P4 (4.5 hp)


16 Jan 2024
3 Jun 2024

Pace of study


Form of study

Normal Daytime

Language of instruction


Course location

KTH Campus

Number of places

Places are not limited

Planned modular schedule


For course offering

Spring 2024 Start 16 Jan 2024 programme students

Application code



For course offering

Spring 2024 Start 16 Jan 2024 programme students


Boualem Djehiche (


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Course coordinator

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Headings with content from the Course syllabus FSF3971 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  1. Optimal control. Dynamic programming, the HJB Equation, the maximum principle
  2. Backward stochastic differential equations.
  3. Forward-backward stochastic differential equations. Duality.
  4. Mean-field type control
  5. Mean-field games
  6. Applications

Intended learning outcomes

After completing the course the students are expectedto

  • Explain the dynamic programming principle and its connection to partial differential equations

  • Have a good understanding of the maximum principle

  • Have a good understanding of backward stochastic differential equations.

  • Outline the foundations mean-field games and its relation to control and BSDEs

  • Explain and motivate the methods in different applications

  • Be able to solve problems and discuss research questions related to the theory. 

Literature and preparations

Specific prerequisites

A Master’s degree in mathematics, applied mathematics or related field including at least 30 ECTS in mathematics and SF3940 Probability. 

Recommended prerequisites

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The literature consists of a draft of the following book:

T. Basar, B. Djehiche and H. Tembine (2014-2017), Mean-Field-Type Game: Foundations and New Directions

Examination and completion

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

Grading scale

P, F


  • HEM1 - Home assignments, 3.5 credits, grading scale: P, F
  • TENM - Oral exam, 4.0 credits, grading scale: P, 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.

Homework and an oral exam.

Other requirements for final grade

Homework and an oral exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted


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

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

No information inserted


Boualem Djehiche (

Postgraduate course

Postgraduate courses at SCI/Mathematics