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FSF3951 Optimal Control and Filtering 5.0 credits

Administer About course

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3951 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Optimal control. Dynamic programming and the HJB Equation, the Verification Theorem. The linear quadratic regulator. Optimal investment theory and the Merton fund separation theorems. The martingale approach to optimal investment problems.

  • Filtering. Nonlinear filtering and the Fujisaki-Kallianpur-Kunita equations. The Kalman and Wenham filters. Optimal control problems under partial observations. The partially observed linear quadratic regulator. Optimal investment under partial information.

  • Equilibrium models in economics. The simplest production and endowment equilibrium models in continuous time.

Intended learning outcomes

After completing the course the students are expected to

  • Explain the dynamic programming principle and its connection to partial differential equations Have a good understanding of the linear quadratic regulator

  • Outline the foundations of filtering theory including the Kalman filter, non-linear filtering and problems with partial information

  • Explain and motivate the use of equilibrium models in economics

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

Literature and preparations

Specific prerequisites

Masters degree in mathematics, or in computational mathematics or in computer science/engineering with at least 30 cu in mathematics and 20 cu in statistics.  

Completed courses SF2940 Probability theory and SF2852 Optimal control or equivalent

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

The literature consists of lecture notes which will be downloadable during the course.

Examination and completion

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

Grading scale

P, F

Examination

  • HEM1 - Home assignments, 5.0 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.

Other requirements for final grade

Masters degree in mathematics, or in computational mathematics or in computer science/engineering with at least 30 cu in mathematics and 20 cu in statistics.  

Completed courses SF2940 Probability theory and SF2852 Optimal control or equivalent.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Profile picture Henrik Hult

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

SCI/Mathematics

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

Contact

Henrik Hult (hult@kth.se)

Postgraduate course

Postgraduate courses at SCI/Mathematics