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.
FSF3951 Optimal Control and Filtering 5.0 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3951 (Spring 2019–)Headings with content from the Course syllabus FSF3951 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
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
Literature
The literature consists of lecture notes which will be downloadable during the course.
Examination and completion
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.
If the course is discontinued, students may request to be examined during the following two academic years.
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.
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.
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
Education cycle
Third cycle