Course Lecture notes:
the lecturer post on this page notes for each lecture. In order to access and download them you need to log-in with your University of Helsinki account . To log-in follow the link (KIRJAUDU) on the top-right of this page.
Exercises: see TEHTÄVÄT
Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty, "Nonlinear Programming: Theory and Algorithms" John Wiley & Sons, 2006. on-line access granted by the Helsinki University Library (follow the link given in the section INTERNET of the Library web-page).
Optimal control in general
1) Lawrence C. Evans, "An Introduction to Mathematical Optimal Control Theory Version 0.2", Lecture Notes Department of Mathematics University of California, Berkeley. Available for download from Evans's web page at Berkeley.
2) Daniel Liberzon, "Calculus of Variations and Optimal Control Theory. A Concise Introduction", Princeton University Press 2012
Stochastic Differential Equations, Stochastic Optimal Control and finance applications
1) Björk, Tomas, "Arbitrage theory in continuous time", Oxford University Press 2009. 3rd ed
on-line access grantrd by the Helsinki University Library
2) Ramon van Handel, "ACM 217: Stochastic Calculus and Stochastic Control" (Caltech, Spring 2007).
Available for download from van Handel's web page at Princeton University
Exercise set 01. Non-linear programming
Exercise set 02. Optimal deterministic control
Exercise set 03. Stochastic differential equations
Exercise set 04: Quadratic regulator
Master's Programme in Mathematics and Statistics is responsible for the course.
The course belongs to the Mathematics and Applied mathematics module.
The course is available to students from other degree programmes.
Basic notions of probability theory and stochastic calculus.
Elementary overview of optimal control theory
Recommended time/stage of studies for completion: 1. or 2. year
Term/teaching period when the course will be offered: varying
Deterministic and stochastic control. Dynamic programming theory. Hamilton-Jacobi-Bellman equation. Filtering theory. Optimal investment with partial information..
Exam and excercises, Course will be graded with grades 1-5
Exam, other methods will be described later