Kaisa_2012_3_photo by Veikko Somerpuro

Course Topics :
i Non-linear programming
ii Optimal deterministic control
iii Optimal stochastic control
iv Some applications

Lecture notes content

Lecture 01: Unconstrained optimization
Lecture 02: Convexity
Lecture 03: Karush-Kuhn-Tucker conditions
Lecture 04: From non-linear programming to optimal deterministic control
Lecture 05: ODE's and optimal control
Lecture 06: Pontryagin's principle
Lecture 07: Hamilton-Jacobi-Bellman equation for deterministic optimal control
Lecture 08: Ito lemma and Wiener process (Brownian motion).
Lecture 09: Stochastic integrals and martingales.
Lecture 10: Stochastic differential equations and Stratonovich calculus.
Lecture 11: An overview of the relations between stochastic and partial differential equations
Lecture 12: Hamilton-Jacobi-Bellman equation for stochastic optimal control.
Lecture 13: Optimal stopping.
Lecture 14: Some financial applications

23.10.2017 klo 09:00 - 13.12.2017 klo 23:59


No lecture on Monday 20.11 and Wednesday 22.11
Lectures rescheduled for
Thursday 02.11 14-16 in C124
Thursday 09.11 14-16 in C124
Thursday 16.11 14-16 in C124
No lecture on Wednesday 13.12
Lecture rescheduled for
Thursday 07.12 14-16 in C124

Ma 30.10.2017
14:15 - 16:00
Ke 1.11.2017
12:15 - 14:00
To 2.11.2017
14:15 - 16:00
Ma 6.11.2017
14:15 - 16:00
Ke 8.11.2017
12:15 - 14:00
To 9.11.2017
14:15 - 16:00
Ma 13.11.2017
14:15 - 16:00
Ke 15.11.2017
12:15 - 14:00
To 16.11.2017
14:15 - 16:00
Ma 27.11.2017
14:15 - 16:00
Ke 29.11.2017
12:15 - 14:00
Ma 4.12.2017
14:15 - 16:00
To 7.12.2017
14:15 - 16:00
Ma 11.12.2017
14:15 - 16:00

Muu opetus

06.11. - 13.11.2017 Ma 12.15-14.00
27.11. - 11.12.2017 Ma 12.15-14.00
Paolo Muratore Ginanneschi
Opetuskieli: englanti


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

Nonlinear programming:
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


Optional course.

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