Print syllabusStochastic control theory
General data
| Course ID: | 1000-1M23TOS |
| Erasmus code / ISCED: |
11.1
|
| Course title: | Stochastic control theory |
| Name in Polish: | Teoria sterowania stochastycznego |
| Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
| Course groups: |
Elective courses for 2nd stage studies in Mathematics |
| ECTS credit allocation (and other scores): |
6.00
|
| Language: | English |
| Main fields of studies for MISMaP: | mathematics |
| Type of course: | elective monographs |
| Requirements: | Probability Theory II 1000-135RP2 |
| Prerequisites: | Probability Theory II 1000-135RP2 |
| Prerequisites (description): | Working knowledge of discrete-time processes. Markov processes, martingales, stopping times. |
| Mode: | Classroom |
| Short description: |
The course is the introduction to the stochastic control theory. The material will contain numerous examples and applications in economy, reliability theory and analysis. Most of the considerations will be carried out for the discrete-time processes. |
| Full description: |
The course is devoted to the survey of basic tools of the stochastic control theory, the considerations will be illustrated by numerous examples and applications. Most of the material will be discussed in the context of discrete-time processes. In particular, the presentation will cover the maximum principle, the Hamilton-Jacobi-Bellman equation and dynamic programming. 1. Introduction. Selected examples in the deterministic control theory. (2 lectures) 2. Dynamic programming, examples (2 lectures). 3. Maximum principle. The Hamilton-Jacobi-Bellman equation (3 lectures). 4. A distinguished case: optimal stopping theory (4 lectures). 5. Elements of optimal control theory for continuous-time processes (3-4 lectures). |
| Bibliography: |
1. P. D. Bertsekas, S. E. Shreve, Stochastic optimal control. The discrete time case. Mathematics in Science and Engineering, 139. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. 2. A. Seierstad, Stochastic control in discrete and continuous time. Springer, New York, 2009. 3. Up-to-date lecture notes will be available at https://www.mimuw.edu.pl/~ados/teaching/index.html |
| Learning outcomes: |
Knowledge and skills. A Student: 1. Gives examples of deterministic control problems and formulates the general methods of the investigation. 2. Knows the concept of dynamic programming and applies it in the study of the problems of optimal control theory. 3. Formulates the maximum principle and knows its connections to the Hamilton-Jacobi-Bellman equation. 4. Formulates and solves basic problems in optimal stopping theory, both for the finite and infinite horizon. 5. Knows basic facts concerning the optimal control theory for continuous-time processes. 6. Knows the up-to-date achievements of the theory, enabling the individual research in the area. Social competence. A Student 1. Understands the role of the control theory as a tool for the investigation of certain mechanisms of Nature |
| Assessment methods and assessment criteria: |
Two written homework assignments during the semester and a final oral exam. |
Classes in period "Winter semester 2023/24" (past)
| Time span: | 2023-10-01 - 2024-01-28 |
 
MO TU W TH WYK-MON
CW
FR |
| Type of class: |
Classes, 30 hours
Monographic lecture, 30 hours
|
|
| Coordinators: | Adam Osękowski | |
| Group instructors: | Adam Osękowski | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Copyright by University of Warsaw.
