401-4938-14L  Stochastic Optimal Control

Semester Spring Semester 2017
Lecturers M. Soner
Periodicity two-yearly course
Language of instruction English

Catalogue data

Abstract Dynamic programming approach to stochastic optimal control problems will be developed. In addition to the general theory, detailed analysis of several important control problems will be given.
Objective Goals are to achieve a deep understanding of

1. Dynamic programming approach to optimal control;
2. Several classes of important optimal control problems and their solutions.
3. To be able to use this models in engineering and economic modeling.
Content In this course, we develop the dynamic programming approach for the stochastic optimal control problems. The general approach will be described and several subclasses of problems will also be discussed in including:
1. Standard exit time problems;
2. Finite and infinite horizon problems;
3. Optimal stoping problems;
4. Singular problems;
5. Impulse control problems.

After the general theory is developed, it will be applied to several classical problems including:
1. Linear quadratic regulator;
2. Merton problem for optimal investment and consumption;
3. Optimal dividend problem of (Jeanblanc and Shiryayev);
4. Finite fuel problem;
5. Utility maximization with transaction costs;
6. A deterministic differential game related to geometric flows.

Textbook will be

Controlled Markov Processes and Viscosity Solutions, 2nd edition, (W.H. Fleming and H.M. Soner) Springer-Verlag, (2005).

And lecture notes will be provided.
Literature Controlled Markov Processes and Viscosity Solutions, 2nd edition, (W.H. Fleming and H.M. Soner) Springer-Verlag, (2005).

And lecture notes will be provided.
Prerequisites / Notice Basic knowledge of Brownian motion, stochastic differential equations and probability theory is needed.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits 4 credits
Examiners M. Soner
Type session examination
Language of examination English
Course attendance confirmation required No
Repetition The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination oral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Main link Course webpage
Only public learning materials are listed.


Number Title Hours Lecturers
401-4938-14 V Stochastic Optimal Control 2 hrs
Thu 13-15 HG F 26.3 »
M. Soner


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Offered in

Programme Section Type
Doctoral Department of Mathematics Graduate School W Information
Mathematics Master Selection: Financial and Insurance Mathematics W Information
Computational Science and Engineering Master Systems and Control W Information