401-4938-14L  Stochastic Optimal Control

SemesterSpring Semester 2017
LecturersM. Soner
Periodicitytwo-yearly course
Language of instructionEnglish



Catalogue data

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

And lecture notes will be provided.
Prerequisites / NoticeBasic 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 credits4 credits
ExaminersM. Soner
Typesession examination
Language of examinationEnglish
Course attendance confirmation requiredNo
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkCourse webpage
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Courses

NumberTitleHoursLecturers
401-4938-14 VStochastic Optimal Control2 hrs
Thu13-15HG F 26.3 »
M. Soner

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterSelection: Financial and Insurance MathematicsWInformation
Computational Science and Engineering MasterSystems and ControlWInformation