Stochastic Optimal Control Spring 2017

Instructors

Lecturer: Prof. H. Mete Soner

• e-mail: hmsoner@ethz.ch;
• Office HG G 54.3;
• Office Hours: by appointment.

Coordinator: Matti Kiiski

• e-mail: matti.kiiski@math.ethz.ch;
• Office HG G 47.2;
• Office Hours: by appointment.

Course

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:

• Standard exit time problems;
• Finite and infinite horizon problems;
• Optimal stoping problems;
• Singular problems;
• Impulse control problems.

After the general theory is developed, it will be applied to several classical problems including:

• Linear quadratic regulator;
• Merton problem for optimal investment and consumption;
• Optimal dividend problem of (Jeanblanc and Shiryayev);
• Finite fuel problem;
• Backward Stochastic Differential Equations (if time permits).

Material

We will follow

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

Lectures

The lecture take place in HG F 26.3, Thursday 13-15. Tentative Schedule of Lectures:

• February 23. Deterministic optimal control; Linear Quadratic regulator; Dynamic Programming.
• March 2. Minimal time problem. General Structure of an optimal control problem. Discussion of Dynamic Programming.
• March 9. Optimal investment and consumption problem of Merton; infinite horizon problem, explicit solution, verification theorem, optimal wealth process; finite horizon, pure investment problem.
• March 16. Finite fuel problem; general structure of a singular control problem.
• March 23 (Lecture by Max Reppen). Optimal dividend policy.
• March 30. A discrete deterministic game and its continuous time limit.
• April 6. Stochastic target problems; time evaluation of reachability sets and a stochastic representation for geometric flows.
• April 13. Theoretical treatment of dynamic programming.
• April 20. Easter.
• April 27. No Class.
• May 4. Dynamic programming equation; viscosity solutions.
• May 11. Utility maximization under transaction costs.
• May 18. Utility maximization under transaction costs.
• June 1. Concluding remarks and examples; classification of different control problems.

Exam

There will be a 20 minutes long oral examination at the end of the semester.