Department of Mathematics

Stochastic Optimal Control

Please note that this page is old.
Check in the VVZ for a current information.
Instructors: Prof. Dr. H. Mete Soner and Albert Altarovici Lectures: Thursday 13-15 HG E 1.2

First Lecture: Thursday, February 20, 2014

Examination and ECTS Points: Session examination, oral 20 minutes. 4 ECTS Points.


The goals of the course are to:

  1. achieve a deep understanding of the dynamic programming approach to optimal control;
  2. distinguish several classes of important optimal control problems and realize their solutions;
  3. be able to use these models in engineering and economic modelling.


Basic knowledge of Brownian motion, stochastic differential equations and probability theory is needed.


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 including:

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


We will follow:

Lecture notes will also be provided during the course.

Tentative Schedule

Date Topics
February 20 Deterministic optimal control; Linear Quadratic regulator; Dynamic Programming.
February 27 Minimal time problem. General Structure of an optimal control problem. Discussion
of Dynamic Programming.
March 6 Optimal investment and consumption problem of Merton; infinite horizon problem, explicit solution,
verification theorem, optimal wealth process; finite horizon, pure investment problem.
March 13 A discrete deterministic game and its continuous time limit.
March 20 Stochastic target problems; time evaluation of reachability sets and a stochastic representation for geometric flows.
March 27 Finite fuel problem; general structure of a singular control problem.
April 3 Optimal dividend policy.
April 10 Theoretical treatment of dynamic programming.
April 17 Dynamic programming equation; viscosity solutions
May 8 Utility maximization under transaction costs.
May 15 Utility maximization under transaction costs - continued.
May 22 Concluding remarks and examples; classification of different control problems

Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne graphische Elemente dargestellt. Die Funktionalität der Website ist aber trotzdem gewährleistet. Wenn Sie diese Website regelmässig benutzen, empfehlen wir Ihnen, auf Ihrem Computer einen aktuellen Browser zu installieren. Weitere Informationen finden Sie auf
folgender Seite.

Important Note:
The content in this site is accessible to any browser or Internet device, however, some graphics will display correctly only in the newer versions of Netscape. To get the most out of our site we suggest you upgrade to a newer browser.
More information

© 2016 Mathematics Department | Imprint | Disclaimer | 21 May 2014