14.451 | Fall 2009 | Graduate
Dynamic Optimization Methods with Applications


A list of topics by session is given in the calendar below.

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session


This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.


The prerequisites for this course are 14.06 Advanced Macroeconomics or permission of the instructor.



Stokey, Nancy L., and Robert E. Lucas, Jr., with Edward C. Prescott. Recursive Methods in Economic Dynamics. Cambridge, MA: Harvard University Press, 1989. ISBN: 9780674750968.

Acemoglu, Daron. Introduction to Modern Economic Growth. Princeton, NJ: Princeton University Press, 2008. ISBN: 9780691132921.

Chiang, Alpha C. Elements of Dynamic Optimization. Long Grove, IL: Waveland Press, 1999. ISBN: 9781577660965.

Luenberger, David. Optimization by Vector Space Methods. New York, NY: Wiley-Interscience, 1997. ISBN: 9780471181170. First published in 1969 by John Wiley and Sons, Inc.

Kamien, Morton I., and Nancy L. Schwartz. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. 2nd ed. San Diego, CA: Elsevier, 1991. ISBN: 9780444016096.

Course Requirements

There will be several problem sets and a final exam. The problem sets will cover numerical methods related to lecture material.


Problem sets 40%
Final exam 60%


1-7 Discrete time: deterministic models Problem set 1 out in Ses #1, problem set 1 due in Ses #4, problem set 2 out in Ses #5, and problem set 2 due in Ses #7
8-9 Discrete time: stochastic models Problem set 3 out in Ses #8
10-12 Continuous time Problem set 3 due in Ses #10, problem set 4 out in Ses #11
  Final exam Problem set 4 due
Course Info
As Taught In
Fall 2009