Dynamic Optimization Methods with Applications
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Exams; Lecture Notes; Problem Sets
- Before you start: The prerequisites for this course are 14.06 Advanced Macroeconomics or permission of the instructor.
MIT OpenCourseWare details
- As taught in: Fall 2009
- Department: Economics
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Graduate course on dynamic programming and optimal control: the principle of optimality, Euler equations, stochastic models and the maximum principle.
How should someone act today knowing every choice shapes tomorrow’s options? This graduate economics class gives a general command of the tools for such problems, first in discrete time with dynamic programming, then with uncertainty, then in continuous time through optimal control. Economic examples run through it, including one problem set on pricing iPhones.
What You Will Achieve
- Apply the principle of optimality and Euler equations
- Analyze deterministic and stochastic dynamics
- Use the maximum principle in continuous time
- Assess saddle-path stability
Program Overview
Discrete Time: Deterministic Models
Seven sessions build the core theory.
- Vector spaces
- The principle of optimality
- Concavity and differentiability of the value function
- Euler equations
Discrete Time: Stochastic Models
Two sessions add uncertainty.
- Stochastic dynamic programming
- Stochastic Euler equations
- Stochastic dynamics
Continuous Time
The last sessions change the setting.
- Calculus of variations
- The maximum principle
- Discounted infinite-horizon optimal control
- Saddle-path stability
Course Completion
Job Outlook
These methods underpin macroeconomic research, and they also apply in quantitative finance and operations research.
Good for: Economics doctoral students, and quantitative readers who want dynamic optimization taught with economic problems.
Keep in mind: From fall 2009, with lecture notes that stop at lecture 10 of 12, so continuous time is thin. The two required books are separate, and no solutions are listed for the problem sets or final.
Bottom line: A compact, tool-focused treatment that is well worth working through alongside its two required books.
Frequently Asked Questions
Which books are required?
Recursive Methods in Economic Dynamics by Stokey and Lucas with Prescott, and Introduction to Modern Economic Growth by Acemoglu. Three others are recommended.
What was on the final exam?
It ran two hours, with short problems and two longer ones, about burglars and about reaching the center in continuous time.
Does it need numerical work?
The syllabus says the problem sets cover numerical methods related to the lectures, alongside theory topics such as contraction mapping and Banach spaces.
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