ARE 263


Methods of Dynamic Analysis and Control

Fall Semester, 2012

Department of Agricultural and Resource Economics   
University of California at Berkeley

Syllabus (including some Readings)

Time and Location:

We meet in 14 Haviland Tuesdays and Thursdays 12:40-2:00 pm. There will be no class on Thursday, September 6th.

Course Requirements

Problem sets (approximately 6-8 of these). You can work on problem sets in groups no larger than 3. In case you work in a group, please hand in your own copy and state the names of your collaborators on the front page.

Final exam.

Instructors

Larry Karp:  330 Giannini Hall (karp@berkeley.edu); office hours:  Wednesday, 4-5 p.m., or by appointment

Christian Traeger322 Giannini Hall (traeger@berkeley.edu); office hours:  Wednesday, 2-3 p.m., or by appointment.


List of Topics

  1. Basics of Dynamic Optimization  (Figure , Some solutions for PS#1)
  2. A Climate Change Application  (Figure , Original paper by Golosov et al.)
  3. Taxes Vs Quota and the Linear-Quadratic Problem  (Figure)
  4. Learning  (Figures 1  Figures 2)
  5. Numerical Methods and some Integrated Assessment of Climate Change  (Matlab Code)
  6. Ordinary Differential Equations  (Figures)
  7. Pontryagin's Maximum Principle
  8. Dynamic Programming in Continuous Time
  9. Continuous Time Stochastics  (Problem Set 5)
  10. Event Uncertainty
  11. Non-Convex Optimization
  12. Discounting
  13. Dynamic Games and Hyperbolic Discounting
  14. Disentangled Risk Aversion
  15. Ambiguity Aversion

Summary of Lectures (updated after each lecture)

 

******************************************************************

 

Material below this line stems from the 2010 lecture and serves only as an approximate lecture outlook.

Summary of lectures (Final)

 

Chapter 1 (Basics of dynamic optimization) 9/9/2010

Figures for Chapter 1

Technical appendix

Chapter 2 (Taxes Vs Quota and the LQ problem) 9/15/2010

Figures for Chapter 2

Chapter 3 (Reactions to risk) 9/15/2010

Figures for Chapter 3

Chapter 4 (Anticipated learning, 2 periods) 9/15/2010

Figures for Chapter 4

Chapter 5 (Anticipated learning, multiperiod) 9/15/2010

Figures for Chapter 5

Chapter 6 (Basics of continuous time dynamics) 10/11/2010

Figures for Chapter 6

Chapter 7 (The Maximum Principle) 10/05/2010

Chapter 8 (DPE in continous time) 11/01/2010

Chapter 9 (Event uncertainty) 10/05/2010

Chapter 10 (Stochastic Control) 11/02/2010

Chapter 11 (Nonconvex Control Problems) 11/03/2010

Chapter 12 (Discounting) 11/08/2010
       Notes 1 of 3
       Notes 2 of 3
       Notes 3 of 3    11/16/2010

Chapter 13 (Time Inconsistency) 11/18/2010

Chapter 14 (Disentangling Risk Aversion from Intertemporal Substitutability)
                   11/29/2010

Chapter 15 (Ambiguity) 12/01/2010

 

Problem sets and solutions

Problem set # 1, due September 7:
Problems at end of Chapter 1 (first set of lecture notes).  Your suggestions and corrections for Chapter 1 of the notes.  (Please be specific.  The purpose of this part of the assignment (for you) is to give you an incentive to read the notes caredfully, and (for us) to help us improve the notes.

 

Problem set #2, due September 16:
Problem at end of Chapter 2 (the chapter on the linear-quadratic problem).  The second and third problems are based on

P vs Q mulitiplicative

P vs Q additive

 

Problem set # 3: Due November 2

Model description and problem

Matlab code

 

Problem set # 4:  Due November 11.  The files Predator Prey and Prey are matlab files that you can use to answer the first question in the problem set.  To answer one problem you will probably have to read the Appendix "units".

Problem set

Predator Prey

Prey

Appendix: units

 

Problem set # 5: Due November 25. The problem asks you to solve a simple linear quadratic stochastic control problem in continuous time, similar to the one we analyzed in class.

Problem set

 

 

Old exams:

exam 2001     exam 2002  exam 2003   exam 2004 and key  exam 2006 and key