ECN 218

 SEMINAR IN MATHEMATICAL ECONOMICS: STOCHASTIC DYNAMIC PROGRAMMING
 
Spring 2008
 
Professor  Fred  Chen  (105 Carswell Hall chenfh@wfu.edu)
Professor Miaohua Jiang (340 Manchester Hall jiangm@wfu.edu)
 
TEXT 
 
Lecture Notes on Stochastic Dynamic Programming
 
COURSE MECHANICS 
 
Handouts and written assignments will be distributed regularly. 
Solutions to assignments should be written up and turned in 
on time. Late work will not be accepted. Your performance in the course will be evaluated on the 
basis of the quality of your contributions to class discussion 
and presentation (10 %), written assignments (30 %), a mid-term 
examination (30 %), and a final examination (30 %), 
 
OFFICE HOURS 
 
Chen   3:00 pm -4:30 pm T R and by appointment, 
  
Jiang 10:00 am - 11:00 am M W F and 2:00 pm - 3:00 pm M and by appointment
appointment
 
COURSE OUTLINE 
 
1.  Basic Concepts in Probability Theory
 
 Random variables, discrete and continuous probability space, 
conditional probability and independence, expected values, stochastic process
 
2. Backward Induction and Finite-Horizon Dynamic Programming
 
Principle of optimality, a gambling model, a
stock-option model, a sequential allocation model
 
3. Infinite-Horizon Discounted Dynamic Programming
 
Existence of an optimal policy, the optimality equation
(Bellman equation), method of successive approximations
 
 Economic examples
 
 a machine replacement model
 
 optimal extraction of a non-renewable resource
 
 optimal growth---the Brock-Mirman model
 
 optimal consumption, savings, and the Permanent Income Hypothesis
 
 optimal investment in R\&D
 
 optimal capital accumulation
 
 
4. Optimal Stopping and the Multi-Armed Bandit Problem
 
Economic examples
 
 job search and search unemployment
 
 sequential search for the lowest price
 
 the secretary problem
 
 the gold mining problem
 
 Pandora's problem\medskip
 
Midterm Examination Schedule: March 4 T (or 6 R), Evening, 2 hours
 
Final Examination Schedule: May 6 T 2:00 pm - 5:00 pm