202325901-economics.pdf - DYNAMIC DECISION MODELS ALP E...

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DYNAMIC DECISION MODELS ALP E. ATAKAN 1. Course Description 1.1. Overview. The goal of this course is familiarize students with dynamic optimization techniques for both discrete and continuous time stochastic problems. In particular the course will present results in discrete time dynamic programming and continuous time optimal control. 1.2. Texts. I recommend that you purchase Ross (1983) and Stokey, Lucas, and Prescott (1989). 1.3. Grading. The grade will be based on a midterm exam (February 4), a final exam and homework assignments. 1.4. Office Hours. Wednesdays 1 - 2:30. 2. Course Outline (1) Introduction and warm-up (a) Finite horizon dynamic programming. Examples: Ross (1983), ch. 1 Reading: Ross (1983), ch. 1 (2) Mathematical preliminaries (a) Continuity, compactness and convexity of correspondences (b) Berge’s theorem of the maximum under convexity (c) Contraction mapping theorem, Blackwell’s sufficient conditions for a contrac- tion Reading: Stokey, Lucas, and Prescott (1989), ch. 3 (3) Deterministic and countable state dynamic programming with discounting (a) Bellman’s functional equation and the principle of optimality (b) Value iteration and policy improvement (c) Linear programming solution (d) Contraction mapping theorem, Blackwell’s sufficient conditions for a contrac- tion Ross (1983), Ch. 2 1
2 ALP E. ATAKAN (e) Some examples: - The classical one sector growth model - A consumption-savings problem - A seller with unknown demand - Weitzman (1979) or Pandora’s problem - Multi-armed bandit problems, Ross (1983), ch.7; or Whittle (1980)

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