[Forside] [Hovedområder] [Perioder] [Udannelser] [Alle kurser på en side]
LEARNING OBJECTIVES:
Having completed this course, the student will be able to
· reflect on advanced dynamic models
· reflect on solution techniques in discrete and continuous-time
· theorize on dynamic stochastic optimal control problems
· reflect on models of optimal saving under uncertainty
· relate basic concepts of probability theory
· apply numeric solution techniques to continuous-time macroeconomic models.
COURSE DESCRIPTION:
This course provides a toolbox for solving dynamic
optimization problems in (stochastic) economic models. In particular, we review most of the mathematical tools required for typical graduate courses in economics including the calculus of variations, optimal control theory, and dynamic programming. We then thoroughly study models in discrete and continuous time under uncertainty. Throughout the course, the optimization problems are illustrated using various examples. A particular focus will be on formulating and solving dynamic models in modern macroeconomics.
COURSE SUBJECT AREAS:
Part I: Basic mathematical
(i) Topics in integration and differential equations (rules of transformation,
differentiation, solution techniques)
(ii) Qualitative theory (phase plane analysis, stability for nonlinear systems)
(iii) Calculus of variation (Euler equation, transversality condition)
(iv) Control theory (maximum principle, variable final time, infinite horizon)
(v) Dynamic programming (Bellman equation, envelope theorem, multiple
variables)
(vi) `Dynamic macroeconomic modeling with Matlab' by Timo Trimborn (University of Hannover) on numerical solutions to continuous-time dynamic
macroeconomic models (DGPE course, March 5-6 2009).
(vii) Basic concepts of probability theory (probability model, stochastic processes, functions of random variables)
Part II: Stochastic models in discrete time
(i) Topics in difference equations (basic concepts, solution techniques)
(ii) Stochastic difference equations (state-space representation, indeterminacy)
(iii) Discrete-time optimization (dynamic programming, stochastic control iv) Overlapping-generations, multi-period models (real-business-cycles)
(v) Asset pricing in a closed economy
Part III: Stochastic models in continuous time
(i) Stochastic differential equations and rules for differentials (Itô's formula)
(ii) Solution techniques (Option pricing)
(iii) Stochastic dynamic control problems (Bellman equation)
(iv) Optimal saving under uncertainty (Poisson uncertainty, Brownian motions)
(v) Matching models, capital asset pricing, real-business-cycles.
REQUIRED COURSES:
Macro 1 (7005).
LECTURER:
Olaf Posch.
TEACHING METHOD:
Lectures and take-home problem sets.
LITERATURE:
· Jensen, Bjarne S. and Tapio Palokangas, Stochastic Economic Analysis, Copenhagen Business School Press, 2007
· Ljungqvist, Lars and Thomas Sargent, Recursive macroeconomic theory, MIT Press, 2004
· Spanos, A., Probability Theory and Statistical Inference, Cambridge Univ. Press, 1999
· Sydsaeter, Knut., Peter Hammond, Atle Seierstad, and Arne Strøm, Further Mathematics for Economic Analysis, Prentice Hall, 2005, chapters 4 - 12 (approx. 290 p.))
· Stokey, Nancy L. and Robert E. Lucas Jr. and Edward C. Prescott, Recursive Methods in Economic Dynamics, Harvard Univ. Press, 1989
· Wälde, Klaus, Applied Intertemporal Optimization, Lecture Notes, 2007
Lecture notes: approx. 120 pages.
In total approx. 410 pages.
FORM OF ASSESSMENT:
7-point grading scale (Take-home assignment)
EXAMINATION AIDS ALLOWED:
All
