# Graduate School UHH: Stochastic Dynamic Programming

Institution: Graduate School at Faculty of Economics and Social Sciences – University of Hamburg

Lecturer: Prof. Dr. Olaf Posch

Schedule:
Friday, 16.10.15 – Friday, 18.12.15
weekly 09:00 – 12:00

Place: University of Hamburg, Von Melle Park 9

Registration: You can register for the course until 15.10.2015 (13:00) via Geventis.

Course description:
Course objective. This course provides a toolbox for solving dynamic optimization problems in stochastic macroeconomic models. In particular, we briefly review optimal control theory and dynamic programming. We then thoroughly study models in discrete time and continuous time under uncertainty. The optimization problems are illustrated by various examples of dynamic stochastic general equilibrium (DSGE) models.

Course outline.
Part I: Basic mathematical tools
(i) Control theory (maximum principle, Euler equation, transversality condition)
(ii) Dynamic programming (Bellman equation, envelope theorem, multiple variables)
(iii) An example: Lucas’ model of endogenous growth
Part II: Stochastic models in discrete time
(i) Stochastic control problems
(ii) Analyzing equilibrium dynamics
(iii) An example: Real business cycles (RBC)
(iv) An example: A new Keynesian model for monetary analysis
(v) Solving dynamic equilibrium models with Dynare
Part III: Stochastic models in continuous time
(i) Stochastic differential equations and rules for differentials (Itˆo’s formula)
(ii) An example: Merton’s model of growth under uncertainty
(iii) Stochastic dynamic control problems (Bellman equation)
(iv) An example: Continuous-time RBC (under Gaussian and/or Poisson uncertainty)
(v) An example: The matching approach to unemployment
(vi) An example: Walde’s model of endogenous growth cycles

Reading list. Sydsæter, Hammond, Seierstad, and Strøm (2008, chap. 4-12, 290 pages), Chang (2004, chap. 4, 50 pages), Walde (2012), various articles suggested as complementary material during the course

References
Chang, F.-R. (2004): Stochastic optimization in continuous time. Cambridge Univ. Press.
Sydsæter, K., P. Hammond, A. Seierstad, and A. Strøm (2008): Further Mathematics for Economic Analysis. Prentice Hall.
Walde, K. (2012): Applied Intertemporal Optimization. Lecture Notes, Gutenberg University Mainz, http://www.waelde.com/aio.

Further information