# WiSo-Graduate School UHH: Stochastic Dynamic Programming

Institution: Graduate School at Faculty of Business, Economics and Social Sciences – Universität Hamburg

Lecturer: Prof. Dr. Olaf Posch (WiSo-Fakultät, UHH)

Schedule: Freitags, 09:00 – 12:00 Uhr (ab 11.11.2016) wöchentlich

Place: Universität Hamburg, further information in Geventis

Registration: You can register for the course until 30.09.2016 (13 Uhr) via Geventis

Course description:
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

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.