Stochastic Dynamic Programming

Course objective.

This course provides a toolbox for solving optimization problems in stochastic dynamic models with a focus on applications in macroeconomics and finance. In particular, we briefly review optimal control theory and dynamic programming. Wethen thoroughly study models in discrete time and continuous time under uncertainty. Theoptimization problems are illustrated by various examples.

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 (NK) 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 (Itô’s formula)

(ii) An example: Merton’s model of growth under uncertainty

(iii) Stochastic dynamic control problems (Bellman equation)

(iv) Examples:

(a) Continuous-time RBC (under Gaussian and/or Poisson uncertainty)

(b) Continuous-time NK Model

(c) The matching approach to unemployment

(d) Endogenous growth cycles

Reading list

Sydsæter, Hammond, Seierstad, and Strøm (2008, chap. 4-12, 290 pages),
Chang (2004, chap. 4, 50 pages), Wälde (2012); a couple of research articles will be 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.

Wälde, K. (2012): Applied Intertemporal Optimization. Know Thyself Acad. Publishers,
http://www.waelde.com/pdf/AIO.pdf.