315201 Intertemporal Optimization in Economics and Business (V) (WiSe 2004/2005)

Dynamic optimization (or intertemporal optimization) plays a more and more important role in economics and business studies, since economic agents may consider not only what happens today but also what may happen in the future. A dynamic optimization problem poses the question of what is the optimal magnitude of a choice variable in each period of time within the planning period (discrete-time case) or at each point of time in a given time interval (continuous-time case). In this course, the techniques for optimization in intertemporal models -- discrete- or continuous-time, deterministic or stochastic -- will be introduced. Applications of these techniques in the field of economics and business will also be shown.

Content:

1. Introduction

Part I Discrete-time models

2. Deterministic models
2.1 Optimization priciples (Lagrange multiplicator, Bellman equation
Euler equation, Hamilitonian)
2.2 Pratice of Optimation (dynamic programming, Howard algorithm)
2.3 Examples on economics and business
2.4 linear quaratic dynamic programming and Kalman Filter
3. Stochastic models
3.1 optimization priciples
3.2 examples
4. Numerical implementation
4.1 computational alogorithm
4.2 approximation methods
4.3 numerical performance

Part II Continuous-time models

5. Calculus of variation
6. Optimal control theory

Bibliography

• Carter, M., "Foundations of mathematical economics" (2001)
• Chiang, A.C., ?Elements of dynamic optimization? (1992)
• Judd, K.L., "Numerical methods in Economics"(1998)
• Kamin, M.L. and Schwartz, N.L., "Dynamic Optimization" (1991)
• Sargent, T.M., "Recursive macroeconomic theory" (2000)
• Stokey, N.L. and Lucas, R.E., Jr., "Recursive methods in economic dynamics" (1989, 1996)