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Lehrende: Prof. Dr. Olaf Posch
Veranstaltungsart:
Interaktive Lehrveranstaltung
Anzeige im Stundenplan:
Dynamic Optimization
Semesterwochenstunden:
3
Credits:
6,0
Unterrichtssprache:
Englisch
Min. | Max. Teilnehmerzahl:
- | 45
Kommentare/ Inhalte:
This course provides a toolbox for solving dynamic optimization problems in economic models. In particular, we review the mathematical tools required for courses in economics including calculus of variation, control theory, and dynamic programming. We then study models in continuous and discrete time. Throughout the course, the optimization problems are illustrated using various examples in economics. The course is designed to be accessible to anybody who has had a basic training in mathematical analysis of dynamic systems such as topics in difference and differential equations.
Dynamic Optimization:
- Basics in static optimization (local extreme points, equality constraints, inequality constraints, comparative statics)
- Calculus of variations (dynamic systems, variational problems, Euler equation, optimal savings problem, terminal conditions, phase diagrams)
- Control theory (control problems, maximum principle, adjoint variables, current value formulations, infinite horizon)
- Discrete-time optimization (dynamic programming, Euler equation, infinite horizon, maximum principle, multivariate optimization)
Attending this course allows students to strengthen their profile with a strong focus on methods in economics. It is highly recommended to students considering writing a thesis within dynamic economic theory such as economic growth, resources economics, climate systems and business cycle theorys above and/or interested in further studies in economics.
Lernziel:
After this course, the students are able to ...
- reflect on static optimization problems with equality and inequality constraints
- theorize on variational problems and control problems
- formulate and solve dynamic optimization problems in economics
- apply the maximum principle and the Euler equation
- apply control theory and dynamic programming solution techniques
- relate to concepts for finite and infinite horizon problems
Objective: Students develop their skills on theoretical mathematical concepts for solving dynamic optimization problems in economics.
Vorgehen:
- this course emphasizes economics not only to motivate a mathematical topic, but also to help acquire mathematical intuition
- focus on techniques particularly useful in economics and not necessarily on mathematical proofs
- the examples in this lecture cover a wide range of models in economics
- every section includes worked examples and problems for students to solve as exercises
Dynamic Optimization: Interactive Lecture (3 SWS)
Literatur:
- Sydsæter, Knut, Peter Hammond, Atle Seierstad and Arne Strøm, Further Mathematics for Economic Analysis (FMEA), Prentice Hall, 2nd edition, 2008
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