Lehrende: Prof. Dr. Olaf Posch
Veranstaltungsart: Vorlesung
Anzeige im Stundenplan: Stochastic
Semesterwochenstunden: 2
Credits: 6,0
Unterrichtssprache: Englisch
Min. | Max. Teilnehmerzahl: - | -
Weitere Informationen: Geöffnet für Economics-Masterstudierende
Kommentare/ Inhalte: The lecture "Stochastic Dynamic Programming" goes virtual. All lectures will be held via the platform Zoom, there is no recording of the lectures. For more information see https://www.rrz.uni-hamburg.de/services/weitere/medienkompetenz/videokonferenzen/zoom.html Participation is restricted to registered students. Please check this platform for the necessary information for obtaining online access.
Lernziel: 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. We then thoroughly study models in discrete time and continuous time under uncertainty. The optimization problems are illustrated by various examples.
Vorgehen: 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 (Itˆo’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
Literatur:
Zusätzliche Hinweise zu Prüfungen: TAKE-HOME EXAM: Time to process the exam: 90 min Time frame in which the exam can be completed: First exam:26.02.2021, provision of the tasks/assignments at 9:00 am, submission no later than 05.03.2021 (4:00 pm) Second exam: 26.03.2021, provision of the tasks/assignments at 9:00 am, submission no later than 02.04.2021 (4:00 pm) The examiner of your course will provide information about the hand out of examination tasks / assignments and their submission.“ Please note that the exam will take place in the form of of a take-home exam. All participants have 90 minutes to answer the exam questions and will be given additional time to upload the required documents on a shared folder. There will be the possibility for clarifying questions. Please make sure that your programs are properly installed and ready to use as there will be no technical assistence during the exam. There will be four problem sets with the possibility of improving the final grade of the exam by 0.3/0.4 (good performance) or 0.6/0.7 (exceptional performance) points. The minimum number of solved problems sets must be three out of the four problem sets (respecting the deadlines) in order to qualify for the grade improvement. Handing in the problem sets is not required to take the exam.
