Dynamic optimization

Constrained optimization is at the heart of many models in economics. Most models of economic behaviour require optimization of some sort of utiltiy or profit function. Dynamic optimization (dynamic programming) and optimal control considers models of (constrained) optimization over time. This allows us to construct economic models that involve time. The main objective of this course is to provide the analytic skills and tools to solve and analyse discrete time dynamic optimization models with and without uncertainty. In addition, considerable time is spend on implementing these tools to use simulations on a computer. The final part of the course looks at finite horizon dynamic programming
problems like the shortest path and knapsack problem.
Contents:

•  Vector spaces, norms, Banach spaces
• Contraction mappings, Blackwell’s theorem
• Berge’s optimization theorem,
• Discrete dynamic optimization under certainty,
• Algorithms to solve discrete dynamic optimization problems under certainty
  • Value function iteration,
  • Interpolation,
  • Howard improvement
• Discrete dynamic optimization under uncertainty,
• Algorithms to solve discrete dynamic optimization problems under uncertainty.
• Finite horizon dynamic programming with applications to shortest path problems, currency exchange, knapsack problems, longest common subsequence, etc. We analyse these problems, look at their complexity and see how we can efficiently implement them.

The main goal of this course are:

• Provide the student with the necessary mathematical skills and tools to set up and anlyze discrete time dynamic optimization models. 
• Show how mathematical modelling can be used to analyze economic questions 
• Provide the students with the tools to simulate dynamic optimization models using Python or Julia

Required and Corequired knowledge and skills

The course is self containt but is quite advanced and has a rapid pace. It is adviced that students have some prior knowledge in terms of mathematics.

• Lectures
• Group work

References, bibliography, and recommended reading

Some reference books

• Ferguson B. and Lim G. (2003), “Discrete time dynamic models”, Routledge.
• Acemoglu D. (2009), “Introduction to modern economic growth”, Princeton University Press, Princeton.
• Ljungqvist L. and Sargent T. J., (2000), “Recursive macroeconomic theory”, MIT Press.
• Stokey N., Lucas R. E. and Prescott E. C., (1989), “Recursive methods in economic dynamics”, Harvard University Press.

Course notes

• Syllabus
• Université virtuelle

Contacts

email: thomas.demuynck@ulb.be

Campus

Solbosch

Method(s) of evaluation

• written examination
• Oral presentation
• Group work

written examination

• Open book examination

• Open question with developed answer

Oral presentation

Group work

• written open book exam
• report on simulation exercise
• in class presentation of results

Mark calculation method (including weighting of intermediary marks)

75% of the final grade is an open book written exam. 25% of the final grade is based on a simulation exercise (group work) + presentation of results.

Language(s) of evaluation

• english