M04 – PARIS‐SACLAY 08/02/2016 ‐ 12/02/2016

Advanced topics in the optimal control of economic systems

Raouf Boucekkine
Senior IUF member

Abstract of the course

This course reviews some selected advanced topics in the optimal control of economic and demo-economic systems. Three main topics will be studied. The first focus will be on age-structured models in economy and demography and the associated infinite- dimensional optimization problems. Adapted methods based on calculus of variations and dynamic programming will be presented and applied to  a series of economic and demo-economic problems. The second topic concerns the optimal control of spatio-temporal systems typically governed by parabolic partial differential equations with an application to optimal economic growth. Finally, some recent optimal regime switching problems will be treated with applications to ecological economics.


1) Optimal control of age-structured populations
  • Examples
  • A generic problem: Optimal replacement in the vintage capital growth model
  • Case 1:  state equations as functional integro-differential equations (delay or neutral)
  • Case 2: state equations as partial differential equations
  • Maximum principle and dynamic programming methods in infinite dimension
2) Optimal control of spatio-temporal dynamics
  • A generic example: The spatial Ramsey model
  • Optimal control of parabolic partial differential equations
  • The dynamic programming approach
3) Optimal regime switching
  • Examples from ecological economics
  • Multi-stage optimal control: insight and limits