- Bifurcations of optimal vector fields
- CeNDEF working paper
- Number of pages
- University of Amsterdam
- Document type
- Working paper
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations as problem parameters are varied. The solutions are represented as the integral curves of a multi-valued `optimal' vector field on state space. Generically, there are three types of integral curves: stable points, open intervals that are forward asymptotic to a stable point and backward asymptotic to an unstable point, and half-open intervals that are forward asymptotic to a stable point and backward asymptotic to an indifference point; the latter are initial states to multiple optimal trajectories. We characterize all bifurcations that occur generically in one- and two-parameter families. Most of these are related to global dynamical bifurcations of the state-costate system of the problem.
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.