Monotone Dynamic Programming
Martin Kaae Jensen, Jel-classification C · 2003
By integrating dynamic programming with the theory of order preserving dynamical systems (Hirsch (1982), Smith (1995)) this paper develops a new approach to stability analysis in continuous-time dynamic optimization models. The main results provide simple conditions on the primitives of a model which imply that steady states exist and are globally stable for initial conditions in an open dense set. If the steady state is unique or lattice methods are employed in their study; this completely resolves all stability questions. The methods' applicability is demonstrated through examples from investment theory, growth theory, and renewable resource economics.