The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Hamiltonians

  • Karl Shell
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1166

Abstract

Hamiltonian dynamics arises not only in economic optimization problems but also in descriptive economic models in which there is perfect foresight about asset prices. Hamiltonian dynamics applies in discrete time as well as in continuous time. In discrete time, the system of differential equations is replaced by a closely related system of difference equations. The theory accommodates differential correspondences or difference correspondences, which naturally arise in economics. The Hamiltonian approach through the Hamiltonian function has proved remarkably successful in establishing sufficient conditions for the saddle-point property and related stability questions in a class of optimal economic growth models.

Keywords

Continuous and discrete time models Duality Hamilton, W. R. Hamiltonian dynamical system Hamiltonian function Hamiltonians Lyapunov functions Optimal-growth theory Overlapping generations models Poincaré, J. H. Pontryagin’s maximum principle Saddle-point property Transversality conditions 
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Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Karl Shell
    • 1
  1. 1.