A Useful Transformation of Hamiltonians Occurring in Optimal Control Problems in Economic Analyses

Abstract

The introduction of a discounting term into the objective functional can be troublesome in terms of analysis by the standard maximum principle formulation. This is because it renders the Hamiltonian and the adjoint equations depend explicitly on time. In finite horizon problems it makes the switching point analysis difficult. In case of infinite horizon, which is usual in economic problems, it does not admit long-run stationary equilibriums. A technique discussed by Arrow to alleviate these difficulties is applied to various standard control problems occuring in economics and management science. This transforms the Hamiltonian and the corresponding adjoint system into an explicitly time-independepent form and hence autonomous in all but one case. A natural consequence of the transformation is current-value interpretations of the Hamiltonian and the adjoint variables.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1971
Accession Number
AD0735473

Entities

People

  • Suresh P. Sethi

Organizations

  • Carnegie Mellon University

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Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Autonomous Systems
  • Boundaries
  • Boundary Value Problems
  • Calculus Of Variations
  • Difference Equations
  • Differential Equations
  • Economic Analysis
  • Economic Models
  • Economic Systems
  • Economics
  • Equations
  • Equations Of State
  • Integrals
  • Standards
  • Stationary

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  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design