A current value Hamiltonian Approach for Discrete time Optimal Control Problems arising in Economic Growth

TL;DR

This paper introduces a novel discrete time current value Hamiltonian method for solving nonlinear difference equations in economic growth, extending Pontryagin's maximum principle to improve the analysis of optimal control problems.

Contribution

It develops a new method for constructing first integrals of current value Hamiltonian systems in discrete time, enhancing tools for economic growth models.

Findings

Extended Pontryagin's maximum principle to discrete systems.

Established a new method for first integral construction.

Applicable to nonlinear difference equations in economics.

Abstract

Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.