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A note on first-order and transversality conditions in infinite-horizon continuous-time optimal control models

Stefano Bosi, David Desmarchelier, Ngoc-Sang Pham

Abstract

We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present some applications to economic models.

A note on first-order and transversality conditions in infinite-horizon continuous-time optimal control models

Abstract

We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present some applications to economic models.

Paper Structure

This paper contains 5 sections, 2 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Problem statement and results
  3. Necessary conditions
  4. Sufficient conditions
  5. Applications

Key Result

Proposition 1

Consider the problem (P). Assume that an admissible pair $(c^*(\cdot), x^*(\cdot))$ is an interior solution. Assume that $c^*(t)\in \mathbb{R}_{++}$$\forall t$. (1) Then there exists a continuous and piecewise differentiable function $\lambda: \mathcal{T}\to \mathbb{R}$ such that (2) If Assumptions assum_Ut and tvc_assumption_general hold,Actually, in our proof, we only need condition in Assumpt

Theorems & Definitions (9)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 1
  • Remark 2
  • Example 1
  • Remark 3
  • Remark 4