Transversality Conditions for Higher Order Infinite Horizon Discrete Time Optimization Problems

TL;DR

This paper investigates higher order difference problems in infinite horizon discrete time optimization, deriving Euler's and transversality conditions using a squeezing argument, and highlighting the necessity of specific assumptions through a counterexample.

Contribution

It introduces a novel derivation of transversality conditions for higher order problems and clarifies the assumptions needed for their validity.

Findings

Derived Euler's and transversality conditions for higher order difference problems

Identified two key assumptions necessary for the conditions to hold

Provided a counterexample demonstrating the importance of these assumptions

Abstract

In this paper, we examine higher order difference problems. Using the "squeezing" argument, we derive both Euler's condition and the transversality condition. In order to derive the two conditions, two needed assumptions are identified. A counterexample, in which the transversality condition is not satisfied without the two assumptions, is also presented.