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NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

Published online by Cambridge University Press:  14 October 2014

A. Kerem Coşar  and
Edward J. Green
A. Kerem Coşar*
Affiliation:
University of Chicago
Edward J. Green
Affiliation:
The Pennsylvania State University
*
Address correspondence to: A. Kerem Coşar, University of Chicago, Booth School of Business, 5807 South Woodlawn Avenue, Chicago, IL 60637, USA; e-mail: [email protected].
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Abstract

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

Keywords

Dynamic OptimizationTransversality Condition
Type
Articles
Information
Macroeconomic Dynamics , Volume 20 , Issue 3 , April 2016 , pp. 667 - 684
Copyright
Copyright © Cambridge University Press 2014 

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