Lie Symmetries and Essential Restrictions in Economic Optimization

33 Pages Posted: 22 Jan 2018

See all articles by Gadi Perets

Gadi Perets

University of Claude Bernard Lyon 1 - Department of Mathematics

Eran Yashiv

Tel Aviv University - Eitan Berglas School of Economics; CEP, LSE; IZA Institute of Labor Economics; Centre for Economic Policy Research (CEPR)

Date Written: January 2018

Abstract

In optimization problems in Economics there are explicit or implicit assumptions about the underlying structure. In particular, one typically assumes that optimal behavior will remain invariant, in a sense to be precisely defined. Inter alia, this relates to the rationale for empirical estimation of invariant structural models.

This paper has three goals. First, to show how relevant restrictions pertaining to this invariance can be derived using the algebraic technique of Lie symmetries of differential equations. Importantly, the symmetries provide solutions of the optimization problems in question or generate rich information with respect to the properties of the solutions, when no closed-form solutions exist. Second, to provide an example of implementation of this algebra, using an issue of substance, thereby gaining insight on a key topic in utility theory and consumer-investor choice. Third, to outline topics that are at the research frontier, which would be amenable to such analysis, thereby providing a road map for a potentially important new literature.

Keywords: consumption and portfolio choice, differential equations, economic optimization, Finance., HARA utility, invariance, Lie symmetries, Macroeconomics, Structural Econometrics

Suggested Citation

Perets, Gadi and Yashiv, Eran, Lie Symmetries and Essential Restrictions in Economic Optimization (January 2018). CEPR Discussion Paper No. DP12611, Available at SSRN: https://ssrn.com/abstract=3106815

Gadi Perets (Contact Author)

University of Claude Bernard Lyon 1 - Department of Mathematics ( email )

43 Bl du 11 novembre 1918
Lyon, Villeurbanne cedex 69622
France

Eran Yashiv

Tel Aviv University - Eitan Berglas School of Economics ( email )

P.O. Box 39040
Ramat Aviv, Tel Aviv, 69978
Israel
+972 3 640 9715 (Phone)
+972 3 640 9908 (Fax)

HOME PAGE: http://www.tau.ac.il/~yashiv/

CEP, LSE ( email )

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London, WC2A 2AE
United Kingdom

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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