Citation

Discussion Paper Details

Please find the details for DP12611 in an easy to copy and paste format below:

Full Details

Title: Lie Symmetries and Essential Restrictions in Economic Optimization

Author(s): Gadi Perets and Eran Yashiv

Publication Date: January 2018

Keyword(s): consumption and portfolio choice, differential equations, economic optimization, Finance, HARA utility, invariance, Lie symmetries, Macroeconomics and Structural Econometrics

Programme Area(s): Financial Economics and Monetary Economics and Fluctuations

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.

For full details and related downloads, please visit: https://cepr.org/active/publications/discussion_papers/dp.php?dpno=12611

Bibliographic Reference

Perets, G and Yashiv, E. 2018. 'Lie Symmetries and Essential Restrictions in Economic Optimization'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=12611