An Elementary Exposition of the No Strong Arbitrage Principle for Financial Markets

Robert Becker

No 2017-005, CAEPR Working Papers from Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington

Abstract: A Linear Pricing Rule is established for the No Strong Arbitrate Principle (NSAP) in a finite state, single period asset pricing model. The (NSAP) condition is a statement about the inconsistency of a particular system of linear inequalities. The novelty here lies in the use of the Kuhn-Motzkin-Fourier elimination technique that derives the corresponding dual linear inequality system using elementary methods only. The advantage is that a familiar computational scheme yields the relationship between the (NSAP) inequalities and their dual system. Indeed, the method uncovers why the dual inequality system is, in fact, a dual system in the first place. Students and researchers unfamiliar with systems of dual linear inequalities and Theorems of the Alternative may find the approach taken here as a way to better understand the motivation and use of these techniques.

Keywords: No Strong Arbitrage; arbitrage; Farkas Lemma; Kuhn-Motzkin-Fourier Elimination; state prices; linear inequalities (search for similar items in EconPapers)
JEL-codes: C61 D53 G10 G12 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2017-05
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