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

Abstract

A Linear Pricing Rule is established for the No Strong Arbitrage 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.