An elementary linear functional approach to the fundamental theorem of asset pricing

Abstract

An elementary linear functional analytic proof of the fundamental theorem of asset pricing for the one-period model of the financial market with a finite state space is proposed. The introductory presentation is largely inspired from Pliska. It is based on a special case of the separating hyper-plane theorem. This equivalent form of the classical Hahn-Banach separation theorem is proved by means of standard tools from linear algebra, vector geometry and convex analysis.