Fundamental Theorem of Asset Pricing

Abstract

The Fundamental Theorem of Asset Pricing refers to a collection of results characterizing arbitrage-free markets in terms of either extensions or representations of the pricing functional. The first version of the Fundamental Theorem of Asset Pricing states that the absence of arbitrage opportunities is equivalent to the existence of a strictly-positive linear extension of the pricing functional from the marketed space to the entire payoff space. Each of these extensions can be viewed as a hypothetical pricing rule in a complete arbitrage-free market under which the original basic securities preserve their prices. The other versions of the Fundamental Theorem of Asset Pricing are based on this extension result and provide useful representations of the pricing functional in terms of Riesz densities. The mathematical prerequisites for this chapter have been developed in detail in Chap. 4.