Fundamental Theorem of Asset Pricing

Abstract

In this chapter we generalize the Fundamental Theorem of Asset Pricing to a multi-period economy. The main result states that the absence of arbitrage opportunities is equivalent to the existence of a time-consistent family of strictly-positive conditional linear extensions of the pricing functionals. In line with the interpretation provided in the context of a single-period model, each of these extensions can be viewed as a hypothetical pricing rule in a complete market under which the original basic securities maintain 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 functionals in terms of Riesz densities. A critical tool will be the extension results for conditional linear functionals established in Chap. 12.