The second fundamental theorem of asset pricing: a new approach

This article presents a new definition of market completenessthat is independent of the notions of no arbitrage and equivalentmartingale measures. Our definition has many advantages, allshown herein. First, it preserves the Second Fundamental Theoremof Asset Pricing, even in complex economies. Second, under ourdefinition, the market can be complete yet arbitrage opportunitiesexist. This is important in practice, and stands in contrastto the traditional definitions. Third, under the assumptionsof no arbitrage and when used in the standard models, our definitionis equivalent to the traditional one.