Spanning and completeness in markets with contingent claims (Q1090586)

We characterize financial markets that are ''complete'' or that contain portfolios which ''span'' all measurable functions of a particular asset payoffs, either finite and infinite dimensional. These results are then employed to describe the extent to which options trading is sufficient to complete markets, to investigate the existence of ''efficient funds'', and to establish the extent of market completeness required to ensure the unanimity and irrelevance results of modern corporation finance.