Efficiency analysis, shortage functions, arbitrage, and martingales

This paper shows that standard tools of efficiency analysis, directional distance functions, can be used to characterize the investment‐returns technology. That ability to characterize the investment‐returns technology and fundamental duality relationships imply that directional distance functions can be used to detect the presence of an arbitrage, to value financial assets in the absence of an arbitrage lying in the span of the market and to place bounds on the no‐arbitrage values of assets lying outside the span of the market.