No arbitrage and preferences

We show that the classical concepts of No Arbitrage (NA) and of No Free Lunch with Vanishing Risk (NFLVR) are intimately linked with the preferences of the agents acting in the market. We point out that the difference, from an economic perspective, between NA and NFLVR rests on selection of the class of monotone, respectively monotone and concave, utility functions that determines the absence of a Market Free Lunch (MFL), a concept introduced in Frittelli 2004. We finally prove the equivalence between the absence of MLF and the existence of an equivalent sigma -martingale measure