Some remarks on arbitrage and preferences in securities market models

We introduce the notion of a Market Free Lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize No Arbitrage (NA) and No Free Lunch with Vanishing Risk (NFLVR) in terms of the Market Free Lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, resp. monotone and continuous, utility functions that determines the absence of the Market Free Lunch. We also provide a direct proof of the equivalence between the absence of a Market Free Lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure.