SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS

Marco Frittelli

Mathematical Finance, 2004, vol. 14, issue 3, 351-357

Abstract: 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, respectively 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.

Date: 2004
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