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SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS
Author(s) -
Frittelli Marco
Publication year - 2004
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2004.00194.x
Subject(s) - semimartingale , martingale (probability theory) , arbitrage , monotone polygon , mathematical economics , equivalence (formal languages) , economics , mathematics , econometrics , financial economics , discrete mathematics , geometry
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.