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No free lunch with vanishing risk (NFLVR) is a concept used in mathematical finance as a strengthening of the no-arbitrage condition. In continuous time finance the existence of an equivalent martingale measure (EMM) is no more equivalent to the no-arbitrage-condition (unlike in discrete time finance), but is instead equivalent to the NFLVR-condition. This is known as the first fundamental theorem of asset pricing.
Informally speaking, a market allows for a free lunch with vanishing risk if there are admissible strategies, which can be chosen arbitrarily close to an arbitrage strategy, i.e., these strategies start with no wealth, end up with positive wealth with probability greater zero (free lunch) and the probability of ending up with negative wealth can be chosen arbitrarily small (vanishing risk).[1]
^Delbaen, Schachermayer, Freddy, Walter (2008). The Mathematics of Arbitrage (corrected 2nd ed.). Berlin Heidelberg: Springer-Verlag. p. 78. ISBN 978-3-540-21992-7.{{cite book}}: CS1 maint: multiple names: authors list (link)
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