No free lunch with vanishing risk (NFLVR) is a no-arbitrage argument. We have free lunch with vanishing risk if by utilizing a sequence of tame self-financing portfolios which converge to an arbitrage strategy, we can approximate a self-financing portfolio (called the free lunch with vanishing risk).
For a semimartingale S, let where a strategy is admissible if it is permitted by the market. Then define . S is said to satisfy no free lunch with vanishing risk if such that is the closure of C in the norm topology of .
Fundamental theorem of asset pricingEdit
If is a semimartingale with values in then S does not allow for a free lunch with vanishing risk if and only if there exists an equivalent martingale measure such that S is a sigma-martingale under .
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