**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*).^{[1]}

## Mathematical representationEdit

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 .^{[2]}

## 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 .^{[3]}

## ReferencesEdit

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