No free lunch with vanishing risk

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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 time 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 representation[edit]

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 pricing[edit]

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]


  1. ^ Dothan, Michael (2008). "Efficiency and Arbitrage in Financial Markets" (pdf). International Research Journal of Finance and Economics (19). Retrieved February 5, 2011. 
  2. ^ Delbaen, Freddy; Schachermayer, Walter (2006). The mathematics of arbitrage. 13. Birkhäuser. ISBN 978-3-540-21992-7. 
  3. ^ Delbaen, Freddy; Schachermayer, Walter. "What is... a Free Lunch?" (pdf). Notices of the AMS. 51 (5): 526–528. Retrieved October 14, 2011.