- 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 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 representation
For a semimartingale S, let where a strategy is admissible if it 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
Main article: fundamental theorem of asset pricingIf 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]
References
- ^ Dothan, Michael (2008). "Efficiency and Arbitrage in Financial Markets" (pdf). International Research Journal of Finance and Economics (19). http://www.eurojournals.com/irjfe_19_08.pdf. Retrieved February 5, 2011.
- ^ Delbaen, Freddy; Schachermayer, Walter (2006). The mathematics of arbitrage. 13. Birkhäuser. ISBN 9783540219927.
- ^ Delbaen, Freddy; Schachermayer, Walter. "What is... a Free Lunch?" (pdf). Notices of the AMS 51 (5): 526–528. http://www.ams.org/notices/200405/what-is.pdf. Retrieved October 14, 2011.
Categories:- Financial markets
- Mathematical finance
- Economics and finance stubs
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