“No free lunch with vanishing risk”的意思、由来-开放百科全书

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No free lunch with vanishing risk

释义

Mathematical representation
Fundamental theorem of asset pricing
References

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

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

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]

References

1. ^{{cite journal|first=Michael|last=Dothan|title=Efficiency and Arbitrage in Financial Markets|journal=International Research Journal of Finance and Economics|issue=19|year=2008|url=http://www.eurojournals.com/irjfe_19_08.pdf|format=pdf|accessdate=February 5, 2011}}
2. ^{{cite book|first1=Freddy|last1=Delbaen|first2=Walter|last2=Schachermayer|title=The mathematics of arbitrage|volume=13|publisher=Birkhäuser|year=2006|isbn=978-3-540-21992-7}}
3. ^{{cite journal|title=What is... a Free Lunch?|first1=Freddy|last1=Delbaen|first2=Walter|last2=Schachermayer|journal=Notices of the AMS|volume=51|number=5|pages=526–528|url=http://www.ams.org/notices/200405/what-is.pdf|format=pdf|accessdate=October 14, 2011}}

3 : Arbitrage|Financial markets|Mathematical finance

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