No free lunch with vanishing risk
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).
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 .[1]
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 .[2]
gollark: No.
gollark: As previously stated, no and I don't want to.
gollark: I agree.
gollark: I also disagree with the people saying they should teach stuff like doing taxes; there are entirely too many random "life skills" and they change lots. They should probably teach stuff like the ability to look this up on the internet on demand, and to usefully work from this information, rather than specific things.
gollark: How DARE I not have done some particular hobby you like. I will fetch my time machine and immediately rectify this.
References
- Delbaen, Freddy; Schachermayer, Walter (2006). The mathematics of arbitrage. 13. Birkhäuser. ISBN 978-3-540-21992-7.
- Delbaen, Freddy; Schachermayer, Walter. "What is... a Free Lunch?" (pdf). Notices of the AMS. 51 (5): 526–528. Retrieved October 14, 2011.
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