The fundamental theorem of asset pricing for continuous processes under small transaction costs

A version of the fundamental theorem of asset pricing is proved for continuous asset prices with small proportional transaction costs. Equivalence is established between: (a) the absence of arbitrage with general strategies for arbitrarily small transaction costs , (b) the absence of free lunches wi...

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Bibliographic Details
Published in:Annals of finance 2010-03, Vol.6 (2), p.157-191
Main Authors: Guasoni, Paolo, Rásonyi, Miklós, Schachermayer, Walter
Format: Article
Language:English
Subjects:
Analysis
Arbitrage
Brownian motion
Costs
Economic Theory/Quantitative Economics/Mathematical Methods
Economics and Finance
Finance
Macroeconomics/Monetary Economics//Financial Economics
Pricing policies
Quantitative Finance
Random variables
Research Article
Studies
Transaction costs
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Summary:A version of the fundamental theorem of asset pricing is proved for continuous asset prices with small proportional transaction costs. Equivalence is established between: (a) the absence of arbitrage with general strategies for arbitrarily small transaction costs , (b) the absence of free lunches with bounded risk for arbitrarily small transaction costs , and (c) the existence of -consistent price systems—the analogue of martingale measures under transaction costs—for arbitrarily small . The proof proceeds through an explicit construction, as opposed to the usual separation arguments. The paper concludes comparing numéraire-free and numéraire-based notions of admissibility, and the corresponding martingale and local martingale properties for consistent price systems.
ISSN:1614-2446
1614-2454
DOI:10.1007/s10436-008-0110-x