Annals of Finance

, Volume 6, Issue 2, pp 157–191 | Cite as

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

  • Paolo Guasoni
  • Miklós Rásonyi
  • Walter Schachermayer
Research Article

Abstract

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 \({\varepsilon > 0}\), (b) the absence of free lunches with bounded risk for arbitrarily small transaction costs \({\varepsilon > 0}\), and (c) the existence of \({\varepsilon}\)-consistent price systems—the analogue of martingale measures under transaction costs—for arbitrarily small \({\varepsilon > 0}\). 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.

Keywords

Transaction costs No arbitragem Consistent price systems 

JEL Classification

G10 G11 G12 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Paolo Guasoni
    • 1
  • Miklós Rásonyi
    • 2
  • Walter Schachermayer
    • 3
  1. 1.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  2. 2.Computer and Automation Institute of the Hungarian Academy of SciencesBudapestHungary
  3. 3.Faculty of MathematicsUniversity of ViennaWienAustria

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