Finance and Stochastics

, Volume 16, Issue 4, pp 741–777 | Cite as

The fundamental theorem of asset pricing under transaction costs

  • Paolo Guasoni
  • Emmanuel Lépinette
  • Miklós Rásonyi
Article

Abstract

This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes.

The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The RNFLVR condition implies that admissible strategies are predictable processes of finite variation.

The Appendix develops an extension of the familiar Stieltjes integral for càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices.

Keywords

Arbitrage Fundamental theorem of asset pricing Transaction costs Admissible strategies Finite variation 

Mathematics Subject Classification

91B28 62P05 26A45 60H05 

JEL Classification

G12 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Paolo Guasoni
    • 1
    • 2
  • Emmanuel Lépinette
    • 3
  • Miklós Rásonyi
    • 4
    • 5
  1. 1.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  2. 2.School of Mathematical SciencesDublin City UniversityDublin 9Ireland
  3. 3.CeremadeParis Dauphine UniversityParis Cedex 16France
  4. 4.School of MathematicsUniversity of EdinburghEdinburghUK
  5. 5.MTA SZTAKI, Institute for Computer Science and ControlPázmány Péter Catholic UniversityBudapestHungary

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