The Fundamental Theorem of Asset Pricing Under Transaction Costs

35 Pages Posted: 23 Mar 2011 Last revised: 15 Apr 2012

See all articles by Paolo Guasoni

Paolo Guasoni

Boston University - Department of Mathematics and Statistics; Dublin City University - School of Mathematical Sciences; University of Bologna - Department of Statistics

Emmanuel Lepinette

Université Paris-Dauphine - CEREMADE, CNRS

Miklos Rasonyi

University of Edinburgh - School of Mathematics

Date Written: March 12, 2011

Abstract

This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded cadlag (right-continuous, left-limited) processes. The Robust No Free Lunch with Vanishing Risk (RNFLVR) condition 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 cadlag integrands and finite-variation integrators, which is central to modeling transaction costs with discontinuous prices.

Keywords: Arbitrage, Fundamental Theorem of Asset Pricing, Transaction Costs, Admissible Strategies, Finite Variation

JEL Classification: G12

Suggested Citation

Guasoni, Paolo and Guasoni, Paolo and Lepinette, Emmanuel and Rasonyi, Miklos, The Fundamental Theorem of Asset Pricing Under Transaction Costs (March 12, 2011). Boston U. School of Management Research Paper No. 2011-7, Available at SSRN: https://ssrn.com/abstract=1784440 or http://dx.doi.org/10.2139/ssrn.1784440

Paolo Guasoni (Contact Author)

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

Emmanuel Lepinette

Université Paris-Dauphine - CEREMADE, CNRS ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Miklos Rasonyi

University of Edinburgh - School of Mathematics ( email )

United Kingdom

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