Asymptotic Arbitrage with Small Transaction Costs

21 Pages Posted: 5 Feb 2015

See all articles by I. Klein

I. Klein

University of Vienna - Department of Statistics and Decision Support Systems

Emmanuel Lepinette

Université Paris-Dauphine - CEREMADE, CNRS

Lavinia Ostafe

University of Vienna

Date Written: February 4, 2013

Abstract

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs in terms of contiguity properties of sequences of equivalent probability measures induced by consistent price systems. These results are analogous to the frictionless case. Our setting is simple, each market contains two assets. The proofs use quantitative versions of the Halmos-Savage Theorem and a monotone convergence result of nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs; but with transaction costs there does not exist any form of asymptotic arbitrage.

Suggested Citation

Klein, Irene and Lepinette, Emmanuel and Ostafe, Lavinia, Asymptotic Arbitrage with Small Transaction Costs (February 4, 2013). Available at SSRN: https://ssrn.com/abstract=2560176 or http://dx.doi.org/10.2139/ssrn.2560176

Irene Klein

University of Vienna - Department of Statistics and Decision Support Systems ( email )

Universitaetsstr. 5
Vienna, A-1010
Austria

Emmanuel Lepinette (Contact Author)

Université Paris-Dauphine - CEREMADE, CNRS ( email )

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

Lavinia Ostafe

University of Vienna ( email )

Bruenner Strasse 72
Vienna, Vienna 1090
Austria

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