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Asymptotic Arbitrage in Large Financial Markets with Friction

30 Pages Posted: 13 Apr 2012  

Emmanuel Lepinette

Université Paris-Dauphine - CEREMADE, CNRS

Lavinia Ostafe

University of Vienna

Date Written: April 12, 2012


In the modern version of Arbitrage Pricing Theory suggested by Kabanov and Kramkov the fundamental fi nancially meaningful concept is an asymptotic arbitrage. The 'real world' large market is represented by a sequence of 'models' and, though each of them is arbitrage free, investors may obtain non-risky pro ts in the limit. Mathematically, absence of the asymptotic arbitrage is expressed as contiguity of envelopes of the sets of equivalent martingale measures and objective probabilities. The classical theory deals with frictionless markets. In the present paper we extend it to markets with transaction costs. Assuming that each model admits consistent price systems, we relate them with families of probability measures and consider their upper and lower envelopes. The main result concerns the necessary and sufficient conditions for absence of asymptotic arbitrage opportunities of the first and second kinds expressed in terms of contiguity. We provide also more speci fic conditions involving Hellinger processes and give applications to particular models of large fi nancial markets.

Keywords: large financial market, asymptotic arbitrage, transaction costs, contiguity

JEL Classification: G11, G13

Suggested Citation

Lepinette, Emmanuel and Ostafe, Lavinia, Asymptotic Arbitrage in Large Financial Markets with Friction (April 12, 2012). Available at SSRN: or

Emmanuel Lepinette (Contact Author)

Université Paris-Dauphine - CEREMADE, CNRS ( email )

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

Lavinia Ostafe

University of Vienna ( email )

Bruenner Strasse 72
Vienna, Vienna 1090

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