Asymptotic arbitrage with small transaction costs

Irene Klein (), Emmanuel Lépinette and Lavinia Perez-Ostafe ()

Finance and Stochastics, 2014, vol. 18, issue 4, 917-939

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 λ n on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λ n -consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998 ; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996 ). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996 ) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λ n >0 on market n; there does not exist any form of asymptotic arbitrage. In one case, (λ n ) can even converge to 0, but not too fast. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Large financial market; Asymptotic arbitrage; Transaction costs; Consistent price system; Monotone convergence for local martingales; 60G44; 91B24; 91B70; G11; G12 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00780-014-0242-y

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