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Asymptotic arbitrage with small transaction costs

Author

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  • Irene Klein
  • Emmanuel Lépinette
  • Lavinia Perez-Ostafe

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

Suggested Citation

  • Irene Klein & Emmanuel Lépinette & Lavinia Perez-Ostafe, 2014. "Asymptotic arbitrage with small transaction costs," Finance and Stochastics, Springer, vol. 18(4), pages 917-939, October.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:4:p:917-939
    DOI: 10.1007/s00780-014-0242-y
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    References listed on IDEAS

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    Cited by:

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    2. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    3. Fatma Haba & Antoine Jacquier, 2015. "Asymptotic Arbitrage In The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-18, December.

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    More about this item

    Keywords

    Large financial market; Asymptotic arbitrage; Transaction costs; Consistent price system; Monotone convergence for local martingales; 60G44; 91B24; 91B70; G11; G12;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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