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Article Dans Une Revue Finance and Stochastics Année : 2014

Asymptotic arbitrage with small transaction costs

Irene Klein
  • Fonction : Auteur
Lavinia Perez-Ostafe
  • Fonction : Auteur

Résumé

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties of sequences of equivalent probability measures induced by $\la_n$--consistent price systems. These results are analogous to the frictionless case. Our setting is simple, each market $n$ contains two assets with continuous price processes. The proofs use quantitative versions of the Halmos--Savage Theorem and a monotone convergence result of nonnegative local martingales. Moreover, we present an example admitting a strong asymptotic arbitrage without transaction costs; but with transaction costs $\la_n>0$ on market $n$ ($\la_n\to0$ not too fast) there does not exist any form of asymptotic arbitrage.

Dates et versions

hal-00748568 , version 1 (05-11-2012)

Identifiants

Citer

Irene Klein, Emmanuel Lépinette, Lavinia Perez-Ostafe. Asymptotic arbitrage with small transaction costs. Finance and Stochastics, 2014, 18 (4), pp.917-939. ⟨10.1007/s00780-014-0242-y⟩. ⟨hal-00748568⟩
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