Asymptotic arbitrage with small transaction costs

Irene Klein, Emmanuel Lépinette () and Lavinia Perez-Ostafe
Additional contact information
Emmanuel Lépinette: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: 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.

Keywords: monotone convergence for local martingales; large nancial market; asymptotic arbitrage; transaction costs; consistent price system; monotone convergence for local martingales. (search for similar items in EconPapers)
Date: 2014-08-19
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Published in Finance and Stochastics, 2014, 18 (4), pp.917-939. ⟨10.1007/s00780-014-0242-y⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00748568

DOI: 10.1007/s00780-014-0242-y

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().