Consistent Price Systems and Arbitrage Opportunities of the Second Kind in Models with Transaction Costs

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Consistent Price Systems and Arbitrage Opportunities of the Second Kind in Models with Transaction Costs

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dc.contributor.author Lépinette-Denis, Emmanuel
dc.contributor.author Kabanov, Yuri
dc.date.accessioned 2010-07-22T15:11:08Z
dc.date.available 2010-07-22T15:11:08Z
dc.date.issued 2012
dc.identifier.uri http://basepub.dauphine.fr/xmlui/handle/123456789/4652
dc.language.iso en en
dc.subject Consistent price systems en
dc.subject No Free Lunch en
dc.subject Arbitrage en
dc.subject Transaction costs en
dc.subject Martingales en
dc.subject Set-valued processes en
dc.subject.ddc 332 en
dc.subject.classificationjel G13 en
dc.subject.classificationjel G11 en
dc.title Consistent Price Systems and Arbitrage Opportunities of the Second Kind in Models with Transaction Costs en
dc.type Article accepté pour publication ou publié
dc.description.abstracten In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial endowments laying outside the solvency region but ending inside. Such a phenomenon was discovered by M. R´asonyi in the discrete-time framework. In this note we consider a rather abstract continuous-time setting and prove necessary and sufficient conditions for the property which we call No Free Lunch of the 2nd Kind, NFL2. We provide a number of equivalent conditions elucidating, in particular, the financial meaning of the property B which appeared as an indispensable “technical” hypothesis in previous papers on hedging (super-replication) of contingent claims under transaction costs. We show that it is equivalent to another condition on the “richness” of the set of consistent price systems, close to the condition PCE introduced by R´asonyi. In the last section we deduce the R´asonyi theorem from our general result using specific features of discrete-time models. en
dc.relation.isversionofjnlname Finance and Stochastics
dc.relation.isversionofjnlvol 16
dc.relation.isversionofjnlissue 1
dc.relation.isversionofjnldate 2012
dc.relation.isversionofjnlpages 135-154
dc.relation.isversionofdoi http://dx.doi.org/10.1007/s00780-010-0144-6
dc.description.sponsorshipprivate oui en
dc.relation.isversionofjnlpublisher Springer en
dc.subject.ddclabel Economie financière en

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