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

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

DSpace/Manakin Repository

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

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