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The Dalang Morton Willinger Theorem under cone constraints

dc.contributor.authorNapp, Clotilde
HAL ID: 741006
ORCID: 0000-0002-7008-5949
dc.date.accessioned2009-06-30T11:56:57Z
dc.date.available2009-06-30T11:56:57Z
dc.date.issued2003
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/560
dc.language.isoenen
dc.subjectCone constraints; Dalang–Morton–Willinger theorem; Arbitrage; Short sale constraintsen
dc.subject.ddc332en
dc.titleThe Dalang Morton Willinger Theorem under cone constraintsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherINSEE Ecole Nationale de la Statistique et de l'Administration Economique;
dc.contributor.editoruniversityother;France
dc.description.abstractenThe Dalang–Morton–Willinger theorem [Stochastics Stochastic Rep. 29 (1990) 185] asserts, for a discrete-time perfect market model, that there is no arbitrage if and only if the discounted price process is a martingale with respect to an equivalent probability measure. The financial market is supposed to be perfect in the sense that there is no transaction cost, no imperfection on the numéraire, no short sale constraint, no constraint on the amounts invested, etc.In this note, we explore the same issue in the presence of such imperfections, more precisely, in the presence of polyhedral convex cone constraints. We first obtain a generalization of the Dalang–Morton–Willinger theorem [Stochastics Stochastic Rep. 29 (1990) 185]: we prove that under polyhedral convex cone constraints, absence of arbitrage is equivalent to the existence of a discount process such that, taking this process as a deflator, the net present value of any available investment opportunity is nonpositive.We then apply this general result to specific market imperfections fitting in the convex cone framework, like short sale constraints, solvability constraints, constraints on the quantities, amounts or proportions invested. We improve a result of Pham–Touzi [J. Math. Econ. 31 (2) (1999) 265]. We show that our model enables to deal with financial markets with possible imperfections on the numéraire (like different borrowing and lending rates, or more general convex cone constraints involving the numéraire).en
dc.relation.isversionofjnlnameJournal of Mathematical Economics
dc.relation.isversionofjnlvol39en
dc.relation.isversionofjnlissue1/2en
dc.relation.isversionofjnldate2003
dc.relation.isversionofjnlpages111-126en
dc.identifier.urlsitehttp://halshs.archives-ouvertes.fr/halshs-00151469/en/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelEconomie Financièreen


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