Investment and Arbitrage Opportunities with Short Sales Constraints

Laurence Carassus (carassus@math.jussieu.fr) and Elyes Jouini (jouini@ceremade.dauphine.fr)
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Laurence Carassus: 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, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Elyes Jouini: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper we consider a family of investment projects defined by their deterministic cash flows. We assume stationarity—that is, projects available today are the same as those available in the past. In this framework, we prove that the absence of arbitrage opportunities is equivalent to the existence of a discount rate such that the net present value of all projects is nonpositive if the projects cannot be sold short and is equal to zero otherwise. Our result allows for an infinite number of projects and for continuous as well as discrete cash flows, generalizing similar results established by Cantor and Lippman (1983, 1995) and Adler and Gale (1997) in a discrete time framework and for a finite number of projects.

Date: 1998-01-07
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Published in Mathematical Finance, 1998, 8 (3), pp.169-178. ⟨10.1111/1467-9965.00051⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-04833315

DOI: 10.1111/1467-9965.00051

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