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Investment and Arbitrage Opportunities with Short Sales Constraints
Author(s) -
Carassus Laurence,
Jouini Elyès
Publication year - 1998
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00051
Subject(s) - arbitrage , cash flow , terminal value , investment (military) , economics , net present value , mathematical economics , cash , value (mathematics) , econometrics , financial economics , microeconomics , finance , mathematics , operating cash flow , production (economics) , statistics , politics , political science , law
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.