(1) L.I.B.R.E., Université de Franche-Comté, Avenue de lObservatoire, 25030 Besançon Cedex, France;(2) Department für Mathematik,, Eidgenössische Technische Hochschule Zürich, ETH-Zentrum, 8092 Zürich, Schweiz;(3) Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France;(4) Central Economics and Mathematics Institute, Moscow, Russia;(5) Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France
Abstract:
We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. We also give an application to the CAPM.Received: November 2003, Mathematics Subject Classification (2000): 60G44JEL Classification: G13, G11Freddy Delbaen: This research was done during the stay of the author at Université de Franche-Comté.
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Observatoire, 25030 Besançon Cedex, France;(2) Department für Mathematik,, Eidgenössische Technische Hochschule Zürich, ETH-Zentrum, 8092 Zürich, Schweiz;(3) Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France;(4) Central Economics and Mathematics Institute, Moscow, Russia;(5) Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France