Investment and arbitrage opportunities with short sales constraints

Elyès Jouini (1) , Laurence Carassus

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper we consider a family of investment project defined by their deterministic cash flows. We assume stationarity-that is, projects available today are the same as those avalaible in the past. In this framework, we prove that the absence of arbitrage opportunities is equivalent tto the existence of a discount rate such that the net value 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 et lippman (1983,1995) and Andler and gales (1997) in a discrete time frameworkand for a finite number of project.

Mots clés: Investment; short sales constraint; stationnary; arbitrage; radon measure; Laplace transform

Domaines: Economies et finances

Elyès Jouini, Laurence Carassus. Investment and arbitrage opportunities with short sales constraints. Mathematical Finance, 1998, 8, pp.169-178. ⟨halshs-00167140⟩