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On the Starting and Stopping Problem: Application in Reversible Investments

Laboratoire de Statistique et Processus, Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France
Département de Mathématiques, Université d’Evry Val d’Essonne, Bd. F. Mitterand, 91025 Evry Cedex, France
hamadene{at}univ-lemans.fr
monique.jeanblanc{at}univ-evry.fr

In this work, we solve completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process. We use backward stochastic differential equations (BSDEs) and Snell envelopes. Finally, we give some numerical results.

Key Words: real options; BSDEs; Snell envelope; stopping time; stopping and starting
History: Received: February 12, 2004; revision received: September 5, 2005;