title: A non-local free boundary problem arising in a theory of financial bubbles.
abstract: We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is [Formula: see text] and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero.
authors.affiliation: CAMS, EHESS, 190-198, avenue de France, 75244 Paris Cedex 13, France hb@ehess.fr.
authors.forename: Henri
authors.initials: H
authors.lastname: Berestycki
authors.affiliation: Universié Paris-Est, CERMICS, Ecole des Ponts ParisTech, 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-las-Vallée Cedex 2, France.
authors.forename: Regis
authors.initials: R
authors.lastname: Monneau
authors.affiliation: Department of Economics, Columbia University, 420 West 118th St., New York, NY 10027, USA Department of Economics, Princeton University and NBER.
authors.forename: José A
authors.initials: JA
authors.lastname: Scheinkman
keywords: asset–price bubble; finitely lived financial asset; free boundary; heterogeneous beliefs; non-local problem; obstacle problem