A Non Local Free Boundary Problem Arising in a Theory of Financial Bubbles

56 Pages Posted: 4 Nov 2013 Last revised: 13 Nov 2013

Henri Berestycki

Centre d’Analyse et de Mathématique Sociales (CAMS, CNRS-EHESS)

Regis Monneau

Université Paris Est - CERMICS

Jose A. Scheinkman

Columbia University; Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: November 12, 2013

Abstract

In this paper, we consider an evolution non local free boundary problem that arises in the modeling 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 the convexity in space of the solution, and various monotonicity properties of the solution and of the free boundary with respect to parameters of the problem.

In order 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 moreover that the free boundary is Lipschitz continuous, and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero.

Keywords: Asset-price bubble, finitely lived financial asset, heterogeneous beliefs, obstacle problem, free boundary, non local problem

JEL Classification: C6, G12

Suggested Citation

Berestycki, Henri and Monneau, Regis and Scheinkman, Jose A., A Non Local Free Boundary Problem Arising in a Theory of Financial Bubbles (November 12, 2013). Available at SSRN: https://ssrn.com/abstract=2349839 or http://dx.doi.org/10.2139/ssrn.2349839

Henri Berestycki

Centre d’Analyse et de Mathématique Sociales (CAMS, CNRS-EHESS) ( email )

Regis Monneau

Université Paris Est - CERMICS ( email )

6 et 8 avenue Blaise Pascal
Marne-la-Vallée, Champs sur marne 77420
France

Jose A. Scheinkman (Contact Author)

Columbia University ( email )

420 W. 118th Street
New York, NY 10027
United States

HOME PAGE: http://www.princeton.edu/~joses

Princeton University - Department of Economics ( email )

26 Prospect Avenue
Princeton, NJ 08544
United States
609-258-4020 (Phone)
609-258-6419 (Fax)

HOME PAGE: http://www.princeton.edu/~joses

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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