Bubbles in Assets with Finite Life

39 Pages Posted: 12 Jun 2015 Last revised: 22 Nov 2016

Henri Berestycki

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

Cameron Bruggeman

Columbia University

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 20, 2016

Abstract

We study the speculative value of a finitely lived asset when investors disagree and short sales are limited. In this case, investors are willing to pay a speculative value for the resale option they obtain when they acquire the asset. Using martingale arguments, we characterize the equilibrium speculative value as a solution to a fixed point problem for a monotone operator F. A Dynamic Programming Principle applies and is used to show that the minimal solution to the fixed-point problem is a viscosity solution of a naturally associated (non-local) obstacle problem. Combining the monotonicity of the operator F and a comparison principle for viscosity solutions to the obstacle problem, we obtain several comparison of solution results. We also use a characterization of the exercise boundary of the obstacle problem to study the effect of an increase in the costs of transactions on the value of the bubble and on the volume of trade, and in particular to quantify the effect of a small transaction (Tobin) tax.

Keywords: Asset-price bubble, finitely-lived financial asset, heterogeneous beliefs

JEL Classification: G1, G12, G14, G18

Suggested Citation

Berestycki, Henri and Bruggeman, Cameron and Monneau, Regis and Scheinkman, Jose A., Bubbles in Assets with Finite Life (November 20, 2016). Available at SSRN: https://ssrn.com/abstract=2617078 or http://dx.doi.org/10.2139/ssrn.2617078

Henri Berestycki

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

Cameron Bruggeman

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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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