A Mathematical Theory of Financial Bubbles

115 Pages Posted: 24 Jul 2012 Last revised: 4 Nov 2012

Date Written: June 26, 2012

Abstract

Over the last 10 years or so a mathematical theory of bubbles has emerged, following a martingale theory based on an absence of arbitrage, as opposed to an equilibrium theory. This paper attempts to explain the major developments of the theory as it currently stands, including equities, options, forwards and futures, and foreign exchange. It also presents the recent development of a theory of bubble detection. Critiques of the theory are presented, and a defense is offered. Alternative theories, especially for bubble detection, are sketched.

Keywords: strict local martingale, bubble, stochastic differential equation, detection, foreign exchange

JEL Classification: G13, G12, G28, G24, G23, G32

Suggested Citation

Protter, Philip, A Mathematical Theory of Financial Bubbles (June 26, 2012). Available at SSRN: https://ssrn.com/abstract=2115895 or http://dx.doi.org/10.2139/ssrn.2115895

Philip Protter (Contact Author)

Columbia University ( email )

Mail Code 4403
New York, NY 10027
United States
2128511245 (Phone)
2128512164 (Fax)

HOME PAGE: http://www.stat.columbia.edu/~protter/

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