Shifting martingale measures and the birth of a bubble as a
submartingale
by Francesca Biagini1, Hans Föllmer 2 and Sorin Nedelcu1
1
Department of Mathematics, Ludwig-Maximilians Universität, Theresienstrasse 39, 80333 Munich, Germany
E-mail:
(email:biagini@math.lmu.de and nedelcu@math.lmu.de) and
2
Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
(email:foellmer@mathematik.hu-berlin.de)
Abstract
In an incomplete financial market model, we study a flow in the space of
equivalent martingale measures and the corresponding shifting perception of the fundamental
value of a given asset. This allows us to capture the birth of a perceived
bubble and to describe it as an initial submartingale which then turns into a supermartingale
before it falls back to its initial value zero.
Key words: Bubbles, Strict local martingales, Submartingales, Equivalent
martingale measures, Stochastic volatility
JEL Classification:C60, C65, G12
Mathematics Subject Classification (2000): 91G99, 60G07, 60G44