On the martingale property of certain local martingales
File(s)
Author(s)
Mijatovic, A
Urusov, A
Type
Journal Article
Abstract
The stochastic exponential Zt=exp{Mt−M0−(1/2)⟨M,M⟩t} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the process Z to be a true martingale in the case where Mt=∫t0b(Yu)dWu and Y is a one-dimensional diffusion driven by a Brownian motion W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting. These conditions are deterministic and expressed only in terms of the function b and the drift and diffusion coefficients of Y. As an application we provide a deterministic criterion for the absence of bubbles in a one-dimensional setting.
Date Issued
2012-02
Citation
Probability Theory and Related Fields, 2012, 152 (1-2), pp.1-30
ISSN
0178-8051
Publisher
Springer-Verlag
Start Page
1
End Page
30
Journal / Book Title
Probability Theory and Related Fields
Volume
152
Issue
1-2
Copyright Statement
Copyright © 2010, Springer-Verlag. The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-010-0314-7
Identifier
http://www2.imperial.ac.uk/~amijatov
Publication Status
Published