On the Martingale Property of Certain Local Martingales

Aleksandar Mijatovic and Mikhail Urusov

Papers from arXiv.org

Abstract: The stochastic exponential $Z_t=\exp\{M_t-M_0-(1/2) _t\}$ 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 $M_t=\int_0^t b(Y_u)\,dW_u$ 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: 2009-05, Revised 2010-10
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://arxiv.org/pdf/0905.3701 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0905.3701

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().