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On the martingale property of certain local martingales
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Mijatović, Aleksandar and Urusov, Mikhail (2012) On the martingale property of certain local martingales. Probability Theory and Related Fields, Vol. 152 (No. 1-2). pp. 1-30. doi:10.1007/s00440-010-0314-7 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-010-0314-7
Abstract
The stochastic exponential Zt=expMt−M0−(12)MMt 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=0tb(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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||
Publisher: | Springer | ||||
ISSN: | 0178-8051 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol. 152 | ||||
Number: | No. 1-2 | ||||
Page Range: | pp. 1-30 | ||||
DOI: | 10.1007/s00440-010-0314-7 | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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