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Mijatović, Aleksandar; Urusov, Mikhail
Probability theory and related fields, 02/2012, Volume: 152, Issue: 1-2Journal Article
The stochastic exponential 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 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.
