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On the martingale property of stochastic exponentials

Wong, Bernard; Heyde, C C

Description

We present a necessary and sufficient condition for a stochastic exponential to be a true martingale. It is proved that the criteria for the true martingale property are related to whether a related process explodes. An alternative and interesting interpretation of this result is that the stochastic exponential is a true martingale if and only if under a 'candidate measure' the integrand process is square integrable over time. Applications of our theorem to problems arising in mathematical...[Show more]

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
URI: http://hdl.handle.net/1885/79561
Source: Journal of Applied Probability
DOI: 10.1239/jap/1091543416

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