A new sufficient condition for uniform integrability of stochastic exponentials

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Given a continuous local martingale M, the associated stochastic exponential is a local martingale, but not necessarily a true martingale. To know whether is a true martingale is important for many applications, e.g. if Girsanov’s theorem is applied to perform a change of measure. We give a generalization of the well-known Novikov’s and Kazamaki’s criteria which provides a new proof based on the properties of a certain backward stochastic differential equation.