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Symmetric processes and Ocone martingales

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In a recent paper, Mike Tehranchi provided a link between continuous symmetric martingales and the self-duality property of their stochastic exponentials. We explore this link further by providing a characterization of Ocone martingales in terms of certain associated stochastic exponentials. Moreover, we discuss quasi self-dual processes which have received attention in connection with semi-static hedges of barrier options. Joint work with Michael Schmutz.

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