Abstract
We prove the max-martingale conjecture of Obłój and Yor. We show that for a continuous local martingale and a function , is a local martingale if and only if there exists a locally integrable function such that . This readily implies, via Lévy's equivalence theorem, an analogous result with the maximum process replaced by the local time at .
Citation
Jan Obloj. "A complete characterization of local martingales which are functions of Brownian motion and its maximum." Bernoulli 12 (6) 955 - 969, dec 2006. https://doi.org/10.3150/bj/1165269146
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