On local martingale and its supremum : harmonic functions and beyond

@inproceedings{Oblj2004OnLM,
  title={On local martingale and its supremum : harmonic functions and beyond},
  author={Jan Obl{\'o}j and Marc Yor},
  year={2004}
}
We discuss certain facts involving a continuous local martingale N and its supremum N . A complete characterization of (N, N)-harmonic functions is proposed. This yields an important family of martingales, the usefulness of which is demonstrated, by means of examples involving the Skorokhod embedding problem, bounds on the law of the supremum, or the local time at 0, of a martingale with a fixed terminal distribution, or yet in some Brownian penalization problems. In particular we obtain new… CONTINUE READING
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