On local martingale and its supremum: harmonic functions and beyond
Obloj, Jan ; Yor, Marc
HAL, hal-00003504 / Harvested from HAL
Text on HAL
We discuss certain facts involving a continuous local martingale $N$ and its supremum $\overline{N}$. A complete characterization of $(N,\overline{N})$-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 bounds on the law of the local time at $0$, which involve the excess wealth order.
Publié le : 2004-12-09
Classification:  harmonic function,  Skrokhod's embedding problem,  excess wealth order,  continuous local martingale,  supremum process,  60G44, 60G42, 60G40, 60E15,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00003504,
     author = {Obloj, Jan and Yor, Marc},
     title = {On local martingale and its supremum: harmonic functions and beyond},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003504}
}

Obloj, Jan; Yor, Marc. On local martingale and its supremum: harmonic functions and beyond. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003504/