Let $X$ be a semimartingale, and $S$ its Snell envelope. Under the assumption that $X$ and $S$ are continuous semimartingales in $H^1$, this article obtains a new, maximal, characterisation of $S$, and gives an application to the optimal stopping of functions of diffusions. We present a counterexample to the standard assertion that $S$ is just "a martingale on the go-region and $X$ on the stop-region."
Publié le : 1993-01-14
Classification:
Local time,
semimartingale,
Snell envelope,
smooth pasting,
supermartingale,
SDE,
maximal solution,
forward-backward equation,
60G40,
60H20,
60G44,
60J55,
60J25,
60J60,
60G07
@article{1176989407,
author = {Jacka, S. D.},
title = {Local Times, Optimal Stopping and Semimartingales},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 329-339},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989407}
}
Jacka, S. D. Local Times, Optimal Stopping and Semimartingales. Ann. Probab., Tome 21 (1993) no. 4, pp. 329-339. http://gdmltest.u-ga.fr/item/1176989407/