Given a two-parameter filtration $(\mathscr{F}_z)$ satisfying the conditional independence assumption (F4), we prove the existence of an optimal stopping point for adapted processes $(X_z)$ indexed by $\mathbb{N}^2$ or $\mathbb{R}^2_+$ which are of class $(D)$, and have regularity properties which generalize the usual one-parameter ones, and are expressed in terms of sequences of 1- and 2-stopping points.
Publié le : 1985-08-14
Classification:
Optimal stopping,
stopping point,
optional increasing path,
tactic,
extreme point,
Choquet's theorem,
conditional independence,
60G40,
60G99,
60G20,
60G57
@article{1176992916,
author = {Millet, Annie},
title = {On Randomized Tactics and Optimal Stopping in the Plane},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 946-965},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992916}
}
Millet, Annie. On Randomized Tactics and Optimal Stopping in the Plane. Ann. Probab., Tome 13 (1985) no. 4, pp. 946-965. http://gdmltest.u-ga.fr/item/1176992916/