On randomized tactics and optimal stopping in the plane
type: Item
instance of: scholarly article
title: On randomized tactics and optimal stopping in the plane
zbMATH Open document ID: 0579.60034
author: Annie Millet
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: This paper considers an optimal stopping problem for two-dimensional stochastic processes \((X_ z)\), indexed by \(N^ 2\) or by \(R^ 2\). The approach generalizes that of \textit{J. M. Bismut} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 38, 169-198 (1977; Zbl 0336.60070)], \textit{N. El Karoui} [École d'été de probabilités de Saint-Flour IX-1979, Lect. Notes Math. 876, 74-238 (1981; Zbl 0472.60002)], and \textit{G. A. Edgar}, \textit{A. Millet} and \textit{L. Sucheston} [Martingale theory in harmonic analysis and Banach spaces, Proc. NSF-CBMS Conf., Cleveland/Ohio 1981, Lect. Notes Math. 939, 36-81 (1982; Zbl 0496.60039)] for one-parameter processes, and consists in introducing a set containing the set of stopping points (the set of randomized tactics), showing the existence of our optimal element in the larger set, and then proving that the optimal element can be chosen in the original set of stopping points. For the two-dimensional problem, the properties of the set of randomized tactics are studied, an integral representation of randomized tactics is established, and a necessary condition for the existence of an optimal stopping point is given.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 60G20
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 3928003
zbMATH Keywords: Choquet's theorem
zbMATH Keywords: conditional independence
zbMATH Keywords: optimal stopping problem
zbMATH Keywords: two-dimensional problem
zbMATH Keywords: randomized tactics
zbMATH Keywords: existence of an optimal stopping point
reviewed by: J. Gianini Pettitt
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992916
OpenAlex ID: W1991800663
DOI: 10.1214/AOP/1176992916
description: scientific article; zbMATH DE number 3928003