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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Optimal stopping of two-parameter processes on nonstandard probability spaces


Author: Robert C. Dalang
Journal: Trans. Amer. Math. Soc. 313 (1989), 697-719
MSC: Primary 60G40; Secondary 03H05, 60G07, 60G57
MathSciNet review: 948189
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Abstract: We prove the existence of optimal stopping points for upper semicontinuous two-parameter processes defined on filtered nonstandard (Loeb) probability spaces that satisfy a classical conditional independence hypothesis. The proof is obtained via a lifting theorem for elements of the convex set of randomized stopping points, which shows in particular that extremal elements of this set are ordinary stopping points.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0948189-X
PII: S 0002-9947(1989)0948189-X
Keywords: Optimal stopping, two-parameter process, nonstandard analysis, randomized stopping point
Article copyright: © Copyright 1989 American Mathematical Society