Optimal stopping of two-parameter processes on nonstandard probability spaces

Dalang, Robert C.

doi:10.1090/S0002-9947-1989-0948189-X

Optimal stopping of two-parameter processes on nonstandard probability spaces
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Trans. Amer. Math. Soc. 313 (1989), 697-719 Request permission

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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