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Randomized Stopping Points and Optimal Stopping on the Plane
Nualart, David
Nualart, David
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Abstract
We prove that in continuous time, the extremal elements of the set of adapted random measures on R2+ are Dirac measures, assuming the underlying filtration satisfies the conditional qualitative independence property. This result is deduced from a theorem in discrete time which provides a correspondence between adapted random measures on N2 and two-parameter randomized stopping points in the sense of Baxter and Chacon. As an application we show the existence of optimal stopping points for upper semicontinuous two-parameter processes in continuous time.
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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176989810.
Date
1992-08-02
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Institute of Mathematical Statistics (IMS)
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NualartD_AP_20(2)883.pdf
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Keywords
Optimal stopping, two-parameter processes, randomized stopping point
Citation
Nualart, David. Randomized Stopping Points and Optimal Stopping on the Plane. Ann. Probab. 20 (1992), no. 2, 883--900. http://dx.doi.org/10.1214/aop/1176989810.