RANDOMIZED STOPPING POINTS AND OPTIMAL STOPPING ON THE PLANE

• 成果类型: Article
• 署名作者: NUALART, D
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989810
• 发表日期: 1992
• 页码: 883-900
• 关键词: tactics

摘要

We prove that in continuous time, the extremal elements of the set of adapted random measures on R+2 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.