Comparison of Values of Independent Random Variables in a Bayesian Setting

Abstract

An optimal stopping problem for independent observations in a Bayesian setting is considered. One optimal stopper knows only the prior distributions of the independent X _i 's, while the other stopper knows the conditional distributions of the X _i 's. We show that the extremal relationship of the returns to the two different optimal stoppers is the same as the relationship between an optimal stopper and a “prophet” in a usual corresponding optimal stopping setting.

Keywords:

• Bayesian setting
• Optimal stopping
• Partial information
• Prophet regions
• AMS 2000 Subject Classification: Primary 60G40

Acknowledgments

The author is grateful to Professors T.P. Hill and E. Samuel-Cahn for inspiring discussions which led to this note. This research was supported by the Deutsche Forschungsgemeinschaft, grant Schm-1410/1-1, and the Landau Center for Research in Mathematical Analysis, Jerusalem.

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