Comparison of Values of Independent Random Variables in a Bayesian Setting

摘要

An optimal stopping problem for independent observations in a Bayesian setting is considered. One optimal stopper knows only the prior distributions of the independent Ays, 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.