Comparisons are made between the expected returns using measurable and non-measurable stop rules in discrete-time stopping problems. In the independent case, a natural sufficient condition ("preservation of independence") is found for the expected return of every bounded non-measurable stopping function to be equal to that of a measurable one, and for that of every unbounded non-measurable stopping function to be arbitrarily close to that of a measurable one. For non-negative and for uniformly-bounded independent random variables, universal sharp bounds are found for the advantage of using non-measurable stopping functions over using measurable ones. Partial results for the dependent case are obtained.



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URL: https://digitalcommons.calpoly.edu/rgp_rsr/60