The Advantage of Using Non-Measurable Stop RulesThe Annals of Probability
AbstractComparisons 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.
Citation InformationTheodore P. Hill and Victor C. Prestien. "The Advantage of Using Non-Measurable Stop Rules" The Annals of Probability Vol. 11 Iss. 2 (1983) p. 442 - 450
Available at: http://works.bepress.com/tphill/6/