The Annals of Probability

The Advantage of Using Non-Measurable Stop Rules

Theodore P. Hill and Victor C. Pestien

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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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Ann. Probab., Volume 11, Number 2 (1983), 442-450.

First available in Project Euclid: 19 April 2007

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Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 90C39: Dynamic programming [See also 49L20]

Optimal stopping theory non-measurable stopping function stop rule


Hill, Theodore P.; Pestien, Victor C. The Advantage of Using Non-Measurable Stop Rules. Ann. Probab. 11 (1983), no. 2, 442--450. doi:10.1214/aop/1176993609.

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