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.
@article{1176993609,
author = {Hill, Theodore P. and Pestien, Victor C.},
title = {The Advantage of Using Non-Measurable Stop Rules},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 442-450},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993609}
}
Hill, Theodore P.; Pestien, Victor C. The Advantage of Using Non-Measurable Stop Rules. Ann. Probab., Tome 11 (1983) no. 4, pp. 442-450. http://gdmltest.u-ga.fr/item/1176993609/