OPTIMAL STOPPING-RELATED INEQUALITIES FOR IID RANDOM-VARIABLES WHEN THE FUTURE IS DISCOUNTED

Comparisons are made between the maximal expected gain of a prophet an d the maximal expected reward of an ordinary player observing a sequen ce of uniformly bounded i.i.d. random variables when the future is dis counted. The player uses pure threshold stopping times which are asymp totically optimal. Both finite and infinite sequences of random variab les are treated. Also, comparisons between optimal stopping values and expected rewards obtained by using asymptotically optimal pure thresh old stopping time are given. (C) 1994 Academic Press, Inc.