A Survey of Prophet Inequalities in Optimal Stopping Theory
نویسنده
چکیده
The Illain purpose of this paper is to provide a brief survey of what has CODle to be known as "prophet inequalities" or ~~prophet problerns" in the t heory of optirnal stopping. rrhis survpy includes surnrnaries of the basic results, subs e quent extensioIls and variations of these results, Blain proof tools an d techniques (with concrete exarllples), a,ad a list of open problenls. Although the terrIl "prophet" has been used in other rnathernatical a nd proba bilistic contexts, the expression "prophet inequality" in optirnal stoppin g theory is generally associated with the following problern. Given a class C of sequenc es of integrable randolll variables X == (Xl, X2,"')' find universal inequalities valid for all X in C which cornpare the expected suprerllUrl1 of the sequence with the optirnal stopping value of the sequence. That is, if M denotes the expect ed
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