Prophet inequalities for finite stage multiparameter optimal stopping problems

This paper is concerned with the optimal stopping problem for discrete time multiparameter stochastic processes with the index set Nd . In the classical optimal stopping problems, the comparisons between the expected reward of a player with complete foresight and the expected reward of a player using nonanticipating stop rules, known as prophet inequalities, have been studied by many authors. Prophet inequalities in the case of finite stage two-parameter optimal stopping problems are extended to the case of finite stage general multiparameter optimal stopping problems. © 2005 Elsevier Inc. All rights reserved