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.