Prophet inequalities for two-parameter optimal stopping problems

This paper is concerned with the optimal stopping problem for discrete time two parameter stochastic processes with the index set N². 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. We shall study the prophet inequalities for optimal stopping problems for finite stage two-parameter stochastic processes.