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.