Discrete time multi-parameter optimal stopping problems with multiple plays and switching costs

This paper is concerned with the optimal stopping problem for discrete time multi-parameter stochastic processes with the index set Na .The strategy with multiple plays is introduced and the rules of switching and stopping, which maximize the expected total discounted reward including switching costs in addition to a running reward process and a terminal reward process, are constructed by developing the dynamic programming approach. General results in this paper are also specialized to the Markov case.