Two-parameter optimal stopping problem with switching costs

This paper is concerned with the optimal stopping problem for discrete time two-parameter stochastic processes with index set N². We introduce switching costs in addition to a running reward process and a terminal reward process, construct optimal tactics, that is, the rules of switching and stopping, which maximize the expected total discounted reward including switching costs. A dynamic programming approach is developed. We also specialize our general results to two-parameter Markov case.