Structural results for partially observed replacement problems

This paper discusses the structure of the optimal policy and the properties of the optimal value function under certain assumptions on the problem parameters for the partially observed Markov decision process problems. It has been shown that a stronger partial order on the information vector than first order stochastic dominance is essential to guarantee the existence of the monotonic behaviour of the optimal value function and policy. This paper also compares the result of this paper with previous findings and outlines the usefulness of this result in the study of POMDP models.