Markov decision processes with random horizon

In this paper the authors formulate Markov Decision Processes with Random Horizon (MDPRH). They show the optimality equation for the MDPRH. However there may not exist optimal stationary strategies, or •-optimal stationary strategies for the processes. When the MDPRH has the probability distribution for the planning horizon with infinite support, the authors show a Turnpike Planning Horizon Theorem. Then they evaluate rolling strategies and they develop an algorithm obtaining an optimal first stage decision. Finally, some numerical experiments on a simple inventory model are done to understand the phenomena.