Target Value Criterion in Markov Decision Processes

We apply the Target Value Criterion to an MDP with a random planning horizon, derive an optimality equation and prove the existence of an optimal stationary policy in a generalized state space. The structure of the value function is exploited to approximate the target space by a finite subset and to derive upper and lower bounds as well as nearly optimal policies. As an extension we combine the Total Reward Criterion and the Target Value Criterion in a penalty approach.