Strong n-discount and finite-horizon optimality for continuous-time Markov decision processes

This paper studies the strong n(n = −1, 0)-discount and finite horizon criteria for continuous-time Markov decision processes in Polish spaces. The corresponding transition rates are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. Under mild conditions, the authors prove the existence of strong n(n = −1, 0)-discount optimal stationary policies by developing two equivalence relations: One is between the standard expected average reward and strong −1-discount optimality, and the other is between the bias and strong 0-discount optimality. The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.