Note on discounted continuous-time Markov decision processes with a lower bounding function

We consider the discounted continuous-time Markov decision process (CTMDP), where the negative part of each cost rate is bounded by a drift function, say w, whereas the positive part is allowed to be arbitrarily unbounded. Our focus is on the existence of a stationary optimal policy for the discounted CTMDP problems out of the more general class. Both constrained and unconstrained problems are considered. Our investigations are based on the continuous-time version of the Veinott transformation. This technique has not been widely employed in the previous literature on CTMDPs, but it clarifies the roles of the imposed conditions in a rather transparent way.