In this paper, we study continuous time Markov decision processes (CTMDPs) with a denumerable state space, a Borel action space, unbounded transition rates and nonnegative reward function. The optimality criterion to be considered is the first passage risk probability criterion. To ensure the non-explosion of the state processes, we first introduce a so-called drift condition, which is weaker than the well known regular condition for semi-Markov decision processes (SMDPs). Furthermore, under some...