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 suitable conditions, by value iteration recursive approximation technique, we establish the optimality equation, obtain the uniqueness of the value function and the existence of optimal policies. Finally, two examples are used to illustrate our results.
optimal policy, first passage time, continuous time Markov decision processes, risk probability criterion