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...
This paper presents a study the risk probability optimality for finite horizon continuous-time Markov decision process with loss rate and unbounded transition rates. Under drift condition, which is slightly weaker than the regular condition, as detailed in existing literature on the risk probability optimality Semi-Markov decision processes, we prove that the value function is the unique solution of the corresponding optimality equation, and demonstrate the existence of a risk probability optimization...
This paper considers an exponential cost optimality problem for finite horizon semi-Markov decision processes (SMDPs). The objective is to calculate an optimal policy with minimal exponential costs over the full set of policies in a finite horizon. First, under the standard regular and compact-continuity conditions, we establish the optimality equation, prove that the value function is the unique solution of the optimality equation and the existence of an optimal policy by using the minimum nonnegative...
The purpose of this paper is to study the risk probability problem for infinite horizon piecewise deterministic Markov decision processes (PDMDPs) with varying discount factors and unbounded transition rates. Different from the usual expected total rewards, we aim to minimize the risk probability that the total rewards do not exceed a given target value. Under the condition of the controlled state process being non-explosive is slightly weaker than the corresponding ones in the previous literature,...
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