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Keywords:
continuous-time Markov decision processes; loss rate; risk probability criterion; finite horizon; optimal policy; unbounded transition rate
continuous-time Markov decision processes; loss rate; risk probability criterion; finite horizon; optimal policy; unbounded transition rate
Summary:
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 policy using an iteration technique. Furthermore, we provide verification of the imposed condition with two examples of controlled birth-and-death system and risk control, and further demonstrate that a value iteration algorithm can be used to calculate the value function and develop an optimal policy.
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