Minimum risk probability for finite horizon semi-Markov decision processes

This paper studies the risk probability criteria for finite horizon semi-Markov decision processes. The goal is to find an optimal policy with the minimum risk probability that the total reward produced by a system during a finite horizon does not exceed a reward level, where the optimality is over the class of all randomized historic policies which include states, planning horizons and also reward levels. Under mild conditions, the optimality equation and the existence of optimal policies are established, and in addition, an iteration algorithm for solving optimal policies is developed. Our main results are applied to a manufacturing system.