A New Specification of the Multichain Policy Iteration Algorithm in Undiscounted Markov Renewal Programs

We consider the Policy Iteration Algorithm for undiscounted Markov Renewal Programs. Previous specifications of the policy evaluation part of this algorithm all required the analysis of the chain structure for each policy generated. The purpose of this paper is to provide a unique specification of the value vectors as well as an anticycling rule which avoids parsing the transition probability matrices into their subchains.