Normalized Markov Decision Chains I; Sensitive Discount Optimality

In this paper we study sensitive discount optimality criteria for finite state and action, discrete time parameter, stationary generalized Markov decision chains. We extend previous results obtained by Miller and Veinott and Veinott for substochastic transition matrices to arbitrary non-negative matrices with spectral radius not exceeding one. In particular, we generalize their policy improvement algorithm for finding a stationary policy maximizing the expected discounted reward for all sufficiently small positive interest rates.