  This paper shows the usefulness of the Perov contraction theorem, which is a
generalization of the classical Banach contraction theorem, for solving Markov
dynamic programming problems. When the reward function is unbounded, combining
an appropriate weighted supremum norm with the Perov contraction theorem yields
a unique fixed point of the Bellman operator under weaker conditions than
existing approaches. An application to the optimal savings problem shows that
the average growth rate condition derived from the spectral radius of a certain
nonnegative matrix is sufficient and almost necessary for obtaining a solution.
