Perov's contraction principle and dynamic programming with stochastic discounting

This paper shows the usefulness of Perov's contraction principle, which generalizes Banach's principle to a vector-valued metric, for studying dynamic programming problems in discount factor can be stochastic. The discounting condition β<1 is replaced by ρ(B)<1, where B an appropriate nonnegative matrix and ρ denotes spectral radius. Blackwell's sufficient also generalized this setting. Applications asset pricing optimal savings are discussed.