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