Solving the income fluctuation problem with unbounded rewards

Huiyu Li*, John Stachurski

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)

    Abstract

    This paper studies the income fluctuation problem without imposing bounds on utility, assets, income or consumption. We prove that the Coleman operator is a contraction mapping over the natural class of candidate consumption policies when endowed with a metric that evaluates consumption differences in terms of marginal utility. We show that this metric is complete, and that the fixed point of the operator coincides with the unique optimal policy. As a consequence, even in this unbounded setting, policy function iteration always converges to the optimal policy at a geometric rate.

    Original languageEnglish
    Pages (from-to)353-365
    Number of pages13
    JournalJournal of Economic Dynamics and Control
    Volume45
    DOIs
    Publication statusPublished - Aug 2014

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