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Solving the income fluctuation problem with unbounded rewards

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  • Li, Huiyu
  • Stachurski, John

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.

Suggested Citation

  • Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
  • Handle: RePEc:eee:dyncon:v:45:y:2014:i:c:p:353-365
    DOI: 10.1016/j.jedc.2014.06.003
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    References listed on IDEAS

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    Cited by:

    1. Acikgoz, Omer, 2015. "On the Existence of Equilibrium in Bewley Economies with Production," MPRA Paper 69061, University Library of Munich, Germany.
    2. Acikgoz, Omer, 2015. "On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production," MPRA Paper 71066, University Library of Munich, Germany, revised 30 Apr 2016.
    3. repec:eee:jetheo:v:173:y:2018:i:c:p:18-55 is not listed on IDEAS
    4. John Stachurski & Alexis Akira Toda, 2018. "An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity," Papers 1807.08404, arXiv.org, revised Oct 2018.
    5. repec:red:issued:16-391 is not listed on IDEAS

    More about this item

    Keywords

    Coleman operator; Policy iteration; Time iteration; Global convergence;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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