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A polyhedral approximation approach to concave numerical dynamic programming

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  • Fukushima, Kenichi
  • Waki, Yuichiro

Abstract

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.

Suggested Citation

  • Fukushima, Kenichi & Waki, Yuichiro, 2013. "A polyhedral approximation approach to concave numerical dynamic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2322-2335.
  • Handle: RePEc:eee:dyncon:v:37:y:2013:i:11:p:2322-2335
    DOI: 10.1016/j.jedc.2013.06.001
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    References listed on IDEAS

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    1. Christopher Phelan & Robert M. Townsend, 1991. "Computing Multi-Period, Information-Constrained Optima," Review of Economic Studies, Oxford University Press, vol. 58(5), pages 853-881.
    2. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
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    4. Kiyotaki, Nobuhiro & Moore, John, 1997. "Credit Cycles," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 211-248, April.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
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    7. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    8. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
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    Cited by:

    1. Waki, Yuichiro & Dennis, Richard & Fujiwara, Ippei, 0. "The optimal degree of monetary-discretion in a New Keynesian model with private information," Theoretical Economics, Econometric Society.
    2. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    3. Waki, Yuichiro & Dennis, Richard & Fujiwara, Ippei, 2015. "The Optimal Degree of Monetary-Discretion in a New Keynesian Model with Private Information," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-66, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Jenö Pál & John Stachurski, 2011. "Fitted Value Function Iteration With Probability One Contractions," ANU Working Papers in Economics and Econometrics 2011-560, Australian National University, College of Business and Economics, School of Economics.

    More about this item

    Keywords

    Numerical methods; Dynamic programming;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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