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Dynamic programming with shape-preserving rational spline Hermite interpolation

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  • Cai, Yongyang
  • Judd, Kenneth L.

Abstract

Numerical methods for dynamic programming often use value function iteration and interpolation. We present a novel shape-preserving rational spline approximation method that improves value function iteration in terms of both stability and accuracy compared to more common methods.

Suggested Citation

  • Cai, Yongyang & Judd, Kenneth L., 2012. "Dynamic programming with shape-preserving rational spline Hermite interpolation," Economics Letters, Elsevier, vol. 117(1), pages 161-164.
    • Handle: RePEc:eee:ecolet:v:117:y:2012:i:1:p:161-164
    DOI: 10.1016/j.econlet.2012.05.004
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    References listed on IDEAS

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    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. Robert Fourer & David M. Gay & Brian W. Kernighan, 1990. "A Modeling Language for Mathematical Programming," Management Science, INFORMS, vol. 36(5), pages 519-554, May.
    3. Yongyang Cai & Kenneth L. Judd, 2010. "Stable and Efficient Computational Methods for Dynamic Programming," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 626-634, 04-05.
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    Citations

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    Cited by:

    1. Yongyang Cai & Kenneth Judd & Jevgenijs Steinbuks, 2017. "A nonlinear certainty equivalent approximation method for dynamic stochastic problems," Quantitative Economics, Econometric Society, vol. 8(1), pages 117-147, March.
    2. Yongyang Cai & Kenneth Judd, 2015. "Dynamic programming with Hermite approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 245-267, June.
    3. Maliar, Lilia & Maliar, Serguei, 2013. "Envelope condition method versus endogenous grid method for solving dynamic programming problems," Economics Letters, Elsevier, vol. 120(2), pages 262-266.
    4. Klein, T.J.; & Salm, M.; & Upadhyay, S.;, 2024. "Patient cost-sharing and redistribution in health insurance," Health, Econometrics and Data Group (HEDG) Working Papers 24/15, HEDG, c/o Department of Economics, University of York.
    5. Yongyang Cai & Kenneth L. Judd & Rong Xu, 2013. "Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs," NBER Working Papers 18709, National Bureau of Economic Research, Inc.
    6. Yongyang Cai & Kenneth Judd, 2013. "Shape-preserving dynamic programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 407-421, June.
    7. Yongyang Cai & Kenneth Judd & Greg Thain & Stephen Wright, 2015. "Solving Dynamic Programming Problems on a Computational Grid," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 261-284, February.
    8. Klein, Tobias J. & Salm, Martin & Upadhyay, Suraj, 2024. "Patient Cost-Sharing and Redistribution in Health Insurance," IZA Discussion Papers 16778, Institute of Labor Economics (IZA).

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    More about this item

    Keywords

    Numerical dynamic programming; Shape-preserving approximation; Hermite interpolation; Rational function spline; Value function iteration;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • 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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