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Dynamic Programming with Hermite Approximation

Author

Listed:
  • Yongyang Cai
  • Kenneth L. Judd

Abstract

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data is easily obtained from solving the Bellman equation and can be used to approximate value functions. We illustrate this method with one-, three-, and six-dimensional examples. We find that value function iteration with Hermite approximation improves accuracy by one to three digits using little extra computing time. Moreover, Hermite approximation is significantly faster than Lagrange for the same accuracy, and this advantage increases with dimension.

Suggested Citation

  • Yongyang Cai & Kenneth L. Judd, 2012. "Dynamic Programming with Hermite Approximation," NBER Working Papers 18540, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:18540
    Note: TWP
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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. Peter Schober & Julian Valentin & Dirk Pflüger, 2022. "Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 185-224, January.
    3. 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.
    4. Wonjun Chang & Michael C. Ferris & Youngdae Kim & Thomas F. Rutherford, 2020. "Solving Stochastic Dynamic Programming Problems: A Mixed Complementarity Approach," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 925-955, March.
    5. Yongyang Cai & Kenneth L. Judd & Thomas S. Lontzek, 2013. "The Social Cost of Stochastic and Irreversible Climate Change," NBER Working Papers 18704, National Bureau of Economic Research, Inc.
    6. 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.

    More about this item

    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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