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Upper Bounds on Numerical Approximation Errors

Author

Listed:
  • Raahauge, Peter

    (Department of Finance, Copenhagen Business School)

Abstract

This paper suggests a method for determining rigorous upper bounds on approximation errors of numerical solutions to infinite horizon dynamic programming models. Bounds are provided for approximations of the value function and the policy function as well as the derivatives of the value function. The bounds apply to more general problems than existing bounding methods do. For instance, since strict concavity is not required, linear models and piecewise linear approximations can be dealt with. Despite the generality, the bounds perform well in comparison with existing methods even when applied to approximations of a standard(strictly concave)growth model.

Suggested Citation

  • Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
    • Handle: RePEc:hhs:cbsfin:2004_004
    as

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    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7171
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    References listed on IDEAS

    as
    1. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    2. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    3. Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    4. Bechmann, Ken L. & Raaballe, Johannes, 2000. "A Regulation of Bids for Dual Class Shares. Implication: Two Shares { One Price," Working Papers 2000-5, Copenhagen Business School, Department of Finance.
    5. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
    6. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    7. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    8. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Numerical approximation errors; Bellman contractions; Error bounds;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

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