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Upper Bounds on Numerical Approximation Errors

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  • Raahauge, Peter

    (Department of Finance, Copenhagen Business School)

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    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.

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    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7171
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    Bibliographic Info

    Paper provided by Copenhagen Business School, Department of Finance in its series Working Papers with number 2004-4.

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    Length: 26 pages
    Date of creation: 21 Jun 2006
    Date of revision:
    Handle: RePEc:hhs:cbsfin:2004_004

    Contact details of provider:
    Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark
    Phone: +45 3815 3815
    Email:
    Web page: http://www.cbs.dk/departments/finance/
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    Related research

    Keywords: Numerical approximation errors; Bellman contractions; Error bounds;

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    References

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    1. 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.
    2. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
    3. Wilfredo L. Maldonado & Benar F. Svaiter, 2002. "On the accuracy of the estimated policy function using the Bellman contraction method," Computing in Economics and Finance 2002 30, Society for Computational Economics.
    4. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    6. 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.
    7. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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