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On the accuracy of the estimated policy function using the Bellman contraction method

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  • Wilfredo L. Maldonado
  • Benar F. Svaiter

Abstract

In this paper we show that the approximation error of the optimal policy function in the stochastic dynamic programing problem using the policies defined by the Bellman contraction method is lower than a constant (which depends on the modulus of strong concavity of the one-period return function) times the square root of the value function approximation error. Since the Bellman's method is a contraction it results that we can control the approximation error of the policy function. This method for estimating the approximation error is robust under small numerical errors in the computation of value and policy functions.
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Suggested Citation

  • 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.
    • Handle: RePEc:sce:scecf2:30
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    References listed on IDEAS

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    1. Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
    2. 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.
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    5. Baxter, Marianne & Crucini, Mario J & Rouwenhorst, K Geert, 1990. "Solving the Stochastic Growth Model by a Discrete-State-Space, Euler-Equation Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 19-21, January.
    6. Christiano, Lawrence J, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 23-26, January.
    7. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    8. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
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    Cited by:

    1. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
    2. Maldonado, Wilfredo L. & Moreira, Humberto Luiz Ataíde, 2006. "Solving Euler Equations: Classical Methods and the C¹ Contraction Mapping Method Revisited," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 60(2), November.
    3. repec:ebl:ecbull:v:3:y:2003:i:1:p:1-14 is not listed on IDEAS
    4. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    5. Maldonado, Wilfredo L. & Svaiter, B.F., 2007. "Holder continuity of the policy function approximation in the value function approximation," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 629-639, June.

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    More about this item

    Keywords

    Dynamic Programming; Accuracy of the estimated policy function;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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