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Continuous State Dynamic Programming via Nonexpansive Approximation

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  • John Stachurski

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Abstract

This paper studies fitted value iteration for continuous state dynamic programming using nonexpansive function approximators. A number of nonexpansive approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm.
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Suggested Citation

  • John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
  • Handle: RePEc:kap:compec:v:31:y:2008:i:2:p:141-160
    DOI: 10.1007/s10614-007-9111-5
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    References listed on IDEAS

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    12. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    13. Michael Reiter, 2000. "Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems," Computing in Economics and Finance 2000 254, Society for Computational Economics.
    14. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
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    17. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729 Elsevier.
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    Citations

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    Cited by:

    1. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    2. Richard Anton Braun & Huiyu Li & John Stachurski, 2009. "Computing Densities and Expectations in Stochastic Recursive Economies: Generalized Look-Ahead Techniques," CIRJE F-Series CIRJE-F-620, CIRJE, Faculty of Economics, University of Tokyo.
    3. Fukushima, Kenichi & Waki, Yuichiro, 2013. "A polyhedral approximation approach to concave numerical dynamic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2322-2335.
    4. Robert Kirkby, 2017. "Convergence of Discretized Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 117-153, January.
    5. Huiyu Li, 2015. "Numerical Policy Error Bounds for $$\eta $$ η -Concave Stochastic Dynamic Programming with Non-interior Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 171-187, August.
    6. Jenö Pál & John Stachurski, 2011. "Fitted Value Function Iteration With Probability One Contractions," ANU Working Papers in Economics and Econometrics 2011-560, Australian National University, College of Business and Economics, School of Economics.
    7. Nishimura, Kazuo & Stachurski, John, 2010. "Perfect simulation of stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 577-584, April.
    8. Pál, Jenő & Stachurski, John, 2013. "Fitted value function iteration with probability one contractions," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 251-264.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, January.

    More about this item

    Keywords

    Numerical dynamic programming; Nonexpansive approximation; C61; C63;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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