IDEAS home Printed from https://ideas.repec.org/p/red/sed011/689.html
   My bibliography  Save this paper

A polyhederal approximation approach to concave numerical dynamic programming

Author

Listed:
  • Yuichiro Waki

    (University of Minnesota)

  • Kenichi Fukushima

    (University of Wisconsin - Madison)

Abstract

This paper describes a method for solving concave numerical dynamic programming problems which is based a pair of polyhederal approximations of concave functions. The method is robust in that (i) it is globally convergent, (ii) it produces exact error bounds on the computed value function which can in theory be made arbitrarily tight, and (iii) its implementation boils down to solving a sequence of linear programs. This is true regardless of the dimensionality of the state space, the pattern of binding constraints, and the smoothness of model primitives. Numerical examples suggest that the method is capable of producing accurate solutions in an ecient manner.

Suggested Citation

  • Yuichiro Waki & Kenichi Fukushima, 2011. "A polyhederal approximation approach to concave numerical dynamic programming," 2011 Meeting Papers 689, Society for Economic Dynamics.
  • Handle: RePEc:red:sed011:689
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Christopher Phelan & Robert M. Townsend, 1991. "Computing Multi-Period, Information-Constrained Optima," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(5), pages 853-881.
    2. Aubhik Khan & Julia K. Thomas, 2013. "Credit Shocks and Aggregate Fluctuations in an Economy with Production Heterogeneity," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1055-1107.
    3. Kiyotaki, Nobuhiro & Moore, John, 1997. "Credit Cycles," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 211-248, April.
    4. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    5. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    6. Nishimura, Kazuo & Stachurski, John, 2009. "Equilibrium storage with multiple commodities," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 80-96, January.
    7. 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.
    8. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    9. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    10. Andrew B. Abel & Janice C. Eberly, 1996. "Optimal Investment with Costly Reversibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 581-593.
    11. Julia K. Thomas & Aubhik Khan, 2011. "Default Risk and Aggregate Fluctuations in an Economy with Production Heterogeneity," 2011 Meeting Papers 1333, Society for Economic Dynamics.
    12. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    13. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Waki, Yuichiro & Dennis, Richard & Fujiwara, Ippei, 2018. "The optimal degree of monetary-discretion in a New Keynesian model with private information," Theoretical Economics, Econometric Society, vol. 13(3), September.
    2. 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.
    3. Waki, Yuichiro & Dennis, Richard & Fujiwara, Ippei, 2015. "The Optimal Degree of Monetary-Discretion in a New Keynesian Model with Private Information," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-66, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta†Eksten & Stephen J. Terry, 2018. "Really Uncertain Business Cycles," Econometrica, Econometric Society, vol. 86(3), pages 1031-1065, May.
    2. Xiao, J., 2016. "Corporate Debt Structure, Precautionary Savings, and Investment Dynamics," Cambridge Working Papers in Economics 1666, Faculty of Economics, University of Cambridge.
    3. Fabrizio Perri & Vincenzo Quadrini, 2018. "International Recessions," American Economic Review, American Economic Association, vol. 108(4-5), pages 935-984, April.
    4. Robert Kirkby Author-Email: robertkirkby@gmail.com|, 2017. "Convergence of Discretized Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 117-153, January.
    5. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    6. Safronov, M., 2016. "Experimentation and Learning-by-Doing," Cambridge Working Papers in Economics 1667, Faculty of Economics, University of Cambridge.
    7. Yicheng Wang, 2017. "Debt-Market Friction, Firm-specific Knowledge Capital Accumulation and Macroeconomic Implications," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 19-39, October.
    8. Marios Karabarbounis & Patrick Macnamara, 2021. "Misallocation and Financial Frictions: the Role of Long-Term Financing," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 40, pages 44-63, April.
    9. Joao Ayres & Gajendran Raveendranathan, 2023. "Firm Entry and Exit during Recessions," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 47, pages 47-66, January.
    10. Di Nola, Alessandro, 2015. "Capital Misallocation during the Great Recession," MPRA Paper 68289, University Library of Munich, Germany.
    11. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    12. Barillas, Francisco & Fernandez-Villaverde, Jesus, 2007. "A generalization of the endogenous grid method," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2698-2712, August.
    13. Joao Ayres & Gajendran Raveendranathan, 2018. "The Firm Dynamics of Business Cycles," Department of Economics Working Papers 2018-16, McMaster University.
    14. Miguel H. Ferreira, 2023. "Aggregate Implications of Corporate Bond Holdings by Nonfinancial Firms," Working Papers 967, Queen Mary University of London, School of Economics and Finance.
    15. Bloom, Nick, 2006. "The impact of uncertainty shocks: firm level estimation and a 9/11 simulation," LSE Research Online Documents on Economics 19867, London School of Economics and Political Science, LSE Library.
    16. Iván Alfaro & Nicholas Bloom & Xiaoji Lin, 2024. "The Finance Uncertainty Multiplier," Journal of Political Economy, University of Chicago Press, vol. 132(2), pages 577-615.
    17. Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Solving DSGE models with perturbation methods and a change of variables," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2509-2531, December.
    18. 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.
    19. Moody Chu & Chun-Hung Kuo & Matthew Lin, 2013. "Tensor Spline Approximation in Economic Dynamics with Uncertainties," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 175-198, August.
    20. Giuseppe Fiori & Filippo Scoccianti, 2021. "Aggregate dynamics and microeconomic heterogeneity: the role of vintage technology," Questioni di Economia e Finanza (Occasional Papers) 651, Bank of Italy, Economic Research and International Relations Area.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:red:sed011:689. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.