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Dynamic Programming with Hermite Approximation

  • Yongyang Cai
  • Kenneth L. Judd

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data is easily obtained from solving the Bellman equation and can be used to approximate value functions. We illustrate this method with one-, three-, and six-dimensional examples. We find that value function iteration with Hermite approximation improves accuracy by one to three digits using little extra computing time. Moreover, Hermite approximation is significantly faster than Lagrange for the same accuracy, and this advantage increases with dimension.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 18540.

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Date of creation: Nov 2012
Date of revision:
Publication status: published as Mathematical Methods of Operations Research June 2015, Volume 81, Issue 3, pp 245-267 Date: 13 Feb 2015 Dynamic programming with Hermite approximation Yongyang Cai, Kenneth L. Judd
Handle: RePEc:nbr:nberwo:18540
Note: TWP
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  1. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2011. "Computational suite of models with heterogeneous agents II: Multi-country real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 175-177, February.
  2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  3. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2011. "Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models," Quantitative Economics, Econometric Society, vol. 2(2), pages 173-210, 07.
  4. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
  5. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
  6. Malin, Benjamin A. & Krueger, Dirk & Kubler, Felix, 2011. "Solving the multi-country real business cycle model using a Smolyak-collocation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 229-239, February.
  7. Eric M. Aldrich & Jesús Fernández-Villaverde & Ronald Gallant & Juan F. Rubio-Ramírez, 2010. "Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors," PIER Working Paper Archive 10-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Cai, Yongyang & Judd, Kenneth L., 2012. "Dynamic programming with shape-preserving rational spline Hermite interpolation," Economics Letters, Elsevier, vol. 117(1), pages 161-164.
  9. Yongyang Cai & Kenneth Judd & Greg Thain & Stephen Wright, 2015. "Solving Dynamic Programming Problems on a Computational Grid," Computational Economics, Society for Computational Economics, vol. 45(2), pages 261-284, February.
  10. Yongyang Cai & Kenneth L. Judd & Thomas S. Lontzek, 2013. "The Social Cost of Stochastic and Irreversible Climate Change," NBER Working Papers 18704, National Bureau of Economic Research, Inc.
  11. repec:spr:compst:v:77:y:2013:i:3:p:407-421 is not listed on IDEAS
  12. Yongyang Cai & Kenneth Judd, 2013. "Shape-preserving dynamic programming," Mathematical Methods of Operations Research, Springer, vol. 77(3), pages 407-421, June.
  13. Juillard, Michel & Villemot, Sébastien, 2011. "Multi-country real business cycle models: Accuracy tests and test bench," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 178-185, February.
  14. Trick, Michael A. & Zin, Stanley E., 1997. "Spline Approximations To Value Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 255-277, January.
  15. J. Rust & J. F. Traub & H. Wozniakowski, 2002. "Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?," Econometrica, Econometric Society, vol. 70(1), pages 285-329, January.
  16. Rust, J., 1994. "Using Randomization to Break the Curse of Dimensionality," Working papers 9429, Wisconsin Madison - Social Systems.
  17. Robert Fourer & David M. Gay & Brian W. Kernighan, 1990. "A Modeling Language for Mathematical Programming," Management Science, INFORMS, vol. 36(5), pages 519-554, May.
  18. Yongyang Cai & Kenneth L. Judd & Rong Xu, 2013. "Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs," NBER Working Papers 18709, National Bureau of Economic Research, Inc.
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