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Using Randomization to Break the Curse of Dimensionality

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Author Info

  • Rust, J.

Abstract

This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the curse of dimensionality for a subclass of MDPs known as discrete decision processes (DDPs).

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Bibliographic Info

Paper provided by Wisconsin Madison - Social Systems in its series Working papers with number 9429.

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Length: 49 pages
Date of creation: 1994
Date of revision:
Handle: RePEc:att:wimass:9429

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Postal: UNIVERSITY OF WISCONSIN MADISON, SOCIAL SYSTEMS RESEARCH INSTITUTE(S.S.R.I.), MADISON WISCONSIN 53706 U.S.A.

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Keywords: econometrics ; probability;

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References

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  1. Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-72, November.
  2. Ariel Pakes & Paul McGuire, 1997. "Stochastic Algorithms for Dynamic Models: Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Cowles Foundation Discussion Papers 1144, Cowles Foundation for Research in Economics, Yale University.
  3. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  4. Lars Peter Hansen & Ellen R. McGrattan & Thomas J. Sargent, 1994. "Mechanics of forming and estimating dynamic linear economies," Staff Report 182, Federal Reserve Bank of Minneapolis.
  5. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March Cit.
  6. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  7. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585 Elsevier.
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