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Fitted Value Function Iteration With Probability One Contractions

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  • Jenö Pál
  • John Stachurski

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Abstract

This paper studies a value function iteration algorithm that can be applied to almost all stationary dynamic programming problems. Using nonexpansive function approximation and Monte Carlo integration, we develop a randomized fitted Bellman operator and a corresponding algorithm that is globally convergent with probability one. When additional restrictions are imposed, an OP(n-1/2) rate of convergence for Monte Carlo error is obtained.

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Bibliographic Info

Paper provided by Australian National University, College of Business and Economics, School of Economics in its series ANU Working Papers in Economics and Econometrics with number 2011-560.

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Length: 22 Pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:acb:cbeeco:2011-560

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  1. Josep Pijoan-Mas, 2003. "Precautionary Savings Or Working Longer Hours?," Working Papers wp2003_0311, CEMFI.
  2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
  3. Eva Carceles Poveda & Arpad Abraham, 2004. "Endogenous Trading Constraints with Incomplete Asset Markets," 2004 Meeting Papers 667, Society for Economic Dynamics.
  4. Yuichiro Waki & Kenichi Fukushima, 2011. "A polyhederal approximation approach to concave numerical dynamic programming," 2011 Meeting Papers 689, Society for Economic Dynamics.
  5. Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09.
  6. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Society for Computational Economics, vol. 31(2), pages 141-160, March.
  7. Marimon, Ramon & Scott, Andrew (ed.), 2001. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780199248278, Octomber.
  8. Alan C. Stockman & Linda L. Tesar, 1991. "Tastes and technology in a two-country model of the business cycle: explaining international co-movements," Working Paper 9019, Federal Reserve Bank of Cleveland.
  9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  10. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, 05.
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