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From simple growth to numerical simulations: a primer in dynamic programming

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  • Gianluca Femminis

    ()
    (DISCE, Università Cattolica)

Abstract

These notes provide an intuitive introduction to dynamic programming. The first two Sections present the standard deterministic Ramsey model using the Lagrangian approach. These can be skipped by whom is already acquainted with this framework. Section 3 shows how to solve the well understood Ramsey model by means of a Bellman equation, while Section 4 shows how to "guess" the solution (when this is possible). Section 5 is devoted to applications of the envelope theorem. Section 6 provides a "paper and pencil" introduction to the numerical techniques used in dynamic programming, and can be skipped by the uninterested reader. Sections 7 to 9 are devoted to stochastic modelling, and to stochastic Bellman equations. Section 10 extends the discussion of numerical techniques. An Appendix provides details about the Matlab routines used to solve the examples.

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File URL: http://www.unicatt.it/Istituti/TeoriaEconomica/Quaderni/itemq0745.pdf
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Paper provided by Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE) in its series DISCE - Quaderni dell'Istituto di Teoria Economica e Metodi Quantitativi with number itemq0745.

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Length: nn pages 80
Date of creation: Jul 2007
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Handle: RePEc:ctc:serie6:itemq0745

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Web page: http://www.unicatt.it/Istituti/TeoriaEconomica
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Keywords: Dynamic programming; Bellman equation; Optimal growth; Numerical techniques.;

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  1. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 727-32, May.
  2. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report, Federal Reserve Bank of Minneapolis 171, Federal Reserve Bank of Minneapolis.
  3. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report, Federal Reserve Bank of Minneapolis 232, Federal Reserve Bank of Minneapolis.
  4. Albert Marcet & Guido Lorenzoni, 1998. "Parameterized expectations approach; Some practical issues," Economics Working Papers 296, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Beavis,Brian & Dobbs,Ian, 1990. "Optimisation and Stability Theory for Economic Analysis," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521336055.
  6. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(3), pages 479-513, June.
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Cited by:
  1. Enrico Bellino, 2012. "Pasinetti on Ricardo," DISCE - Quaderni dell'Istituto di Teoria Economica e Metodi Quantitativi, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE) itemq1258, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).

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