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Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm

Author

Listed:
  • Ángel Gavilán

    () (Banco de España)

  • Juan A. Rojas

    () (Banco de España)

Abstract

We propose a new numerical method to solve stochastic models that combines the parameterized expectations (PEA) and the Smolyak algorithms. This method is especially convenient to address problems with occasionally binding constraints (a feature inherited from PEA) and/or a large number of state variables (a feature inherited from Smolyak), i.e. DSGE models that incorporate portfolio problems and incomplete markets. We describe the proposed Smolyak-PEA algorithm in the context of a one-country stochastic neoclassical growth model and compare its accuracy with that of a standard PEA collocation algorithm. Despite estimating fewer parameters, the former is able to reach the high accuracy levels of the latter. We further illustrate the working of this algorithm in a two-country neoclassical model with incomplete markets and portfolio choice. Again, the Smolyak-PEA algorithm approximates the solution of the problem with a high degree of accuracy. Finally, we show how this algorithm can efficiently incorporate both occasionally binding constraints and a partial information approach.

Suggested Citation

  • Ángel Gavilán & Juan A. Rojas, 2009. "Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm," Working Papers 0838, Banco de España;Working Papers Homepage.
  • Handle: RePEc:bde:wpaper:0838
    as

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    File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/08/Fic/dt0838e.pdf
    File Function: First version, February 2009
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    References listed on IDEAS

    as
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    Cited by:

    1. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.

    More about this item

    Keywords

    Portfolio Choice; Dynamic Macroeconomics; Computational Methods;

    JEL classification:

    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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