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Multigrid Techniques in Economics

Author

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  • Adam Speight

    (Computation Institute, University of Chicago, Chicago, Illinois)

Abstract

I present a self-contained introduction to multigrid methods with an emphasis on techniques relevant to dynamic programming and related problems. A probabilistic interpretation of the numerical principles is highlighted. Multigrid solvers are shown to be naturally matched to the challenges posed by intractable structural dynamic models routinely encountered in applied economics. I argue that multigrid techniques have potential to substantially extend the scale and complexity of models under consideration. Multigrid also provides a unified computational framework to extend model solvers to perform sensitivity analysis, calibration, estimation, and counterfactual policy experiments.

Suggested Citation

  • Adam Speight, 2010. "Multigrid Techniques in Economics," Operations Research, INFORMS, vol. 58(4-part-2), pages 1057-1078, August.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-2:p:1057-1078
    DOI: 10.1287/opre.1100.0834
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    References listed on IDEAS

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    1. Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," The Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-341.
    2. Wilson, Robert, 1996. "Nonlinear pricing and mechanism design," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 5, pages 253-293, Elsevier.
    3. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    4. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    5. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1.
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    Cited by:

    1. Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.
    2. Kenneth Judd & Garrett van Ryzin, 2010. "Preface to the Special Issue on Computational Economics," Operations Research, INFORMS, vol. 58(4-part-2), pages 1035-1036, August.

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