Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain
| Autor: | Serguei Maliar, Lilia Maliar, Kenneth L. Judd, Rafael Valero |
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| Přispěvatelé: | Análisis Económico, Universidad de Alicante. Departamento de Fundamentos del Análisis Económico |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Economics and Econometrics
Mathematical optimization Control and Optimization High-dimensional problem jel:C63 jel:C68 Context (language use) Basis function Smolyak method Projection (linear algebra) Intergenerational Risk Sharing Government Transfer Policies Aggregate Shocks Incomplete Markets Stochastic Simulation symbols.namesake Sparse grid Projection method Economics Projection Projection (set theory) Mathematics Adaptive domain Fundamentos del Análisis Económico Applied Mathematics Anisotropic grid Lagrange polynomial Grid sparse grid adaptive domain projection anisotropic grid collocation high-dimensional problem symbols Hypercube Interpolation |
| Popis: | We show how to enhance the performance of a Smolyak method for solving dynamic economic models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given economic model. Finally, we argue that in large-scale economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed. Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution and Department of Economics at Stanford University, University of Alicante, Ivie, MECD and FEDER funds under the projects SEJ-2007-62656 and ECO2012-36719. Rafael Valero acknowledges support from MECD under the FPU program. |
| Databáze: | OpenAIRE |
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