Abstract

http://ssrn.com/abstract=2349281
 
 

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Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models


Johannes Brumm


University of Zurich

Simon Scheidegger


University of Zurich

January 15, 2014


Abstract:     
We present a flexible and scalable method to compute global solutions of high-dimensional stochastic dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximum problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of distributed and shared memory parallelization schemes. This parallelization enables us to efficiently use high-performance computing architectures. Our algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.

Number of Pages in PDF File: 39

Keywords: Adaptive Sparse Grids, High-Performance Computing, International Real Business Cycles, Occasionally Binding Constraints

JEL Classification: C63, C68, F41

working papers series


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Date posted: November 4, 2013 ; Last revised: January 15, 2014

Suggested Citation

Brumm, Johannes and Scheidegger, Simon, Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models (January 15, 2014). Available at SSRN: http://ssrn.com/abstract=2349281 or http://dx.doi.org/10.2139/ssrn.2349281

Contact Information

Johannes Brumm (Contact Author)
University of Zurich ( email )
Rämistrasse 71
Zürich, CH-8006
Switzerland
Simon Scheidegger
University of Zurich ( email )
Rämistrasse 71
Zürich, CH-8006
Switzerland
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