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Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Author:
Johannes Brumm   Simon Scheidegger  


Issue Date:
2014


Abstract(summary):

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 al- gorithm with piecewise multi-linear (hierarchical) basis functions. With increasing dimension, sparse grids grow considerably slower than stan- dard tensor product grids. In addition, the grid scheme we use is au- tomatically 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 com- bination of distributed and shared memory parallelization schemes. This parallelization enables us to efficiently use high-performance computing architectures such as 'Piz Daint' (CRAY XC30) at the Swiss National Supercomputing Centre. Numerical experiments show that our algorithm scales up nicely to more than one thousand compute nodes. To demon- strate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.


Page:
40


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