38. Parallelized Dimensional Decomposition for Dynamic Stochastic Economic Models
Authors: Aryan Eftekhari (University of Lugano)Olaf Schenk (University of Lugano)Simon Scheidegger (University of Zurich)
Abstract: This project explores a technique called Dimensional Decomposition, which allows for the separation of a function into a finite number of lower-dimensional component functions. The method leverages the lack of input-output correlation to effectively reduce the dimensionality of the problem. This program has been integrated with a sparse grid approximation to form an efficient approximation method referred to DDSG (dimensional decomposition with sparse grid). Due to the intrinsic separability and hierarchical construction, in both dimensional decomposition and sparse grid, a highly parallelizable framework has been developed. This framework has been applied in the context of computational economics, in which we provide an efficient solution method for high-dimensional dynamic stochastic models. Our findings show that DDSG can effectively capture model dynamics with relatively low-dimensional component functions, thus mitigating the so-called "curse of dimensionality".
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