Solving portfolio problems with the Smolyak-parameterized expectations algorithm

We propose a new numerical method to solve stochastic models that combines the parameterized expectations (PEA) and the Smolyak algorithms. This method is especially convenient to address problems with occasionally binding constraints (a feature inherited from PEA) and/or a large number of state variables (a feature inherited from Smolyak), i.e. DSGE models that incorporate portfolio problems and incomplete markets. We describe the proposed Smolyak-PEA algorithm in the context of a one-country stochastic neoclassical growth model and compare its accuracy with that of a standard PEA collocation algorithm. Despite estimating fewer parameters, the former is able to reach the high accuracy levels of the latter. We further illustrate the working of this algorithm in a two-country neoclassical model with incomplete markets and portfolio choice. Again, the Smolyak-PEA algorithm approximates the solution of the problem with a high degree of accuracy. Finally, we show how this algorithm can efficiently incorporate both occasionally binding constraints and a partial information approach