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Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids
(2021)
Discrete time dynamic programming to solve dynamic portfolio choice models has three immanent issues: firstly, the curse of dimensionality prohibits more than a handful of continuous states. Secondly, in higher dimensions, even regular sparse grid discretizations need too many grid points for sufficiently accurate approximations of the value function. Thirdly, the models usually require continuous control variables, and hence gradient-based optimization with smooth approximations of the value function is necessary to obtain accurate solutions to the optimization problem. For the first time, we enable accurate and fast numerical solutions with gradient-based optimization while still allowing for spatial adaptivity using hierarchical B-splines on sparse grids. When compared to the standard linear bases on sparse grids or finite difference approximations of the gradient, our approach saves an order of magnitude in total computational complexity for a representative dynamic portfolio choice model with varying state space dimensionality, stochastic sample space, and choice variables.
Correction to: Computational Economics https://doi.org/10.1007/s10614-020-10061-x
The original publication has been updated. In the original publication of this article, under the Introduction heading section, the corrections to the second paragraph’s inline equation were not incorporated. The author’s additional corrections have also been incorporated. The publisher apologizes for the error made during production.