Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids

2019 ◽  
Author(s):  
Dirk Pflüger ◽  
Peter Schober ◽  
Julian Valentin
Keyword(s):  
Portfolio Choice ◽  
Choice Models ◽  
Sparse Grids ◽  
High Dimensional ◽  
B Splines ◽  
Dynamic Portfolio ◽  
Dynamic Portfolio Choice

scholarly journals Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids

2021 ◽  
Author(s):  
Peter Schober ◽  
Julian Valentin ◽  
Dirk Pflüger
Keyword(s):  
Portfolio Choice ◽  
Value Function ◽  
Choice Models ◽  
Sparse Grids ◽  
Continuous Control ◽  
B Splines ◽  
Gradient Based ◽  
Dynamic Portfolio ◽  
Dynamic Portfolio Choice ◽  
The Value Function

AbstractDiscrete 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.

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