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

  • 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.
Author:Peter Schober, Julian Valentin, Dirk Pflüger
Parent Title (English):Computational economics
Publisher:Springer Science + Business Media B.V. ; Proquest
Place of publication:Dordrecht [u.a.] ; [S.l.]
Document Type:Article
Date of Publication (online):2021/01/04
Date of first Publication:2021/01/04
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/06/27
Tag:Curse of dimensionality; Discrete time dynamic programming; Dynamic portfolio choice; Gradient-based optimization; Hierarchical B-splines; Spatially adaptive sparse grids
Page Number:40
First Page:185
Last Page:224
Open Access funding enabled and organized by Projekt DEAL. This work was supported by funding from the German Investment and Asset Management Association (BVI), the Juniorprofessurenprogramm of the Landesstiftung Baden-Württemberg, and the DFG (Cluster of Excellence SimTech EXC310/EXC2075).
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoCreative Commons - Namensnennung 4.0