TY  - JOUR
A1  - Schober, Peter
A1  - Valentin, Julian
A1  - Pflüger, Dirk
T1  - Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids
T2  - Computational economics
N2  - 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.
KW  - Curse of dimensionality
KW  - Dynamic portfolio choice
KW  - Discrete time dynamic programming
KW  - Gradient-based optimization
KW  - Spatially adaptive sparse grids
KW  - Hierarchical B-splines
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63777
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-637774
SN  - 1572-9974
N1  - 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).
VL  - 59
IS  - 1
SP  - 185
EP  - 224
PB  - Springer Science + Business Media B.V. ; Proquest
CY  - Dordrecht [u.a.] ; [S.l.]
ER  -