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

41 Pages Posted: 17 Jun 2019 Last revised: 12 Feb 2020

See all articles by Dirk Pflüger

Dirk Pflüger

University of Stuttgart - Institute for Parallel and Distributed Systems

Peter Schober

Goethe University Frankfurt - Department of Finance

Julian Valentin

University of Stuttgart - Institute for Parallel and Distributed Systems

Date Written: October 21, 2019

Abstract

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.

Keywords: curse of dimensionality, dynamic portfolio choice, discrete time dynamic programming, gradient-based optimization, spatially adaptive sparse grids, hierarchical B-splines

JEL Classification: C61, C63, G11

Suggested Citation

Pflüger, Dirk and Schober, Peter and Valentin, Julian, Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids (October 21, 2019). Available at SSRN: https://ssrn.com/abstract=3393524 or http://dx.doi.org/10.2139/ssrn.3393524

Dirk Pflüger

University of Stuttgart - Institute for Parallel and Distributed Systems ( email )

Keplerstraße 17
Stuttgart, D-70174
Germany

Peter Schober (Contact Author)

Goethe University Frankfurt - Department of Finance ( email )

House of Finance
Theodor-W.-Adorno Platz 3
Frankfurt am Main, Hessen 60323
Germany

Julian Valentin

University of Stuttgart - Institute for Parallel and Distributed Systems

Universitätsstr. 38
Stuttgart, 70569
Germany

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