Solving Dynamic Portfolio Choice Models in Discrete Time Using Spatially Adaptive Sparse Grids

Electronic version of an article published in Sparse Grids and Applications - Miami 2016 (Lecture Notes in Computational Science and Engineering, Vol 123), Garcke J., Pflüger D., Webster C., Zhang G. (Eds), Springer, Cham 2018. ISBN 9783319754253

32 Pages Posted: 17 Nov 2017 Last revised: 13 Mar 2019

See all articles by Peter Schober

Peter Schober

Goethe University Frankfurt - Department of Finance

Date Written: May 17, 2018

Abstract

In this paper, I propose a dynamic programming approach with value function iteration to solve Bellman equations in discrete time using spatially adaptive sparse grids. In doing so, I focus on Bellman equations used in finance, specifically to model dynamic portfolio choice over the life cycle. Since the complexity of the dynamic programming approach --- and other approaches --- grows exponentially in the dimension of the (continuous) state space, it suffers from the so called curse of dimensionality. Approximation on a spatially adaptive sparse grid can break this curse to some extent. Extending recent approaches proposed in the economics and computer science literature, I employ local linear basis functions to a spatially adaptive sparse grid approximation scheme on the value function. As economists are interested in the optimal choices rather than the value function itself, I discuss how to obtain these optimal choices given a solution to the optimization problem on a sparse grid. I study the numerical properties of the proposed scheme by computing Euler equation errors to an exemplary dynamic portfolio choice model with varying state space dimensionality.

Keywords: Dynamic Portfolio Choice, Discrete Time Dynamic Programming, Spatially Adaptive Sparse Grids, High Dimensional Models

JEL Classification: C61, C63, G11

Suggested Citation

Schober, Peter, Solving Dynamic Portfolio Choice Models in Discrete Time Using Spatially Adaptive Sparse Grids (May 17, 2018). Electronic version of an article published in Sparse Grids and Applications - Miami 2016 (Lecture Notes in Computational Science and Engineering, Vol 123), Garcke J., Pflüger D., Webster C., Zhang G. (Eds), Springer, Cham 2018. ISBN 9783319754253, Available at SSRN: https://ssrn.com/abstract=3071570

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

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