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
Date Written: May 17, 2018
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: Suggested Citation