Dynamic Programming in Continuous Time with Adaptive Sparse Grids

This paper proposes a new approach to dynamic programming in continuous time using adaptive sparse grids. The standard finite-difference method, used to solve differential equations on uniform grids, fails on sparse grids. Our paper presents a sparse finite-difference method that leads to consistent solutions on a broad class of non-uniform grids. We demonstrate the power and versatility of our approach across a wide range of economic applications that feature high-dimensional state spaces, occasionally-binding constraints, life-cycles and overlapping generations, kinks and non-convexities, discrete choice, free boundaries, and dynamic games. A code repository accompanies this paper and provides a general-purpose library to solve continuous-time dynamic programming problems on adaptive sparse grids