Solving Heterogeneous agent models in Continuous Time with Adaptive Sparse Grids

This paper proposes a new approach to numerically solving a wide class of heterogeneous agent models in continuous time using adaptive sparse grids. I combine the sparse finite difference method with the sparse finite volume method to solve the Hamilton-Jacobian-Bellman equation and Kolmogorov Forward equation, respectively. My algorithm automatically adapts grids and adds local resolutions in regions of the state space where both the value function and the distribution approximation errors remains large. I demonstrate the power of my approach in applications feature high-dimensional state spaces, occasionally binding constraints, lifecycle and overlapping generations.