The Two-Dimensional Tree–Grid Method

Abstract

In this paper, we introduce a novel, explicit, wide-stencil, two-dimensional (2D) tree–grid method for solving stochastic control problems (SCPs) with two space dimensions and one time dimension, or, equivalently, the corresponding Hamilton– Jacobi–Bellman equation. This new method can be seen as a generalization of the tree–grid method for SCPs with one space dimension that was recently developed by the authors. The method is unconditionally stable and no 2D interpolation is needed in the stencil construction. We prove the convergence of the method and exemplify it in our application to a two-factor uncertain volatility model.