Positivity preserving numerical method for optimal portfolio in a power utility two-dimensional regime-switching model

Abstract

We consider a two-dimensional regime switching model with power utility function. The problem is a system of parabolic partial differential equations with non-linear gradient terms and weakly coupled by non-linear exponential terms. We establish lower bounds for the solutions and then we construct an adequate finite difference method, preserving the qualitative properties of the exact solution. Finally, we present and discuss numerical results.