Numerical analysis of a finite difference scheme for optimal portfolio in a power utility regime-switching model

摘要

In this paper we propose a numerical method for solving regime-switching problem with power utility function. The model is a system of parabolic equations with non-linear gradient term and weakly coupled by exponential non-linearity. First, we approximate the gradient term, involving an auxiliary non-linear function, then we construct implicit-explicit finite difference discretization. We prove discrete comparison principle and on this base we establish minimum principle, i.e. we prove that the numerical solution has the same lower bound as the exact solution. Convergence result in maximal norm is obtained. Numerical results, confirming the theoretical statements are provided.