Positivity Preserving Numerical Method for Optimal Portfolio in a Power Utility Two-Dimensional Regime-Switching Model
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.
This research is supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017.
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