A numerical study for optimal portfolio regime-switching model I. 2D Black-Scholes equation with an exponential non-linear term

A system of weakly coupled semilinear parabolic equations of optimal portfolio in a regime-switching model is suggested by Valdez and Vargiolu (2013). To study the effects from the typical features of the system, i.e. the boundary degeneration, exponential non-linearity and mixed derivative, we consider a representative 2D Black-Scholes semilinear equation model. We construct and analyze sign preserving, flux limited finite difference schemes for the scalar problem. Numerical experiments are discussed.