The Numerical Properties of G-heat equation and Related Application

Abstract

In this paper, we consider the numerical convergence of G-heat equation which was first introduced by Peng. The G-heat equation extends the classical heat equation with uncertain volatility. For G-heat equation is nonlinear partial differential equation(PDE), we prove that the Newton iteration is convergence and the fully implicit discretization is monotone and stable. Then, we have the fully implicit discretization convergence to the viscosity solution of a G-heat equation.