The Numerical Properties of G-heat equation and Related Application
Provides numerical analysis for a nonlinear PDE arising from uncertain volatility, relevant to financial mathematics and stochastic control.
This paper proves the convergence of Newton iteration and the monotonicity and stability of fully implicit discretization for the G-heat equation, establishing convergence to its viscosity solution.
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.