The Numerical Properties of G-heat equation and Related Application

TL;DR

This paper studies the numerical convergence of the G-heat equation, a nonlinear PDE with uncertain volatility, proving convergence of Newton iteration and stability of discretization methods.

Contribution

It establishes the convergence and stability of numerical methods for the G-heat equation, extending classical PDE analysis to uncertain volatility models.

Findings

Newton iteration converges for the G-heat equation

Fully implicit discretization is monotone and stable

Discretization converges to the viscosity solution

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.