Numerical schemes for $G$--Expectations

TL;DR

This paper develops a discrete-time approximation for $G$-expectations, proves convergence as the time step approaches zero, and provides error estimates, advancing the numerical analysis of nonlinear expectation models.

Contribution

It introduces a discrete-time scheme for $G$-expectations, proves its convergence, and derives error bounds, extending previous work with a new approximation theorem for martingales.

Findings

Discrete-time $G$-expectation values converge to continuous $G$-expectation as time step decreases.

Error estimates for the convergence rate are established.

A strong approximation theorem for discrete martingales is developed.

Abstract

We consider a discrete time analog of $G$--expectations and we prove that in the case where the time step goes to 0 the corresponding values converge to the original $G$--expectation. Furthermore we provide error estimates for the convergence rate. This paper is continuation of [4]. Our main tool is a strong approximation theorem which we derive for general discrete time martingales.