$G$-martingale representation in the $G$-L'evy setting

TL;DR

This paper develops a decomposition theorem for martingales under sublinear expectation in the context of $G$-L'evy processes with finite activity, extending classical stochastic calculus to a nonlinear setting.

Contribution

It provides a novel $G$-martingale representation theorem in the $G$-L'evy setting, including continuous and jump components, without assuming drift.

Findings

Decomposition of $G$-martingales into Ito integrals and a non-increasing martingale

Extension of classical L'evy process results to the $G$-framework

Applicable to processes with finite activity and no drift

Abstract

In this paper we give the decomposition of a martingale under the sublinear expectation associated with a $G$-L'evy process X with finite activity and without drift. We prove that such a martingale consists of an Ito integral w.r.t. continuous part of a $G$-L'evy process, compensated Ito-L'evy integral w.r.t. jump measure associated with $X$ and a non-increasing continuous $G$-martingale starting at 0.