Properties of hitting times for $G$-martingale

Abstract

In this article, we consider the properties of hitting times for $G$-martingale and the stopped processes. We prove that the stopped processes for $G$-martingales are still $G$-martingales and that the hitting times for a class of $G$-martingales including $G$-Brownian motion are quasi-continuous. As an application, we improve the $G$-martingale representation theorems in [Song10].

arXiv comment13 pages

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• Some properties on $G$-evaluation and its applications to $G$-martingale decomposition
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Cited by in corpus (7)

• Some properties on $G$-evaluation and its applications to $G$-martingale decomposition
• Note on Viscosity Solution of Path-Dependent PDE and G-Martingales
• Optimal Stopping under Nonlinear Expectation
• Financial markets with volatility uncertainty
• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• Characterizations of processes with stationary and independent increments under $G$-expectation
• A weighted central limit theorem under sublinear expectations