Some properties on $G$-evaluation and its applications to $G$-martingale decomposition

Abstract

In this article, a sublinear expectation induced by $G$-expectation is introduced, which is called $G$-evaluation for convenience. As an application, we prove that any $\xi \in L_G^{\beta }({\Omega }_T)$ with some $\beta >1$ the decomposition theorem holds and any $\beta >1$ integrable symmetric $G$-martingale can be represented as an It${\hat{o}}^{\prime }s$ integral w.r.t $G$-Brownian motion. As a byproduct, we prove a regular property for $G$-martingale: Any $G$-martingale $\{M_t\}$ has a quasi-continuous version

22 pages

References in corpus (3)

• Martingale Representation Theorem for the G-expectation
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Properties of hitting times for $G$-martingale

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