Uniqueness of the representation for $G$-martingales with finite variation

Yongsheng Song (Chinese Academy of Sciences, Beijing)

Abstract


Letting $\{\delta_n\}$ be a refining sequence of Rademacher functions on the interval $[0,T]$, we introduce a functional on processes in the $G$-expectation space by [d(K)=\limsup_n\hat{E}[\int_0^T\delta_n(s)dK_s].\] We prove that $d(K)>0$ if $K_t=\int_0^t\eta_sd\langle B\rangle_s$ with nontrivial $\eta\in M^1_G(0,T)$ and that $d(K)=0$ if $K_t=\int_0^t\eta_sds$ with $\eta\in M^1_G(0,T)$. This implies the uniqueness of the representation for $G$-martingales with finite variation, which is the main purpose of this article.

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Pages: 1-15

Publication Date: March 19, 2012

DOI: 10.1214/EJP.v17-1890

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