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

By Yongsheng Song. 2010

49 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1ce398688c69dc606c34214944c18c7b8fbe2760

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Citations in the corpus

Constructing Sublinear Expectations on Path Space (2012, background): “We recall that not all Borel-measurable random variables are quasi-continuous: for example, the main object under consideration, the volatility of the canonical process, is not quasi-continuous [25].”
A complete representation theorem for G-martingales (2012, methodology): “Unlike [26], we prove the estimates via PDE arguments.”
Backward stochastic differential equations driven by G-Brownian motion (2012, methodology): “Thanks to an original new norm introduced in Song [28, 2012] for decreasing G-martingales, a representation theorem of G-martingales in a complete subspace of LαG(ΩT ) has been obtained by Peng, Song and Zhang [24, 2012].”
Quasi-continuous random variables and processes under the G-expectation framework (2014, background): “5 This definition of quasi-continuous of a process is different from the ones in [15, 16].”