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arXiv · 1201.2629

A Complete Representation Theorem for $G$-martingales

Shige Peng·Yongsheng Song·Jianfeng Zhang
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Abstract

In this paper we establish a complete representation theorem for $G$-martingales. Unlike the existing results in the literature, we provide the existence and uniqueness of the second order term, which corresponds to the second order derivative in Markovian case. The main ingredient of the paper is a new norm for that second order term, which is based on an operator introduced by Song [26].

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Shige Peng, Yongsheng Song, Jianfeng Zhang. 2013-01-22. A Complete Representation Theorem for $G$-martingales. https://arxiv.org/abs/1201.2629

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