A Complete Representation Theorem for $G$-martingales

Details A Complete Representation Theorem for $G$-martingales A Complete Representation Theorem for $G$-martingales

2012-01-12

arxiv.org/abs/1201.2629v1

Mathematics

Probability

22 pages

Scientific paper

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 \cite{Song-unique}.

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