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When the \textit{martingale representation property} holds, we call any localmartingale which realizes the representation a \textit{representation process}.There are two properties of the \textit{representation process} which cangreatly facilitate the computations under the \textit{martingale representationproperty}. Actually, on the one hand, the \textit{representation process} isnot unique and there always exists a \textit{representation process} which islocally bounded and has pathwisely orthogonal components outside of apredictable thin set. On the other hand, the jump measure of a\textit{representation process} satisfies the \textit{finite predictableconstraint}. In this paper, we give a detailed account of these two properties.As application, we will prove that, under the \textit{martingale representationproperty}, the \textit{full viability} of an expansion of market informationflow implies the \textit{drift multiplier assumption}.

Martingale representation processes and applications in the market viability with information flow expansion