When the imartingale representation propertyi/ holds, we call any local martingale which realizes the representation a irepresentation processi/. There are two properties of the irepresentation processi/ which can greatly facilitate the computations under the imartingale representation propertyi/. On the one hand, the irepresentation processi/ is not unique and there always exists a irepresentation processi/ which is locally bounded and has pathwise orthogonal components outside of a predictable thin set. On the other hand, the jump measure of a irepresentation processi/ satisfies the ifinite predictable constrainti/, which implies the imartingale projection propertyi/. In this paper, we give a detailed account of these properties. As application, we will prove that, under the imartingale representation propertyi/, the ifull viabilityi/ of an expansion of market information flow implies the idrift multiplier assumptioni/.
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