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

When the martingale representation property holds, we call any local martingale which realizes the representation a representation process . There are two properties of the representation process which can greatly facilitate the computations under the martingale representation property . On the one hand, the representation process is not unique and there always exists a representation process which is locally bounded and has pathwise orthogonal components outside of a predictable thin set. On the other hand, the jump measure of a representation process satisfies the finite predictable constraint , which implies the martingale projection property . In this paper, we give a detailed account of these properties. As application, we will prove that, under the martingale representation property , the full viability of an expansion of market information flow implies the drift multiplier assumption .