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

Laboratoire de Mathématiques et Modélisation d'Evry, Université d'Evry Val D'Essonne, France

^* E-mail: shiqi.song@univ-evry.fr

Abstract

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.