2015/05/04 by Shiqi Song, Song, Shiqi
Economics, Econometrics and Finance · #60G07 #60G40 #60G44 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1505.00560
openalex publication_date 2015/05/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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. Actually, on the one hand, the representation process is not unique and there always exists a representation process which is locally bounded and has pathwisely orthogonal components outside of a predictable thin set. On the other hand, the jump measure of a representation process satisfies the finite predictable constraint. In this paper, we give a detailed account of these two 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.