2019/12/10 by Constantinos Kardaras, Johannes Ruf, Kardaras, Constantinos +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1912.04652
openalex publication_date 2019/12/10 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We analyse the structure of local martingale deflators projected on smaller\nfiltrations. In a general continuous-path setting, we show that the local\nmartingale part in the multiplicative Doob-Meyer decomposition of projected\nlocal martingale deflators are themselves local martingale deflators in the\nsmaller information market. Via use of a Bayesian filtering approach, we\ndemonstrate the exact mechanism of how updates on the possible class of models\nunder less information result in the strict supermartingale property of\nprojections of such deflators. Finally, we demonstrate that these projections\nare unable to span all possible local martingale deflators in the smaller\ninformation market, by investigating a situation where market completeness is\nnot retained under filtration shrinkage.\n