Semimartingales and Shrinkage of Filtration

2018/03/09 by Bielecki, Tomasz R., Jakubowski, Jacek, Jeanblanc, Monique +1
#60G99 #60H99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1803.03700

Abstract

We consider a complete probability space (Ω,F,ℙ), which is endowed with two filtrations, \mathbbG and \mathbbF, assumed to satisfy the usual conditions and such that \mathbbF ⊂ \mathbbG. On this probability space we consider a real valued special \mathbbG-semimartingale X. The purpose of this work is to study the following two problems: A. If X is \mathbbF-adapted, compute the \mathbbF-semimartingale characteristics of X in terms of the \mathbbG-semimartingale characteristics of X. B. If X is not \mathbbF-adapted, given that the \mathbbF-optional projection of X is a special semimartingale, compute the \mathbbF-semimartingale characteristics of \mathbbF-optional projection of X in terms of the \mathbbG-canonical decomposition and \mathbbG-semimartingale characteristics of X.

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