Expansion of a filtration with a stochastic process: the information drift
Probability
2020-02-18 v2
Abstract
When expanding a filtration with a stochastic process it is easily possible for semimartingale no longer to remain semimartingales in the enlarged filtration. Y. Kchia and P. Protter indicated a way to avoid this pitfall in 2015, but they were unable to give the semimartingale decomposition in the enlarged filtration except for special cases. We provide a way to compute such a decomposition, and moreover we provide a sufficient condition for It\^o processes to remain It\^o processes in the enlarged filtration. This has significance in applications to Mathematical Finance.
Cite
@article{arxiv.1902.06780,
title = {Expansion of a filtration with a stochastic process: the information drift},
author = {Léo Neufcourt and Philip Protter},
journal= {arXiv preprint arXiv:1902.06780},
year = {2020}
}