2019/02/18 by Léo Neufcourt, Neufcourt, Léo, Philip Protter +1
Economics, Econometrics and Finance · Social Sciences · #60G07 #60G35 #60G48 #91G10 #Credit Risk and Financial Regulations #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1902.06780
openalex publication_date 2019/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Itô processes to remain Itô processes in the enlarged filtration. This has significance in applications to Mathematical Finance.