SEMIMARTINGALES AND SHRINKAGE OF FILTRATION

• 成果类型: Article
• 署名作者: Bielecki, Tomasz R.; Jakubowski, Jacek; Jeanblanc, Monique; Nieweglowski, Mariusz
• 署名单位: Illinois Institute of Technology; University of Warsaw; Universite Paris Saclay; Warsaw University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1621
• 发表日期: 2021
• 页码: 1376-1402
• 关键词: local martingales

摘要

We consider a complete probability space (Omega, F, P), which is endowed with two filtrations, G and F, assumed to satisfy the usual conditions and such that F subset of G. On this probability space we consider a real valued Gsemimartingale X. The purpose of this work is to study the following two problems: A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X. B. If X is a special G-semimartingale but not F-adapted, compute the F-semimartingale characteristics of the F-optional projection of X in terms of the G-canonical decomposition and the G-semimartingale characteristics of X. In this paper problem B is solved under the assumption that the filtration F is immersed in G. Beyond the obvious mathematical interest, our study is motivated by important practical applications in areas such as finance and insurance (cf. Structured Dependence Between Stochastic Processes (2020) Cambridge Univ. Press).