INVARIANCE TIMES

• 成果类型: Article
• 署名作者: Crepey, Stephane; Song, Shiqi
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1174
• 发表日期: 2017
• 页码: 4632-4674
• 关键词: Counterparty risk; enlargements; filtrations; valuation; arbitrage

摘要

On a probability space (Omega, A, Q), we consider two filtrations F subset of G and a G stopping time theta such that the G predictable processes coincide with F predictable processes on (0,theta]. In this setup, it is well known that, for any F semimartingale X, the process X theta- (X stopped right before theta) is a G semimartingale. Given a positive constant T, we call theta an invariance time if there exists a probability measure P equivalent to Q on F-T such that, for any (F, P) local martingale X, X theta- is a (G, Q) local martingale. We characterize invariance times in terms of the (F, Q) Azema supermartingale of theta and we derive a mild and tractable invariance time sufficiency condition. We discuss invariance times in mathematical finance and BSDE applications.