PROGRESSIVE ENLARGEMENTS OF FILTRATIONS WITH PSEUDO-HONEST TIMES

• 成果类型: Article
• 署名作者: Li, Libo; Rutkowski, Marek
• 署名单位: University of Sydney; Warsaw University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP955
• 发表日期: 2014
• 页码: 1509-1553
• 关键词: probability; models

摘要

We deal with various alternative decompositions of F-martingales with respect to the filtration G, which represents the enlargement of a filtration F by a progressive flow of observations of a random time that either belongs to the class of pseudo-honest times or satisfies the extended density hypothesis. Several related results from the existing literature are revisited and essentially extended. Results on G-semimartingale decompositions of F-local martingales are crucial for applications in financial mathematics, most notably in the context of credit risk modeling and the study of insider trading where the enlarged filtration plays a vital role. We outline potential applications of our results to problems arising in financial mathematics.