E-martingales and their applications in mathematical finance

• 成果类型: Article
• 署名作者: Choulli, T; Krawczyk, L; Stricker, C
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Marie et Louis Pasteur; University of Warsaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 853-876
• 关键词: follmer-schweizer; DECOMPOSITION; THEOREM; LAWS

摘要

After introducing a new concept, the notion of E-martingale, we extend the well-known Doob inequality (for 1 < p < + infinity) and the Burkholder-Davis-Gundy inequalities (for p = 2) to E-martingales. By means of these inequalities, we give sufficient conditions for the closedness of a space of stochastic integrals with respect to a fixed R-d-valued semimartingale, a question which arises naturally in the applications to financial mathematics. We also provide a necessary and sufficient condition for the existence and uniqueness of the Follmer-Schweizer decomposition.