EXISTENCE, UNIQUENESS AND COMPARISONS FOR BSDES IN GENERAL SPACES

• 成果类型: Article
• 署名作者: Cohen, Samuel N.; Elliott, Robert J.
• 署名单位: University of Oxford; University of Adelaide; University of Calgary
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP679
• 发表日期: 2012
• 页码: 2264-2297
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; consistent

摘要

We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time and allow discrete processes to be embedded with continuous ones. We also present conditions for a comparison theorem and hence construct time consistent nonlinear expectations in these general spaces.