One-dimensional BSDEs with finite and infinite time horizons

详细信息    查看全文

• 作者：ShengJun Fan ; ^a ; ^{shengjunfan@yahoo.cn} ; Long Jiang^a ; ^{jianglong365@hotmail.com} ; DeJian Tian^a ; ^{tiandejian1985@163.com}
• 关键词：Backward stochastic differential equation ; Comparison theorem ; Existence and uniqueness ; Uniformly continuous generator ; Monotonic generator
• 刊名：Stochastic Processes and their Applications
• 出版年：2011
• 出版时间：March 2011
• 年：2011
• 卷：121
• 期：3
• 页码：427-440
• 全文大小：245 K

文摘

This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of BSDEs with linear growth generators. Then, we establish a general comparison theorem for solutions of this kind of BSDEs with weakly monotonic and uniformly continuous generators. Finally, we give an existence and uniqueness result for solutions of this kind of BSDEs with uniformly continuous generators.