Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators

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• 作者：ShengJun Fan ^{f_s_j@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60H10
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：109
• 期：Complete
• 页码：7-15
• 全文大小：380 K

文摘

This paper is devoted to solving a one-dimensional backward stochastic differential equation (BSDE in short) when the generator g$g$ has a semi-linear growth and a general growth in (y,z)$(y,z)$. This condition is not only strictly weaker than the linear growth condition of g$g$ in (y,z)$(y,z)$, but also the (weak) monotonicity and general growth condition of g$g$ in y$y$ together with the linear growth condition of g$g$ in z$z$. We establish, in this setting, three existence results on a solution and the minimal (maximal) solution to the BSDE, where the generator g$g$ may be discontinuous in y$y$. These results virtually unify and improve some existing results.