Existence, uniqueness and comparison theorem on unbounded solutions of general time-interval BSDEs with sub-quadratic generators  

作　　者：Chuang Gu Yan Wang Shengjun Fan 

机构地区：[1]School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2025年第1期31-58,共28页概率、不确定性与定量风险(英文)

摘　　要：This study addresses the existence, uniqueness, and comparison theorem forunbounded solutions of one-dimensional backward stochastic differential equations (BSDEs)with sub-quadratic generators, considering both finite and infinite terminal times. Initially,we establish the existence of unbounded solutions for BSDEs where the generator gsatisfies a time-varying one-sided linear growth condition in the first unknown variable yand a time-varying sub-quadratic growth condition in the second unknown variable z. Next,the uniqueness and comparison theorems for unbounded solutions are proven under a timevaryingextended convexity assumption. These findings extend the results in [12] to thegeneral time-interval BSDEs. Finally, we propose and verify several sufficient conditionsfor ensuring uniqueness, utilizing innovative approaches applied for the first time, even inthe context of finite time-interval BSDEs.

关 键 词：Existence and uniqueness Unboundedd solutions Backward stochastic differential equation Comparison theorem General time-interval Sub-quadratic growth 

分 类 号：O211[理学—概率论与数理统计]