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...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.展开更多
文摘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.
