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
This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic g...This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.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.
基金supported by the National Natural Science Foundation of China(Nos.11631004,12031009).
文摘This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.
