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This paper is devoted to the minimal and maximal bounded solutions for general time interval quadratic backward stochastic differential equations with stochastic conditions. A general existence result is established by the method of convolution, the exponential transform, Girsanov's transform and a priori estimates, where the terminal time is allowed to be finite or infinite, and the generator $g$ is allowed to have a stochastic semi-linear growth and a general growth in $y$, and a quadratic growth in $z$. This improves some existing results at some extent. Some new ideas and techniques are also applied to prove it.
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참고문헌 (19)
참고문헌 신청
E. Pardoux / 1990 / Adapted solution of a backward stochastic differential equations / Systems Control Lett 14 (1) : 55 ~ 61
F. Delbaen / 2011 / On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions / Ann. Inst. Henri Poincare Probab. Stat 47 (2)
F. Delbaen / 2015 / On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case / Discrete Contin. Dyn. Sys
J. Lepeltier / 1997 / Backward stochastic differential equations with contin-uous coefficient / Statist. Probab. Lett 32 (4) : 425 ~ 430
J. Lepeltier / 1998 / Existence for BSDE with superlinear-quadratic coefficient / Stochastics 63 (3-4) : 227 ~ 240
F. Delbaen / 2011 / On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions / Ann. Inst. Henri Poincare Probab. Stat 47 (2)
F. Delbaen / 2015 / On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case / Discrete Contin. Dyn. Sys
J. Lepeltier / 1997 / Backward stochastic differential equations with contin-uous coefficient / Statist. Probab. Lett 32 (4) : 425 ~ 430
J. Lepeltier / 1998 / Existence for BSDE with superlinear-quadratic coefficient / Stochastics 63 (3-4) : 227 ~ 240
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