Minimal and maximal bounded solutions for quadratic BSDEs with stochastic conditions
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2065-2079
Published online July 6, 2017
Printed November 30, 2017
Shengjun Fan, Huanhuan Luo
China University of Mining and Technology, China University of Mining and Technology
Abstract : 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.
Keywords : backward stochastic differential equations, minimal and maximal bounded solutions, stochastic conditions, quadratic growth
MSC numbers : 60H10
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