MCRF
Quadratic BSDEs with mean reflection
Hélène Hibon Ying Hu Yiqing Lin Peng Luo Falei Wang
Mathematical Control & Related Fields 2018, 8(3&4): 721-738 doi: 10.3934/mcrf.2018031

The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the $z$ argument. This work is the sequel of [6] in which a notion of BSDEs with mean reflection is developed to tackle the super-hedging problem under running risk management constraints. By the contraction mapping argument, we first prove that the quadratic BSDE with mean reflection admits a unique deterministic flat local solution on a small time interval whenever the terminal value is bounded. Moreover, we build the global solution on the whole time interval by stitching local solutions when the generator is uniformly bounded with respect to the $y$ argument.

keywords: BSDEs mean reflection quadratic generators BMO martingales
MCRF
Nonlinear backward stochastic evolutionary equations driven by a space-time white noise
Ying Hu Shanjian Tang
Mathematical Control & Related Fields 2018, 8(3&4): 739-751 doi: 10.3934/mcrf.2018032

We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and then give an existence and uniqueness result for nonlinear backward stochastic evolutionary equations. A dual argument plays a crucial role in the proof of these results. Finally, an example is given to illustrate the existence and uniqueness result.

keywords: Backward stochastic evolutionary equation space-time white noise well solvability a priori estimate dual argument

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