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Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles
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In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected G-BSDEs with a lower obstacle that are monotone decreasing. By employing this approach, we establish the well-posedness of the solution of the doubly reflected G-BSDE with the weakest known conditions, and uncover its relationship with the fully nonlinear partial differential equation with double obstacles for the first time.
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Cited by 1 Pith paper
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Mind the jumps: when 2BSDEs meet semi-martingales
Semi-martingale second-order BSDEs with jumps are proved well-posed over a unified class of diffusions, pure-jump processes, and discrete-time processes, while the jump-measure integrands resist model-independent aggregation.
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