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<p>In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by <i>G</i>-Brownian motion (<i>G</i>-BSDE). Our approach involves approximating the solution through a family of penalized reflected <i>G</i>-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 <i>G</i>-BSDE with the weakest known conditions, and uncover its relationship with the fully nonlinear partial differential equation with double obstacles for the first time.</p>

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Doubly reflected backward SDEs driven by G-Brownian motions and fully nonlinear PDEs with double obstacles

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月22日

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  • Hanwu Li,
  • Ning Ning

摘要

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.