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<p>The paper investigates the multi-dimensional backward stochastic differential equations driven by <i>G</i>-Brownian motions (<i>G</i>-BSDEs) with random horizon. We first study the one-dimensional case with the help of the linearization method and quasi-continuous stopping times theory. Based on this, we establish the well-posedness result of the multi-dimensional case with diagonal generators through the Picard iteration argument under a univariate monotonicity assumption. In addition, the comparison principle and stability property are also discussed.</p>

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Multi-dimensional G-Backward Stochastic Differential Equations with Random Horizon

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Yiqing Lin,
  • Guomin Liu,
  • Yue Niu,
  • Falei Wang

摘要

The paper investigates the multi-dimensional backward stochastic differential equations driven by G-Brownian motions (G-BSDEs) with random horizon. We first study the one-dimensional case with the help of the linearization method and quasi-continuous stopping times theory. Based on this, we establish the well-posedness result of the multi-dimensional case with diagonal generators through the Picard iteration argument under a univariate monotonicity assumption. In addition, the comparison principle and stability property are also discussed.