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arXiv · 2407.17768

$G$-BSDEs with mean constraints in time-dependent intervals

Zihao Gu·Hui Zhao
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Abstract

In this paper, we study a collection of mean-reflected backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs), where $G$-expectations are constrained in some time-dependent intervals. To establish well-posedness results, we firstly construct a backward Skorokhod problem with sublinear expectation, and then apply that in the study of doubly mean-reflected $G$-BSDEs involving Lipschitz and quadratic generators under bounded and unbounded terminal conditions. Also we utilize fixed-point argumentations and $θ$-methods while solving these equations. Finally, we extend the results to multi-dimensional doubly mean-reflected $G$-BSDEs with diagonal generators.

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Zihao Gu, Hui Zhao. 2024-07-25. $G$-BSDEs with mean constraints in time-dependent intervals. https://arxiv.org/abs/2407.17768

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