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Mean Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Constraints
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In this paper, we study the backward stochastic differential equations driven by G-Brownian motion with double mean reflections, which means that the constraints are made on the law of the solution. Making full use of the backward Skorokhod problem with two nonlinear reflecting boundaries and the fixed-point theory, the existence and uniqueness of solutions are established. We also consider the case where the coefficients satisfy a non-Lipschitz condition using the Picard iteration argument only for the Y component. Moreover, some basic properties including a new version of comparison theorem and connection with a deterministic optimization problem are also obtained.
Forward citations
Cited by 2 Pith papers
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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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Quadratic BSDEs with double constraints driven by G-Brownian motion
Claims well-posedness for quadratic G-BSDEs with double mean reflections, but the proof silently drops the f term and does not prove the stated f-inclusive theorem.
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