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<p>We consider mean-field reflected generalized non-linear backward stochastic differential equations with jumps. We prove the existence and uniqueness of the solution when the coefficients satisfy stochastic conditions and the barrier is right continuous with left limits. However, in a Markovian framework, where it is coupled with a forward reflected McKean–Vlasov equation with jumps, our result offers a probabilistic interpretation for solutions to non-local Integro-Partial Differential Equation with non-linear Neumann boundary conditions.</p>

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Mean-Field Reflected Generalized BSDEs with Jumps Under Stochastic Conditions

  • 期刊论文

  • 发表日期：

    2025年3月28日

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  • Mohammed Elhachemy

摘要

We consider mean-field reflected generalized non-linear backward stochastic differential equations with jumps. We prove the existence and uniqueness of the solution when the coefficients satisfy stochastic conditions and the barrier is right continuous with left limits. However, in a Markovian framework, where it is coupled with a forward reflected McKean–Vlasov equation with jumps, our result offers a probabilistic interpretation for solutions to non-local Integro-Partial Differential Equation with non-linear Neumann boundary conditions.