$\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients

Badr Elmansouri; Mohamed El Otmani

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arXiv · 2501.15600

$\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients

Badr Elmansouri·Mohamed El Otmani

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Abstract

We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness of solutions in $\mathbb{L}^p$ for $p \in (1,2]$. Our results apply to generators that are stochastic monotone in the $y$-variable, stochastic Lipschitz in the $z$-variable, and satisfy a general stochastic linear growth condition.

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Badr Elmansouri, Mohamed El Otmani. 2025-01-26. $\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients. https://arxiv.org/abs/2501.15600

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