-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients
Pub. online: 4 November 2025
Type: Research Article
Open Access
Open Access
Received
28 January 2025
28 January 2025
Revised
28 August 2025
28 August 2025
Accepted
28 October 2025
28 October 2025
Published
4 November 2025
4 November 2025
Abstract
Multidimensional generalized backward stochastic differential equations (GBSDEs) are studied within a general filtration that supports a Brownian motion under weak assumptions on the associated data. The existence and uniqueness of solutions in ${\mathbb{L}^{p}}$ for $p\in (1,2)$ are established. The 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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