arXiv subjects

Anas Ouknine

Publications and source records attributed to Anas Ouknine.

3 recordsLinked to original sources

arXiv2025

Multivalued backward stochastic differential equations with jumps and moving boundary

We prove existence and uniqueness for a one-dimensional multivalued backward stochastic differential equation with jumps. The equation involves a time-indexed family of maximal monotone operators $k_t(\cdot)$ associated with increasing functions $k(t,\cdot)$ taking values in $\mathbb{R}_-$ and having domains that are intervals with time-dependent boundaries. Existence is obtained by a penalization method under a Lipschitz condition on the driver in $(y,z)$, a monotonicity condition in the jump parameter $\psi$, square-integrability of the terminal condition and the driver, and local-in-time integrability conditions on $k(\cdot,y)$. We also address the extension to the case where the operators $k_t(\cdot)$ act on unbounded intervals.

math.PR↗

arXiv2025

Admitted symmetries of Backward Stochastic Differential Equations

In this article, we introduce the concept of admitted Lie group of transformations for both backward stochastic differential equations (BSDEs) and forward backward stochastic differential equations (FBSDEs), following the approach of Meleshko et al. An application to BSDE is presented.

math.PR↗

arXiv2025

Symmetry Analysis of Semi-Linear Partial Differential Equations and Forward Backward Stochastic Differential Equations

We examine the Lie symmetries of a semi-linear partial differential equations and their connections to the analogous symmetries of the forward-backward stochastic differential equations (FBSDEs), established through the generalized Feynman-Kac formula.

math.PR↗