Doubly reflected BSDEs driven by Inhomogeneous simple Levy processes: Applications to generalized Dynkin games

Badr Elmansouri; Ibtissam Hdhiri

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arXiv · 2607.18531

Doubly reflected BSDEs driven by Inhomogeneous simple Levy processes: Applications to generalized Dynkin games

Badr Elmansouri·Ibtissam Hdhiri

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Abstract

We study doubly reflected backward stochastic differential equations with jumps and two completely separated right-continuous with left limits barriers in a filtration generated by an inhomogeneous Levy process. We establish existence and uniqueness results under a stochastic Lipschitz condition on the driver by means of a penalization method. We also prove a comparison principle and present two closely related applications. The first concerns the nonlinear valuation of an American game option in such a Levy market, while the second addresses the associated generalized Dynkin game under nonlinear expectation. Moreover, under suitable semicontinuity assumptions on the barriers, we establish the existence of a saddle point for the game.

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Badr Elmansouri, Ibtissam Hdhiri. 2026-07-20. Doubly reflected BSDEs driven by Inhomogeneous simple Levy processes: Applications to generalized Dynkin games. https://arxiv.org/abs/2607.18531

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