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

Badr Elmansouri; Ibtissam Hdhiri

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

Probability 2026-07-20 v1

Authors: Badr Elmansouri , Ibtissam Hdhiri

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.

Keywords

doubly reflected BSDEs Lévy processes Dynkin games nonlinear expectation American game options penalization method

Cite

@article{arxiv.2607.18531,
  title  = {Doubly reflected BSDEs driven by Inhomogeneous simple Levy processes: Applications to generalized Dynkin games},
  author = {Badr Elmansouri and Ibtissam Hdhiri},
  journal= {arXiv preprint arXiv:2607.18531},
  year   = {2026}
}