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On RBSDELs with time-delayed generators and RCLL obstacle

  • Mohamed El Jamali ORCID logo EMAIL logo
Published/Copyright: March 28, 2025

Abstract

This paper delves into an in-depth analysis of the solution to a Reflected Backward Stochastic Differential Equation driven by a homogeneous Lévy process (RBSDEL in short) and characterized by a time-delayed generator, along with a lower obstacle Right Continuous Left-hand Limited (RCLL in short). Within our study, we present an a priori estimate and establish the existence and uniqueness of this solution using article [M. El Jamali and M. El Otmani, BSDE with rcll reflecting barrier driven by a Lévy process, Random Oper. Stoch. Equ. 28 2020, 1, 63–77] and the fixed-point theorem.

MSC 2020: 60H05; 60H07

Communicated by Nikolai Leonenko


References

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Received: 2024-07-16
Accepted: 2024-10-11
Published Online: 2025-03-28
Published in Print: 2025-09-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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