Backward stochastic differential equations driven by optional semimartingales with conditional reflecting and regulated barrier
Year: 2026
Type: article
Abstract: We introduce a new type of reflected backward stochastic differential equations (BSDEs) driven by optional semimartingale process with lower optional barrier and so-called regulated trajectories for which the reflection constraint is imposed on its main solution component, denoted as Y by convention, but in terms of its conditional expectation 𝔼 [ Y t | 𝒢 t ] {\mathbb{E}[Y_{t}|\mathcal{G}_{t}]} on a general sub-filtration { 𝒢 t } {\{\mathcal{G}_{t}\}} . This paper is devoted to the question of existence and uniqueness of strong solutions of the conditional RBSDE under Lipschitz conditions and by combining the Snell envelope method with Skorokhod lemma. Thus the connection between optimal stopping problems and linear conditional RBSDEs is given. Moreover, an example of applications to mathematical finance is presented.
Authors: Mouna Haddadi, Khadija Akdim
Institutions: University of Hassan II Casablanca, Cadi Ayyad University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7155643423