RBSDEs with optional barriers: monotone approximation

Siham Bouhadou; Astrid Hilbert; Youssef Ouknine

doi:10.3934/puqr.2022005

Article Contents

2022, Volume 7, Issue 2: 67-84. Doi: 10.3934/puqr.2022005

This issue Previous Article Next Article A note on the cluster set of the law of the iterated logarithm under sub-linear expectations

RBSDEs with optional barriers: monotone approximation

1.
Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Bd. Prince My Abdellah, B.P. 2390, 40000 Marrakech, Morocco
2.
Department of Mathematics, Linnaeus University, Vaxjo 351 95, Sweden
3.
Africa Business School, Mohammed VI Polytechnic University, Lot 660, Hay Moulay Rachid Ben Guerir, 43150, Morocco

^*Corresponding author
^*Corresponding author

Received: July 2021

Accepted: April 03, 2022

Early access: June 2022

Published: June 2022

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Abstract

In this short note we consider reflected backward stochastic differential equations (RBSDEs) with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous. In this case, the barrier is represented as a nondecreasing limit of right continuous with left limit (RCLL) barriers. We combine some well-known existence results for RCLL barriers with comparison arguments for the control process to construct solutions. Finally, we highlight the connection of these RBSDEs with standard RCLL BSDEs.

Keywords:

Reflected backward stochastic differential equation,
g-expectation,
Optional barrier,
Monotone approximation,
Comparison principle.

Mathematics Subject Classification: 60H10, 60G40.

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