Reflected and Doubly Reflected Backward Stochastic Differential Equations with Irregular Obstacles and a Large Set of Stopping Strategies

Ihsan Arharas () and Youssef Ouknine ()
Additional contact information
Ihsan Arharas: Linnaeus University
Youssef Ouknine: Marrakesh, Morocco & Mohammed VI Polytechnic University

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1001-1038

Abstract: Abstract We introduce a new formulation of reflected backward stochastic differential equations (BSDEs) and doubly reflected BSDEs associated with irregular obstacles. In the first part of the paper, we consider an extension of the classical optimal stopping problem over a larger set of stopping systems than the set of stopping times (namely, the set of split stopping times), where the payoff process $$\xi $$ ξ is irregular and in the case of a general filtration. Split stopping times are a powerful tool for modeling financial contracts and derivatives that depend on multiple conditions or triggers, and for incorporating stochastic processes with jumps and other types of discontinuities. We show that the value family can be aggregated by an optional process v, which is characterized as the Snell envelope of the reward process $$\xi $$ ξ over split stopping times. Using this, we prove the existence and uniqueness of a solution Y to irregular reflected BSDEs. In the second part of the paper, motivated by the classical Dynkin game with completely irregular rewards considered by Grigorova et al. (Electron J Probab 23:1–38, 2018), we generalize the previous equations to the case of two reflecting barrier processes.

Keywords: Reflected BSDEs; Doubly reflected BSDEs; Split stopping times; Optimal stopping; 60H20; 60H30; 65C30 (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-024-01331-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-024-01331-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-024-01331-7

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().