# Doubly Reflected BSDEs and ${\cal E}^{f}$-Dynkin games: beyond the right-continuous case

Abstract : We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where $\xi$ is right upper-semicontinuous and $\zeta$ is right lower-semicontinuous, the solution is characterized in terms of the value of a corresponding $\mathcal{E}^f$-Dynkin game, i.e. a game problem over stopping times with (non-linear) $f$-expectation, where $f$ is the driver of the doubly reflected BSDE. In the general case where the barriers do not satisfy any regularity assumptions, the solution of the doubly reflected BSDE is related to the value of "an extension" of the previous non-linear game problem over a larger set of "stopping strategies" than the set of stopping times. This characterization is then used to establish a comparison result and \textit{a priori} estimates with universal constants.
Keywords :
Type de document :
Pré-publication, Document de travail
2017
Domaine :

Littérature citée [37 références]

https://hal.archives-ouvertes.fr/hal-01497914
Contributeur : Miryana Grigorova <>
Soumis le : dimanche 28 mai 2017 - 00:33:05
Dernière modification le : jeudi 11 janvier 2018 - 06:12:30

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DRBSDE_submitted_v2.pdf
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• HAL Id : hal-01497914, version 2
• ARXIV : 1704.00625

### Citation

Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez. Doubly Reflected BSDEs and ${\cal E}^{f}$-Dynkin games: beyond the right-continuous case. 2017. 〈hal-01497914v2〉

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