2018
DOI: 10.1214/18-ejp225
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: We formulate a notion of doubly reflected BSDE in the case where the barriers ξ and ζ do not satisfy any regularity assumption and with general filtration. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where ξ is right upper-semicontinuous and ζ is right lower-semicontinuous, the solution is characterized in terms of the value of a corresponding E f -Dynkin game, i.e. a game problem over stopping times with (non-linear) f -expectation,… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
5

Citation Types

0
33
0

Year Published

2020
2020
2023
2023

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 29 publications
(33 citation statements)
references
References 47 publications
0
33
0
Order By: Relevance
“…In the present paper we generalize the existence and uniqueness results from [11] in several directions. We consider the case of L p -data with p ≥ 1 (in [11] only the case of p = 2 is considered). As for the generator, we assume that it is Lipschitz continuous with respect to z and only continuous and monotone with respect to y (in [11] it is assumed that f is Lipschitz continuous with respect to y and z).…”
Section: Introductionmentioning
confidence: 78%
See 4 more Smart Citations
“…In the present paper we generalize the existence and uniqueness results from [11] in several directions. We consider the case of L p -data with p ≥ 1 (in [11] only the case of p = 2 is considered). As for the generator, we assume that it is Lipschitz continuous with respect to z and only continuous and monotone with respect to y (in [11] it is assumed that f is Lipschitz continuous with respect to y and z).…”
Section: Introductionmentioning
confidence: 78%
“…To our knowledge, RBSDEs with barriers which are not càdlàg and whose solution satisfies (1.2) are treated only in the papers [1,10,11,17]. Among them, only [11] deals with equations with two barriers. In the present paper we generalize the existence and uniqueness results from [11] in several directions.…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations