TY  - GEN
AB  - We formulate a notion of doubly reflected BSDE in the case where the barriers ξ
and ζ 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 ξ is right upper-semicontinuous and ζ is right lower-semicontinuous, the
solution is characterized in terms of the value of a corresponding $\mathcal{E}$<sup>ƒ</sup> -Dynkin game,
i.e. a game problem over stopping times with (non-linear) ƒ-expectation, where ƒ 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 a priori estimates with universal
constants.
DA  - 2018
KW  - Doubly reflected BSDEs
KW  - backward stochastic differential equations
KW  - Dynkin game
KW  - saddle points
KW  - ƒ-expectation
KW  - nonlinear expectation
KW  - game option
KW  - stopping time
KW  - stopping system
LA  - eng
PY  - 2018
SN  - 0931-6558
SP  - 31-
TI  - Doubly Reflected BSDEs and  $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29304468
Y2  - 2024-11-22T10:35:28
ER  -