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

Grigorova M, Imkeller P, Quenez M-C, Ouknine Y (2018) Center for Mathematical Economics Working Papers; 598.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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 $\mathcal{E}$ƒ -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.
Stichworte
Doubly reflected BSDEs; backward stochastic differential equations; Dynkin game; saddle points; ƒ-expectation; nonlinear expectation; game option; stopping time; stopping system
Erscheinungsjahr
2018
Band
598
Seite(n)
31
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2930446

Zitieren

Grigorova M, Imkeller P, Quenez M-C, Ouknine Y. Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case. Center for Mathematical Economics Working Papers. Vol 598. Bielefeld: Center for Mathematical Economics; 2018.
Grigorova, M., Imkeller, P., Quenez, M. - C., & Ouknine, Y. (2018). Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case (Center for Mathematical Economics Working Papers, 598). Bielefeld: Center for Mathematical Economics.
Grigorova, M., Imkeller, P., Quenez, M. - C., and Ouknine, Y. (2018). Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case. Center for Mathematical Economics Working Papers, 598, Bielefeld: Center for Mathematical Economics.
Grigorova, M., et al., 2018. Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case, Center for Mathematical Economics Working Papers, no.598, Bielefeld: Center for Mathematical Economics.
M. Grigorova, et al., Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case, Center for Mathematical Economics Working Papers, vol. 598, Bielefeld: Center for Mathematical Economics, 2018.
Grigorova, M., Imkeller, P., Quenez, M.-C., Ouknine, Y.: Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case. Center for Mathematical Economics Working Papers, 598. Center for Mathematical Economics, Bielefeld (2018).
Grigorova, Miryana, Imkeller, Peter, Quenez, Marie-Claire, and Ouknine, Youssef. Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case. Bielefeld: Center for Mathematical Economics, 2018. Center for Mathematical Economics Working Papers. 598.
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2019-09-06T09:19:01Z
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