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

Miryana Grigorova, Peter Imkeller, Marie-Claire Quenez and Youssef Ouknine
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Miryana Grigorova: Center for Mathematical Economics, Bielefeld University
Peter Imkeller: Center for Mathematical Economics, Bielefeld University
Marie-Claire Quenez: Center for Mathematical Economics, Bielefeld University
Youssef Ouknine: Center for Mathematical Economics, Bielefeld University

No 598, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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.

Keywords: Doubly reflected BSDEs; backward stochastic differential equations; Dynkin game; saddle points; Æ’-expectation; nonlinear expectation; game option; stopping time; stopping system (search for similar items in EconPapers)
Pages: 31
Date: 2018-08-16
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:598

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