Doubly reflected BSDEs with integrable parameters and related Dynkin games

Erhan Bayraktar and Song Yao

Stochastic Processes and their Applications, 2015, vol. 125, issue 12, 4489-4542

Abstract: We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle L and the upper obstacle U of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by pasting local solutions, and show that the Y-component of the unique solution represents the value process of the corresponding Dynkin game under g-evaluation, a nonlinear expectation induced by BSDEs with the same generator g as the doubly reflected BSDE concerned. In particular, the first time τ∗ when process Y meets L and the first time γ∗ when process Y meets U form a saddle point of the Dynkin game.

Keywords: BSDEs; Reflected BSDEs; Doubly reflected BSDEs; g-evaluation/expectation; Penalization; Optimal stopping problems; Pasting local solutions; Dynkin games; Saddle points (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Working Paper: Doubly Reflected BSDEs with Integrable Parameters and Related Dynkin Games (2015)
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DOI: 10.1016/j.spa.2015.07.007

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