Doubly reflected BSDEs with integrable parameters and related Dynkin games

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Bayraktar, Erhan¹  Yao, Song² 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

关键词: BSDEs;    Reflected BSDEs;    Doubly reflected BSDEs;    g-evaluation/expectation;    Penalization;    Optimal stopping problems;    Pasting local solutions;    Dynkin games;    Saddle points;   

DOI  :  10.1016/j.spa.2015.07.007

来源: Elsevier

【 摘 要 】

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 tau* when process Y meets L and the first time gamma* when process Y meets U form a saddle point of the Dynkin game. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free