Well-posedness of mean-field type forward-backward stochastic differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Bensoussan, A.^1,2  Yam, S. C. P.³  Zhang, Z.³ 

[1] Univ Texas Dallas, Jindal Sch Management, Int Ctr Decis & Risk Anal, Richardson, TX 75083 USA

[2] City Univ Hong Kong, Coll Sci & Engn, Dept Syst Engn & Engn Management, Hong Kong, Hong Kong, Peoples R China

[3] Chinese Univ Hong Kong, Dept Stat, Hong Kong, Hong Kong, Peoples R China

关键词: Mean-field type;    Forward-backward stochastic differential equations;    Monotonicity conditions;    Well-posedness;    Linear-quadratic setting;   

DOI  :  10.1016/j.spa.2015.04.006

来源: Elsevier

【 摘 要 】

Being motivated by a recent pioneer work Carmona and Delarue (2013), in this article, we propose a broad class of natural monotonicity conditions under which the unique existence of the solutions to Mean-Field Type (MFT) Forward-Backward Stochastic Differential Equations (FBSDE) can be established. Our conditions provided here are consistent with those normally adopted in the traditional FBSDE (without the interference of a mean-field) frameworks, and give a generic explanation on the unique existence of solutions to common MFT-FBSDEs, such as those in the linear-quadratic setting; besides, the conditions are 'optimal' in a certain sense that can elaborate on how their counter-example in Carmona and Delarue (2013) just fails to ensure its well-posedness. Finally, a stability theorem is also included. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free