Forward-backward SDEs with distributional coefficients

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Issoglio, Elena¹  Jing, Shuai² 

[1] Univ Leeds, Dept Math, Leeds LS2 9JT, W Yorkshire, England

[2] Cent Univ Finance & Econ, Dept Management Sci, Beijing 100081, Peoples R China

关键词: Forward-backward stochastic differential equations;    Distributional coefficients;    Non-linear Feynman-Kac formula;    Weak solutions;    Virtual solutions;    Mild solutions;    Sobolev spaces;    Singular FBSDEs;    Singular PDEs;   

DOI  :  10.1016/j.spa.2019.01.001

来源: Elsevier

【 摘 要 】

Forward-backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced, due to their wide range of applications, from solving non-linear PDEs to pricing American-type options. Here, we consider two new classes of multidimensional FBSDEs with distributional coefficients (elements of a Sobolev space with negative order). We introduce a suitable notion of solution and show its existence and in certain cases its uniqueness. Moreover we establish a link with PDE theory via a non-linear Feynman-Kac formula. The associated semi-linear parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free