BSDEs and SDEs with time-advanced and -delayed coefficients
Abstract
This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently small Lipschitz constant, the existence and uniqueness of such BSDEs is obtained. As an adjoint process, a class of stochastic differential equations (SDEs) is introduced, whose coefficients also depend on the present, the past and the future of its solutions. The existence and uniqueness of such SDEs is proved for a sufficiently small time advance or a sufficiently small Lipschitz constant. A duality between such BSDEs and SDEs is established.
Keywords
Cite
@article{arxiv.1701.05106,
title = {BSDEs and SDEs with time-advanced and -delayed coefficients},
author = {Shiqiu Zheng and Gaofeng Zong},
journal= {arXiv preprint arXiv:1701.05106},
year = {2019}
}
Comments
19 pages, the final version will be published in Stochastics