Backward Stochastic Volterra Integral Equations--- Representation of Adapted Solutions
Probability
2018-02-13 v1
Abstract
For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to obtain in general. Inspired by the decoupling idea of forward-backward stochastic differential equations, in this paper, for a class of BSVIEs, a representation of adapted M-solutions is established by means of the so-called representation partial differential equations and (forward) stochastic differential equations. Well-posedness of the representation partial differential equations are also proved in certain sense.
Keywords
Cite
@article{arxiv.1802.03659,
title = {Backward Stochastic Volterra Integral Equations--- Representation of Adapted Solutions},
author = {Tianxiao Wang and Jiongmin Yong},
journal= {arXiv preprint arXiv:1802.03659},
year = {2018}
}