Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations
Abstract
In this paper, a systematic investigation is carried out for the general solvability of multi-dimensional backward stochastic Volterra integral equations (BSVIEs) with the generators being super-linear in the adjustment variable . Two major situations are discussed: (i) When the free term is bounded with the dependence of the generator on being of ``diagonally strictly'' quadratic growth and being sub-quadratically coupled with off-diagonal components; (ii) When the free term is unbounded having exponential moments of arbitrary order with the dependence of the generator on being diagonally no more than quadratic and being independent of off-diagonal components. Besides, for the case that the generator is super-quadratic in , some negative results are presented.
Cite
@article{arxiv.2211.04078,
title = {Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations},
author = {Shengjun Fan and Tianxiao Wang and Jiongmin Yong},
journal= {arXiv preprint arXiv:2211.04078},
year = {2022}
}