Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations

Shengjun Fan; Tianxiao Wang; Jiongmin Yong

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arXiv · 2211.04078

Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations

Shengjun Fan·Tianxiao Wang·Jiongmin Yong

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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 $Z$. Two major situations are discussed: (i) When the free term is bounded with the dependence of the generator on $Z$ 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 $Z$ being diagonally no more than quadratic and being independent of off-diagonal components. Besides, for the case that the generator is super-quadratic in $Z$, some negative results are presented.

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BibTeX RIS

Shengjun Fan, Tianxiao Wang, Jiongmin Yong. 2022-11-08. Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations. https://arxiv.org/abs/2211.04078

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