Multi-dimensional super-linear backward stochastic Volterra integral equations

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 terminal 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 terminal 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.