Journal of the
Korean Mathematical Society JKMS

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in [19] and the adapted solutions via a new method. A general existence and uniqueness of adapted M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in [13] and [19], which modifies and extends the results in [13] and [19] respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in [7], [14], and [15].

Keywords: backward stochastic Volterra integral equations, adapted solutions, adapted M-solutions, non-Lipschitz conditions, stochastic Lipschitz coefficients

MSC numbers: 60H10, 60H15, 60G55