Solvability of anticipated backward stochastic Volterra integral equations

In this paper, we focus on a new class of equations called the anticipated backward stochastic Volterra integral equations (ABSVIEs, for short). In this class of equations, the generator involves not only the present information of the solution but also its future one. Under the Lipschitz condition, we obtain the existence and uniqueness of the adapted M-solutions. Meanwhile, a comparison theorem is also proved.