Anticipated backward stochastic differential equations with quadratic growth

Abstract

In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator f(⋅), which is of quadratic growth in Z⋅, involves not only the present information of solution (Y⋅,Z⋅) but also its future one. The existence and uniqueness of such BSDEs, under different conditions, are derived for several terminal situations, including small terminal value, bounded terminal value and unbounded terminal value.