In this talk, I will introduce the background of the theory of backward stochastic differential equations (BSDEs, for short) firstly. Then, the recent development and some open problems of BSDEs will be presented. Finally, concerning our latest work, I will introduce the solvability of anticipated backward stochastic differential equations with quadratic growth, which including the case of the one-dimensional situation and multi-dimensional situation. It should be pointed out that 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.
