In this paper we consider one dimensional general mean-field backward stochastic differential equations (BSDEs), i.e., the generator of our mean-field BSDEs depends not only on the solution but also on the law of the solution. We first give a totally new comparison theorem for such type of BSDEs under Lipschitz condition. Furthermore, we study the existence of the solution of such mean-field BSDEs when the coefficients are only continuous and with a linear growth.
The work has been supported in part by the NSF of P.R. China (No. 11222110), Shandong Province (No. JQ201202), NSFC-RS (No. 11661130148, NA150344), 111 Project (No. B12023).