Mean-field backward stochastic differential equations with uniformly continuous generators

Abstract

This paper mainly studies one dimensional mean-field backward stochastic differential equations (MFBSDEs) when their coefficient g is uniformly continuous in (y', y, z), independent of z' and non-decreasing in y'. The existence of the solution of this kind MFBSDEs has been well studied. The uniqueness of the solution of MFBSDE is proved when g is also independent of y. Moreover, MFBSDE with coefficient g+c, in which c is a real number, has non-unique solutions, and it's at most countable.