L^P SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS  

作　　者：Yajie CHEN Chuanzhi XING Xiao ZHANG 陈雅洁;邢传智;张晓(Zhongtai Securities Institute for Financial Studies,Shandong University,Jinan 250100,China;School of Mathem atics and Statistics,Shandong University,Weihai 264209,China)

机构地区：[1]Zhongtai Securities Institute for Financial Studies,Shandong University,Jinan 250100,China [2]School of Mathem atics and Statistics,Shandong University,Weihai 264209,China

出　　处：《Acta Mathematica Scientia》2020年第4期1116-1140,共25页数学物理学报（B辑英文版）

基　　金：supported in part by the NSFC(11222110,11871037);Shandong Province(JQ201202);NSFC-RS(11661130148,NA150344);111 Project(B12023)。

摘　　要：In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.

关 键 词：general mean-field backward stochastic differential equations monotonicity condition continuous condition uniformly continuous condition L^p solution 

分 类 号：O211.63[理学—概率论与数理统计]