典型文献
Mean Field Games with Common Noises and Conditional Distribution Dependent FBSDEs
文献摘要：
In this paper,the authors consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way.They assume that the cost function satisfies a convexity and a weak monotonicity property.They use the sufficient Pontryagin principle for optimality to transform the mean field control problem into existence and uniqueness of solution of conditional distribution dependent forward-backward stochastic differential equation(FBSDE for short).They prove the existence and uniqueness of solution of the conditional distribution dependent FBSDE when the dependence of the state on the conditional distribution is sufficiently small,or when the convexity parameter of the running cost on the control is sufficiently large.Two different methods are developed.The first method is based on a continuation of the coefficients,which is developed for FBSDE by[Hu,Y.and Peng,S.,Solution of forward-backward stochastic differential equations,Probab.Theory Rel.,103(2),1995,273-283].They apply the method to conditional distribution dependent FBSDE.The second method is to show the existence result on a small time interval by Banach fixed point theorem and then extend the local solution to the whole time interval.
文献关键词：
中图分类号：
作者姓名：
Ziyu HUANG;Shanjian TANG
作者机构：
School of Mathematical Sciences,Fudan University,Shanghai 200433,China;Department of Finance and Control Sciences,School of Mathematical Sciences,Fudan University,Shanghai 200433,China
文献出处：
引用格式：
[1]Ziyu HUANG;Shanjian TANG-.Mean Field Games with Common Noises and Conditional Distribution Dependent FBSDEs)[J].数学年刊B辑（英文版）,2022(04):523-548
A类：
FBSDEs,FBSDE,Probab
B类：
Mean,Field,Games,Common,Noises,Conditional,Distribution,Dependent,In,this,paper,authors,consider,mean,field,game,common,noise,allow,state,coefficients,vary,conditional,distribution,nonlinear,way,They,assume,that,cost,function,satisfies,convexity,weak,monotonicity,property,use,Pontryagin,principle,optimality,transform,control,problem,into,existence,uniqueness,solution,dependent,forward,backward,stochastic,differential,short,prove,when,dependence,sufficiently,small,parameter,running,large,Two,methods,are,developed,first,continuation,which,by,Hu,Peng,Solution,equations,Theory,Rel,apply,second,show,result,interval,Banach,fixed,point,theorem,then,extend,local,whole
AB值：
0.526027
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