Peng's maximum principle for a stochastic control problem driven by a fractional and a standard Brownian motion  

作　　者：BUCKDAHN Rainer JING Shuai 

机构地区：[1]Departement de Mathematiques,Universite de Bretagne Occidentale [2]School of Mathematics,Shandong University [3]School of Management Science and Engineering,Central University of Finance and Economics

出　　处：《Science China Mathematics》2014年第10期2025-2042,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No11301560)

摘　　要：We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion. We derive a maximum principle and the associated stochastic variational inequality, which both are generalizations of the classical case.

关 键 词：fractional Brownian motion stochastic control system backward stochastic differential equation variational inequality maximum principle Girsanov transformation Galtchouk-Kunita-Watanabe decomposition 

分 类 号：O211.6[理学—概率论与数理统计] O231[理学—数学]