We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables(t, x) ∈ [0, T ] × Rd. This...We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables(t, x) ∈ [0, T ] × Rd. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear FeynmanKac formula for a general non-Markovian BSDE. Some main properties of solutions of this new PDEs are also obtained.展开更多
基金supported by the Natural Science Foundation of Anhui Province(1508085QA03)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)the National Natural Science Foundation of China(11501009,11371029)
基金Supported in part by NNSFC(10901003)the Research Project of Natural Science Foundation of Anhui Provincial University(KJZ010B345) the Grant for Youth of Anhui Normal University (2009XQN56)
基金supported by Basic Research Program of China(973 Program) Grant(2007 CB814904)NSFC Grant (10325101)Science Foundation of the Ministry of Education of China Grant(200900071110001)
基金supported by National Natural Science Foundation of China(Grant No.10921101)the Programme of Introducing Talents of Discipline to Universities of China(Grant No.B12023)the Fundamental Research Funds of Shandong University
文摘We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables(t, x) ∈ [0, T ] × Rd. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear FeynmanKac formula for a general non-Markovian BSDE. Some main properties of solutions of this new PDEs are also obtained.
