BSDE,path-dependent PDE and nonlinear Feynman-Kac formula

被引：0

作者：

PENG ShiGe ^{[1
,2
]}

WANG FaLei ^{[3
,1
,2
]}

机构：

[1] School of Mathematics, Shandong University

[2] Qilu Institute of Finance, Shandong University

[3] Institute for Advanced Research, Shandong University

来源：

Science China Mathematics | 2016年 / 59卷 / 01期

基金：

中国国家自然科学基金;

关键词：

backward stochastic differential equation; nonlinear Feynman-Kac formula; path-dependent PDE;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

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.

引用

页码：19 / 36

页数：18

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[1] BSDE, path-dependent PDE and nonlinear Feynman-Kac formula
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