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

作者：Peng ShiGe^*; Wang FaLei

来源：Science China Mathematics, 2016, 59(1): 19-36.

DOI：10.1007/s11425-015-5086-1

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

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) a [0, T] x R (d) . 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 Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of solutions of this new PDEs are also obtained.

• 出版日期2016-1
• 单位山东大学