BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula

Abstract

In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE are formulated through a classical backward stochastic differential equation (BSDEs, for short) in which the terminal values and the generators are allowed to be general functions of Brownian paths. In this way we have established a new type of nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of regularities for this new PDE was obtained.

References in corpus (1)

• A regression-based Monte Carlo method to solve backward stochastic differential equations

Cited by in corpus (9)

• On viscosity solutions of path dependent PDEs
• Note on Viscosity Solution of Path-Dependent PDE and G-Martingales
• Weak Functional Itô Calculus and Applications
• Viscosity Solutions of Path-Dependent PDEs and Non-Markovian Forward-Backward Stochastic Equations
• Path-Dependent Optimal Stochastic Control and Viscosity Solution of Associated Bellman Equations
• G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE
• Comparison of viscosity solutions of fully nonlinear degenerate parabolic Path-dependent PDEs
• The Viability Property for Path-dependent SDE under Open Constraints
• A Representation Theorem for Smooth Brownian Martingales