Viscosity Solutions of Path-Dependent PDEs and Non-Markovian Forward-Backward Stochastic Equations

Abstract

It is known that Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac representation formulae for semilinear parabolic PDEs. We show that non-Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac formulae for semilinear path-dependent PDEs. This extends the result proved in Ekren, Keller, Touzi, and Zhang [4] to the case with a possibly degenerate diffusion coefficient in the forward dynamics.

References in corpus (4)

• On viscosity solutions of path dependent PDEs
• Note on Viscosity Solution of Path-Dependent PDE and G-Martingales
• Optimal Stopping under Nonlinear Expectation
• BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula

Cited by in corpus (4)

• An infinite-dimensional approach to path-dependent Kolmogorov equations
• An optimal control problem for functional forward-backward stochastic systems and related Path-dependent HJB equations
• Classical Solutions of Path-dependent PDEs and Functional Forward-Backward Stochastic Systems
• Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs