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

Andrea Cosso

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arXiv · 1202.2502

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

Andrea Cosso

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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.

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Andrea Cosso. 2012-02-12. Viscosity Solutions of Path-Dependent PDEs and Non-Markovian Forward-Backward Stochastic Equations. https://arxiv.org/abs/1202.2502

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