We introduce a notion of approximate viscosity solution for a class of nonlinear path-dependent PDEs (PPDEs), and provide some existence, uniqueness, comparaison and stability results. In the case of Hamilton-Jacobi type equations, the approximate viscosity solution is naturally related to the associated optimal control problem. We then provide conditions under which the solution admits a Dupire’s vertical derivative and s tudy it s regularit y. An application to robust hedging under volatility uncertainty will be discussed.

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