Viscosity solutions of obstacle problems for fully nonlinear path-dependent PDEs

In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in (t,ω), and generator Lipschitz continuous in (y,z,γ). We prove that our definition of viscosity solutions is consistent with the classical solutions, and satisfy a stability result. We show that the value functional defined via the second order reflected backward stochastic differential equation is the unique viscosity solution of the variational inequalities.