Abstract
We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: [Display omitted] where ▪=C([0,T];Rd), (u(⋅,ϕ))t≔(u(t+θ,ϕ))θ∈[−δ,0] and Lu(t,ϕ)≔〈b(t,ϕ),∂xu(t,ϕ)〉+12Tr[σ(t,ϕ)σ∗(t,ϕ)∂xx2u(t,ϕ)].The result is obtained by a stochastic approach. More precisely, we prove a new type of nonlinear Feynman–Kac representation formula associated to a backward stochastic differential equation with time-delayed generator, which is of non-Markovian type. Applications to the large investor problem and risk measures via g–expectations are also provided.
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