“…Finally, we compare the present work with the accompanying one [24]. In fact, when σ(ω, t, x t , θ(t))(≡ σ(ω, t)) is path-invariant and uncontrolled in (1.2), we may take X(t) = X(t) − ξ(t) with ξ(t) = t 0 σ(s) dW (s) for t ∈ [0, T ], and then the optimization (1.1)-(1.2) is equivalent to the following one:…”