Before revision:  As Volterra processes are non-Markovian and non-semimartingale in general , we develop an extended path-dependent Hamilton-Jacobi-Bellman (PHJB) equation system and offer a verification theorem to the solution of the PHJB equation.
After revision:  As Volterra processes are non-Markovian and non-semimartingale models , we develop an extended path-dependent Hamilton-Jacobi-Bellman (PHJB) equation system and offer a verification theorem to the solution of the PHJB equation.